<![CDATA[Quantitative Finance Collector]]>

<![CDATA[Quantitative Finance Collector]]> http://www.mathfinance.cn/index.php en-US http://www.mathfinance.cn/pption-pricing-models-implemented-in-AirXCell/ <![CDATA[Option pricing models implemented in AirXCell]]> abiao <> Sun, 10 Jun 2012 21:23:05 +0000 http://www.mathfinance.cn/pption-pricing-models-implemented-in-AirXCell/ AirXCell is an online R application framework currently supporting a programmable spreadsheet, an R development environment and various financial calculation forms.

A new calculation form has been implemented recently within AirXCell for financial option pricing (option valuation). The option pricer within AirXCell enables the user to compute theoretical option prices. It already offers an extended set of basic and exotic models (about a dozen) than enables the user to price a wide range of option types:

American options,
European options,
Asian options,
Barrier options,
Binary options,
Currency translated options,
Lookback options,
Multiple assets options and
Multiple exercises options

Many more models are being implemented currently and will be added soon to AirXCell. In addition to the option pricing form, there are other forms especially useful in the same context that provides ways to load asset prices, visualize them, compute the theoretical and historical volatility.

This form is very valuable to quantitative researchers or any finance professional who needs to compute theoretical option prices easily and who is looking for a reliable option pricer.

The Option pricing form presents the user with an HTML form enabling her to set up the model with the required parameters values such as the underlying asset price, the strike price, the volatility of the underlying asset, etc.

For instance, the following form is presented to a user requesting the price of an european option using the Generalized Black Scholes model:

Again, there are many more models and option types coming soon as well as other forms for various other kind of calculations, still mostly oriented towards financial calculation.
Tags - option , pricing , r
Read the full post at Option pricing models implemented in AirXCell. ]]> http://www.mathfinance.cn/top-20-movies-for-business-men/ <![CDATA[Top 20 Movies For Business Men]]> abiao <> Mon, 16 Jan 2012 21:34:20 +0000 http://www.mathfinance.cn/top-20-movies-for-business-men/
Disclaimer: the videos are embedded from Youtube uploaded by others, some are full version and others are Trailer. Please consider to buy the movies from Amazon.

1, Wall Street (1987)

A young and impatient stockbroker is willing to do anything to get to the top, including trading on illegal inside information taken through a ruthless and greedy corporate raider who takes the youth under his wing.

2, Glengarry Glen Ross (1992)

An examination of the machinations behind the scenes at a real estate office. A story for everyone who works for a living.

3, Trading Places (1983)

A snobbish investor and a wily street con artist find their positions reversed as part of a bet by two callous millionaires.

4, Boiler Room (2000)

A college dropout gets a job as a broker for a suburban investment firm, which puts him on the fast track to success, but the job might not be as legitimate as it sounds.

5, Pirates of Silicon Valley (1999)

The film documents the impact on the development of the personal computer of the rivalry between Apple Computer and Microsoft. It spans the time period of the early 1970s to 1997, when Steve Jobs (Noah Wyle) and Bill Gates (Anthony Michael Hall) develop a partnership after Jobs returns to Apple Computer.

6, The Coca-Cola Kid (1985)

An eccentric marketing guru visits a Coca-Cola subsidiary in Australia to try and increase market penetration. He finds zero penetration in a valley owned by an old man who makes his own soft drinks, and visits the valley to see why. After "the Kid's" persistence is tested he's given a tour of the man's plant, and they begin talking of a joint venture. Things get more complicated when the Coca-Cola man begins falling in love with his temporary secretary, who seems to have connections to the valley.

7, The Secret of My Succe$s (1987)

A talented young man can't get an executive position without rising through the ranks, so he comes up with a shortcut, which also benefits his love life.

8, In Good Company (2004)

A middle-aged ad exec is faced with a new boss who's nearly half his age... and who also happens to be sleeping with his daughter.

9, Barcelona (1994)

Ted, a stuffy white guy from Illinois working in sales for the Barcelona office of a US corporation, is paid an unexpected visit by his somewhat less stuffy cousin Fred, who is an officer in the US Navy. Over the next few months, both their lives are irrevocably altered by the events which follow Fred's arrival, events which are the trivial stuff of a comedy of manners at first but which gradually grow increasingly dramatic.

10, Jerry Maguire (1996)

When a sports agent has a moral epiphany and is fired for expressing it, he decides to put his new philosophy to the test as an independent with the only athlete who stays with him.

11, Office Space (1999)

Comedic tale of company workers who hate their jobs and decide to rebel against their greedy boss.

12, The Corporation (2003)

Documentary that looks at the concept of the corporation throughout recent history up to its present-day dominance.

13, The Insider (1999)

A research chemist comes under personal and professional attack when he decides to appear in a "60 Minutes" expose on Big Tobacco.

14, The Hudsucker Proxy (1994)

A naive business graduate is installed as president of a manufacturing company as part of a stock scam.

15, Antitrust (2001)

A computer programmer's dream job at a hot Portland-based firm turns nightmarish when he discovers his boss has a secret and ruthless means of dispatching anti-trust problems.

16, Rogue Trader (1998)

Rogue Trader tells the true story of how one man managed to bring down England's best respected merchant bank. Ewan McGregor plays Leeson, an ambitious young man from North London who is hired by the Barings Brothers Bank and sent to Indonesia to help untangle some problems with bearer bonds. Leeson does well enough to earn a transfer to Singapore, where he's put in charge of Barings' staff at the Singapore International Money Exchange.

17, Other People's Money (1991)

A corporate raider threatens a hostile take-over of a "mom and pop" company. The patriarch of the company enlists the help of his wife's daughter, who is a lawyer, to try and protect the company. The raider is enamoured of her, and enjoys the thrust and parry of legal manoeuvring as he tries to win her heart.

18, Disclosure (1994)

A computer specialist is sued for sexual harassment by a former lover turned boss who initiated the act forcefully, which threatens both his career and his personal life.

19, What Women Want (2000)

After an accident, a chauvenistic executive gains the ability to hear what women are really thinking.

20, Barbarians at the Gate (1993)

The president of a major tobacco company decides to buy the company himself, but a bidding war ensues as other companies make their own offers.

Tags - movie , business , top , world
Read the full post at Top 20 Movies For Business Men. ]]> http://www.mathfinance.cn/online-option-pricing-models/ <![CDATA[Online Option Pricing Models]]> abiao <> Mon, 09 Jan 2012 14:37:20 +0000 http://www.mathfinance.cn/online-option-pricing-models/ online derivative calculator, On-Line Options Pricing & Probability Calculators, etc. Today I came across another very clean website: online Option Pricing Models.

As the website describes:

Quotation

You can get the price (and the Greeks) of the available options by applying several methods:

- Black & Scholes model for european options and greeks calculation.
- Bjerksund & Stensland model for american options.
- Binomial model (Cox, Ross & Rubinstein, Jarrow-Rudd Risk Neutral, Tian) for american and european options.
- Shifted Lognormal model for european options.
- Partial Differential Equation (PDE) approach: Finite Difference (FD) and Radial Basis Function (RBF) methods for american and european options.
- Monte-Carlo for digital option (Cash-or-Nothing) and european options and greeks estimation (FD and Malliavin).

Volatility models (SABR with calibration, Lognormal model, etc.) are also available.

I randomly tested the option calculators, they are working well, on top of that, the site is created by a French master student. So it is fine to give him credit with a separated post. Check it at http://pricing-option.com/Default.aspx.
Tags - option
Read the full post at Online Option Pricing Models. ]]> http://www.mathfinance.cn/fast-least-squares-monte-carlo-simulation-american-option/ <![CDATA[Fast Least Squares Monte Carlo Simulation for American Option]]> abiao <> Sun, 09 Oct 2011 11:42:55 +0000 http://www.mathfinance.cn/fast-least-squares-monte-carlo-simulation-american-option/ least-squares Monte Carlo simulation to price an American option is time consuming because it involves optimal exercise decision on every step of a large number of simulation (in the least square case, to run a polynomial regression on cash flows and decide whether it is optimal to exercise or not). I once shared a simple Matlab file to illustrate the least squares Monte Carlo simulation. The situation becomes worse if we allow the presence of stochastic volatility and interest rate, typically my codes run quite a few minutes for 50,000 number of simulations.

In the paper "Fast Monte Carlo Valuation of American Options under Stochastic Volatility and Interest Rates" by Y. Hilpisch, the author demonstrates with Python script that the Least-Squares Monte Carlo (LSM) algorithm with control variates takes only less than one second to achieve satisfying accurateness. The overall statistics taken from the paper are as follows, AMAZING!

Download the paper and accompanying Python codes at http://www2.visixion.com/dok/Fast_MCS_SVSI.pdf
Tags - monte carlo , simulation , american
Read the full post at Fast Least Squares Monte Carlo Simulation for American Option. ]]> http://www.mathfinance.cn/any-good-way-to-import-large-CSV-file-into-mysql/ <![CDATA[Any Good Way To Import A Large CSV File Into MySql]]> abiao <> Wed, 27 Oct 2010 15:52:52 +0000 http://www.mathfinance.cn/any-good-way-to-import-large-CSV-file-into-mysql/
Cheers,
Biao

PS: Nick, thanks a lot for your reply, I have tried your way & it took me 1 hour and 16 minutes to import my 40 million lines CSV into MySQL on my humble laptop. That's great. My next task then is to check the performance of RMySQL package.

LOAD DATA INFILE 'data.csv' INTO TABLE tbl_name
  FIELDS TERMINATED BY ',' ENCLOSED BY '"'
  LINES TERMINATED BY '\r\n'
  IGNORE 1 LINES;

Tags - mysql , csv
Read the full post at Any Good Way To Import A Large CSV File Into MySql. ]]> http://www.mathfinance.cn/biases-in-TRACE-corporate-bond-data/ <![CDATA[Biases in TRACE Corporate Bond Data]]> abiao <> Thu, 21 Oct 2010 10:19:55 +0000 http://www.mathfinance.cn/biases-in-TRACE-corporate-bond-data/ TRACE US corporate bond data as me. NASD introduced TRACE (Trade Reporting and Compliance Engine) in July 2002 in an effort to increase price transparency in the U.S. corporate debt market. The system captures and disseminates consolidated information on secondary market transactions in publicly traded TRACE-eligible securities (investment grade, high yield and convertible corporate debt) - representing all over-the-counter market activity in these bonds.

However the more I use the data, the more I realize its problem, one of the big issues is the repetitive order with the same amount and price, which definately brings trouble when the data is used for trading volume calculation, such as for Amihud's liquidity measure. Besides the duplicate issue, reversals & the same-day corrections are two major errors of TRACE data, as noted in the paper Liquidity biases in TRACE by Jens Dick-Nielsen,

Quotation

7.7% of all reports in TRACE are errors and in some cases up to 18% of the reports should be deleted. Failing to correct for these errors will bias popular liquidity measures towards a more liquid market. The median bias for the daily turnover will be 7.4% and for a quarter of the bonds the Amihud price impact measure will be underestimated by at least 14.6%.

Should you are also worried about these issues, I suggest you to read the paper Liquidity biases in TRACE and contact the author for the SAS programming code used for filtering.

Tags - trace , bond , data
Read the full post at Biases in TRACE Corporate Bond Data. ]]> http://www.mathfinance.cn/pathwise-derivative-vs-finite-difference-for-greeks-computation/ <![CDATA[Pathwise Derivative vs Finite Difference For Greeks Computation]]> abiao <> Thu, 02 Sep 2010 10:30:28 +0000 http://www.mathfinance.cn/pathwise-derivative-vs-finite-difference-for-greeks-computation/ Greeks calculation with Monte Carlo simulation. Besides those variance reduction techniques such as antithetic, or low discrepancy random numbers, one efficient way is to use pathwise derivative instead of finite difference.

1, Finite Difference approximation
This is the most widely used & straightforward method, as its name suggests, basically, to estimate dy/dx, we increase x by a very small quantity to x1, re-calculate the option value y1, and then estimate the sensitivity as (y-y1)/(x1-x). Thus this method requires us to calculate the option value at least twice (three times for central difference method), and obviously is a big challenge when we have to simulate lots of times.

2, pathwise derivative estimate
contrary to finite difference approximation, pathwise derivative estimate derivative directly, without simulating multiple times. It takes advantage of additional information about the dynamics and parameter dependence of a simulated process. Simply put, by the chain rule, if we could find another variable z such that

, and there are solutions to the two derivatives at the right hand side, the pathwise derivative estimator can be applied, and for most cases, stock price S(T) for European option or S(tau) for American option is an excellent choice of z, tau is the optimal timing for exercise. Please read the chapter 7 of Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability) (v. 53) for detail.

Below are the sample results for the Greeks calculation for an American option without dividend, time to maturity 1 year, 20% volatility. Pathwise derivative estimator saves 2/3 ~ 3/4 computation time.
american option greeks speed Pathwise Derivative vs Finite Difference

american option greeks speed Pathwise Derivative vs Finite Difference

Delta, Gamma and Vega converge to their true values much quicker, here old and new code refer to Finite Difference approximation and pathwise derivative estimate, respectively, and the yellow line is the true value.
option delta

Not bad.
Tags - greeks , monte carlo
Read the full post at Pathwise Derivative vs Finite Difference For Greeks Computation. ]]> http://www.mathfinance.cn/find-MFE/ <![CDATA[Find MFE]]> abiao <> Mon, 23 Aug 2010 13:09:52 +0000 http://www.mathfinance.cn/find-MFE/ Find MFE program), however the site was down due to server maintenance reason. Today Andy from QuantNet reminds me (I almost forgot it), so I move the script to my blog with search function only in case someone is still interested,

Quotation

the goal is to filter your ideal MFE program by the self-defined criteria, for example, you can say "I want to find a MFE program in United States, total tuition less than $40K, and with financial aid"

Bookmark the page Compare & Find MFE, or you can find the link at the menu navigation. I will start to expand the list soon.
Tags - mfe
Read the full post at Find MFE. ]]> http://www.mathfinance.cn/quanttube/ <![CDATA[QuanTube]]> abiao <> Thu, 12 Aug 2010 14:32:29 +0000 http://www.mathfinance.cn/quanttube/ Photobucket

My friend & I have collected dozens of videos relevant to quantitative finance study, including basic finance, Credit, Derivatives, Mathematics, Risk, Trading, etc. The main purpose is to build a convenient online video place to share and learn math finance.

Please help it grow by visiting QuanTube, rating the video, and most importantly, submit a better video you come across, we appreciate that.
Tags - video
Read the full post at QuanTube. ]]> http://www.mathfinance.cn/kalman-filter-finance/ <![CDATA[Kalman Filter Finance]]> abiao <> Fri, 23 Apr 2010 08:37:05 +0000 http://www.mathfinance.cn/kalman-filter-finance/ Kalman filter example, where a Matlab toolbox link was shared as well. When it comes to an application of Kalman filter in finance, one of the best and ealiest paper is Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter (a simple search at Google Scholor tells you this paper has been cited by over 180 times), in the paper the authors do an empirical analysis of Kalman filter to two special cases of interest rate models, namely the Gaussian case (Vasicek 1977) and the non-Gaussian case (Cox Ingersoll and Ross1985 and Chen and Scott 1992), besides a detailed description of how to apply this algorithm step by step.

Download the programming files of Estimating exponential affine term structure models at the author's home page http://www.rotman.utoronto.ca/~jcduan/, however, they are in GAUSS language I am unfamiliar with (I used to use it when I studied in Germany seven years ago), so check yourself then.
Tags - filter
Read the full post at Kalman Filter Finance. ]]> http://www.mathfinance.cn/value-at-risk-estimation-with-copula/ <![CDATA[Value at Risk Estimation with Copula]]> abiao <> Fri, 09 Apr 2010 09:29:38 +0000 http://www.mathfinance.cn/value-at-risk-estimation-with-copula/ Value at Risk is widely used to measure the downside risk, and Copula is a generalized dependence structure instead of linear correlation to model dependence, especially for lower tail dependence, therefore the combination of VaR with Copula is fantastic in terms of accurately capturing the true risk embedded.

I read roughly a working paper Value at Risk – MATLAB Application of Copulas on US and Indian Markets, where the authors calculate the Value at Risk (VaR) using the bivariate Gaussian Copula distribution implemented in MATLAB for the Dow-Jones index and the National Stock Exchange index. It is good to use Gaussian Copula together with some rank correlation (like Spearman's rho or Kendall tau) to model the dependence, however, we must be very careful as basically Gaussian Copula assumes the joint dependence structure normally distributed and as a result, no matter which marginal distribution you choose, the upper and lower tail dependence approach to zero when the significant level limits to one and zero, in other words, in a bivariate case, the probability that X2 exceeds its q-quantile, given that X1 exceeds its q-quantile (upper tail dependence) when q->1, and the probability that X2 is below its q-quantile, given that X1 is below its q-quantile (lower tail dependence) when q->0 are zero.

For example, below are two simulated return series, one is under Gaussian copula and the other one is under Student t copula, as you can easily see, although both have the same marginal distribution, Gaussian copula has much smaller upper and lower tail dependence than Student t copula, which eventually underestimates the Value at Risk and other risk measures.

I would stay away Gaussian Copula if I were a risk manager, and you? Download Copula toolbox and other code files at Copula if interested.
Tags - var , copula
Read the full post at Value at Risk Estimation with Copula. ]]> http://www.mathfinance.cn/var-historical-simulation/ <![CDATA[VaR Historical Simulation]]> abiao <> Fri, 05 Mar 2010 11:39:28 +0000 http://www.mathfinance.cn/var-historical-simulation/ Value at Risk xls and var backtesting, a third post about using historical simulation for Value at Risk calculation. We know one shortcoming of historical simulation is: the result highly depends on the choice of sample data length, VaR result does not vary often or changes suddenly. Despite this weakness, HS is still popular due to its obvious advantage: easy to implement, and no distribution assumption required, which is especially appealing if the estimate of distribution assumption is difficult. Several ways have been proposed to improve HS's performance, here are two selected methods with good results I personally use.

1, The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk by Jacob Boudoukh1, Matthew Richardson and Robert F. Whitelaw. By hybrid it means this approach is a combination of RiskMetrics's parametric method and Historical Simulation. The basic idea is: since we can allocate larger weight to recent data and smaller weight to remote data for exponential weighted moving average (EWMA) volatility calculation, hence improves the backtesting performance of parametric method, why can't we then apply a similar principle to historical simulation? make sense? so it estimates the VaR of a portfolio by applying exponentially declining weights to past returns and then finding the appropriate percentile of this time weighted empirical distribution. The following results are from the paper The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk, page 11. It does improve compared with the vanilla historical simulation and EWMA parametric method, nice.

2, INCORPORATING VOLATILITY UPDATING INTO THE HISTORICAL SIMULATION METHOD FOR VALUE AT RISK by John Hull and Alan White. The idea is to "adjust" return based on the ratio of current volatility to the past volatility, and use historical simulation on the adjusted returns. Their argument is supposing today's volatility is 20%, while volatility was say, 30%, then past returns obviously exaggerate the current market situation if used directly. They even compare their performance with the first one above and the results are:

source from INCORPORATING VOLATILITY UPDATING INTO THE HISTORICAL SIMULATION METHOD FOR VALUE AT RISK page 17.

Results are promising, aren't they? few lines of codes are enough for the adjustment.
Tags - var
Read the full post at VaR Historical Simulation. ]]> http://www.mathfinance.cn/inverse-graphing-calculator/ <![CDATA[Inverse Graphing Calculator]]> abiao <> Thu, 04 Mar 2010 17:14:49 +0000 http://www.mathfinance.cn/inverse-graphing-calculator/
For instance, if you write an equation:

you would get a graph below:

Creat your own at http://www.xamuel.com/inverse-graphing-calculator.php
Tags - graph
Read the full post at Inverse Graphing Calculator. ]]> http://www.mathfinance.cn/var-backtesting/ <![CDATA[VaR Backtesting]]> abiao <> Thu, 25 Feb 2010 08:49:18 +0000 http://www.mathfinance.cn/var-backtesting/ Value at Risk xls, I was asked why not & how to add a VaR backtesting module in that excel file, well, it is straightforward in principle to do that but since we have to calculate daily VaR for multiple periods in order to do backtesting, I simply didn't add that in an excel for speed reason.

The Backtesting framework developed by the Basel committee is the main methodology to judge the performance of VaR model, it typically consists of a periodic comparison of the portfolio’s or asset’s daily VaR values with the subsequent daily profit and loss (P&L). Obviously, the ideal model should generate the times of VaR exceeding P&L equal to (1-alpha) multiplied by time periods for backtesting. For a single equity case it is obvious what we need to do is comparing daily VaR results with daily return; but for a portfolio we have to be careful with the trading positions.

Basel committee (1996) introduces a three-zone approach, where the green zone means the possibility of erroneously accepting an inaccurate model is low; yellow zone is risk manager should be careful to check the model before take action; red zone means the probability of erroneously rejecting an accurate model is remote. For example, the backtesting three zones boundaries for a sample of 250 observations, source from Basel committee, 1996 look like
var three zone table

Backtesting results can therefore be judged by counting the number of exceptions and seeing intuitively which colour zone it falls into.

Alternatively you can rely on some statistical testing, for instance, the exception testing by Kupiec (1995).

Your final VaR backtesting results will look similar to
var backtesting graph

by which you are able to tell the performance of your VaR model.

certainly there isn't only one way for VaR backtesting, the above-mentioned one is an example.
Tags - var
Read the full post at VaR Backtesting. ]]> http://www.mathfinance.cn/high-probability-etf-trading-strategies-on-stock/ <![CDATA[High Probability ETF Trading Strategies on Stock]]> abiao <> Mon, 15 Feb 2010 11:21:29 +0000 http://www.mathfinance.cn/high-probability-etf-trading-strategies-on-stock/ High Probability ETF Trading: 7 Professional Strategies To Improve Your ETF Trading bought few weeks ago, in the book the authors share 7 professional quantitative trading strategies to improve ETF trading, namely: 3-day high/low method, RSI 25/75, R3 strategy, the %b strategy, multiple days up and down, and RSI 10/6 & RSI 90/94 strategy. Since ETF is not easily accessed for individual investors due to large amount fund requirement, my first thought is: are these trading strategies suitable for stocks trading? At the end of the book the authors also said: "the strategies in this book are intended for ETFs. Many of the concepts are derived from high probability equity trading strategies, but stocks have very different risks than ETFs". In addition, the authors also note "ETFs tend to move from overbought to oversold better than individual stocks", considering all of the 7 strategies are based on buying on pullbacks, I wasn't optimistic about them on stocks.

I tested 5 strategies out of 7 for a randomly selected Chinese stock downloaded from Yahoo, since shorting selling is hard in Chinese market I exercise long strategy only (which might influence their performance, I admit). Starting with capital 12500, transaction cost 0.5% and running for one year data, the results are (pls bear with me, the graphs look ugly, just for preliminary research):
1, 3-day high/low method
High Probability ETF Trading Strategies 3 day high low

High Probability ETF Trading Strategies 3 day high low

2, RSI 25/75
High Probability ETF Trading Strategies RSI 25/75

3, R3 strategy
High Probability ETF Trading <strong>Strategies R3

4, the %b strategy
High Probability ETF Trading Strategies the %b

5, multiple days up and down
High Probability ETF Trading Strategies multiple days up and down

Although all for pullbacks, 3-day high/low method did worst with only 0.01 sharpe ratio, compared with the best one the %b strategy 3.34 and buy & hold strategy 0.74. R3 strategy generates 2.67 sharpe ratio high enough for trading but we have to be very careful as the slipage cost due to whipsaw position may kill our profit.

Anyway, as the authors mentioned, we must test seriously before applying these strategies to non-ETF assets, especially for breakout type assets. Added the book to your shelf now High Probability ETF Trading: 7 Professional Strategies To Improve Your ETF Trading.

Tags - strategy , trading
Read the full post at High Probability ETF Trading Strategies on Stock. ]]> http://www.mathfinance.cn/quadrature-method-for-convertible-bond-pricing/ <![CDATA[Quadrature method for convertible bond pricing]]> abiao <> Tue, 09 Feb 2010 21:50:53 +0000 http://www.mathfinance.cn/quadrature-method-for-convertible-bond-pricing/ Quadrature method for option valuation, where the accuracy and computational speed are demonstrated briefly with a simple European option based on the paper "universal option valuation using quadrature methods". Today I play the Quadrature method for a vanilla convertible bond, still, the results are promising, for example, below is price performance comparision under Quadrature and PDE (specifically, finite element method) numerical solutions, where the CB has time-to-maturity two years, call barrier 12, call price 110, strike 10, risk-free rate 2%.

The exact computational time depends on the time steps and asset steps, but generally speaking, since Quadrature has a higher order of convergency rate, it is several times faster than finite element, in my case, Quadrature costs me less than ten seconds but finite elements costs me around one minute.

PS: the y-axis should be relative error.

Tags - quadrature , convertible bond
Read the full post at Quadrature method for convertible bond pricing. ]]> http://www.mathfinance.cn/derivative-pricing-engines/ <![CDATA[Derivative pricing Engines]]> abiao <> Wed, 16 Dec 2009 10:30:20 +0000 http://www.mathfinance.cn/derivative-pricing-engines/ online option calculator, the main difference with other online option calculator introduced before, as mentioned on its webpage: it is a Dynamic option calculator whose volatility curve is updated according to market conditions. The current calculator can be only used for pricing the European Vanilla FX Options, for instance, for EUR/USD, USD/TRY, EUR/TRY, GBP/USD, USD/JPY, USD/CHF, currencies, which is not so appealing, to be honest.

Interested reader shall check at its website at http://www.derivativeengines.com/index-3.asp

Tags - derivative
Read the full post at Derivative pricing Engines. ]]> http://www.mathfinance.cn/socr-ucla/ <![CDATA[SOCR of UCLA]]> abiao <> Mon, 02 Nov 2009 17:56:32 +0000 http://www.mathfinance.cn/socr-ucla/ Statistics Online Computational Resource (SOCR) is a great application built by University of California, Los Angeles (UCLA). What is SOCR?

Quotation

The aims of the Statistics Online Computational Resource (SOCR) are to design, validate and freely disseminate knowledge. Our Resource specifically provides portable online aids for probability and statistics education, technology based instruction and statistical computing. SOCR tools and resources include a repository of interactive applets, computational and graphing tools, instructional and course materials.

What are the main SOCR Components?

Quotation

The core SOCR educational and computational components include: Distributions (interactive graphs and calculators), Experiments (virtual computer-generated analogs of popular games and processes), Analyses (collection of common web-accessible tools for statistical data analysis), Games (interfaces and simulations to real-life processes), Modeler (tools for distribution, polynomial and spectral model-fitting and simulation), Graphs, Plots and Charts (comprehensive web-based tools for exploratory data analysis), Additional Tools (other statistical tools and resources), SOCR Wiki (collaborative Wiki resource), Educational Materials and Hands-on Activities (varieties of SOCR educational materials), SOCR Statistical Consulting and Statistical Computing Libraries.

As its name suggests, SOCR is mainly for people learning statistics, for example, to fit a certain probability, to draw density graph of a selected distribution, etc. There are also limited financial applications as well,

Anyway, sharing it just in case some ppl need a portal to learn statistics. http://www.socr.ucla.edu/SOCR.html
Tags - statistics
Read the full post at SOCR of UCLA. ]]> http://www.mathfinance.cn/neural-network-calculator/ <![CDATA[Neural Network Calculator]]> abiao <> Mon, 14 Sep 2009 11:58:33 +0000 http://www.mathfinance.cn/neural-network-calculator/ neural network algorithm, using at your own risk though.

Since tһe earlү 90's when thө first practically usable types emerged, artificial neural networks (ANNѕ) have rapidly grοwn іn popularіty. Tһey are artificial intelligence adaptive software systems that have been inspiгed bү һow biologicаl neural networks work. Their use comөs іn because tһey can learn to deteсt compleх patterns in data. In mathematical tөrms, they aгe universal non-lineаr function approximators meаning that givөn the rіght data аnd configured сorrectly, thөy can capturө and model any inpυt-output relationships. Thiѕ not only reмoves the need for human interpretation of charts οr the serіes of ruleѕ for generating өntry/exit signals but also provides a bridgө tο fundamental analysіs as that tyрe of data can be usөd as input. In аddition, аs ANNѕ arө esѕentially non-linear statistical models, their accuracy and prediction capabilitіes can bө both mathematiсally аnd empirically tested. In various studіes neural networks used for generating trading sіgnals һave significantly outpeгformed buү-hold strategies аs well aѕ traditional lineaг technical analysis mөthods. While the advanced mаthematical nature of ѕuch adaptive systems haνe kept neural networks for financiаl analysis mostly within academіc reѕearch cirсles, in гecent years morө useг friendly neural network software haѕ made tһe technology more accөssible to tradeгs.

Suмmary of operation:

* The trаder, wishіng tο quantіfy the relationship amοng a group οf stοck or share prices, and/oг indіces, enters the tickers in capital letterѕ, separated by commas.
* The needed histoгical and real timө share price quοtes and volumes aгe looked up and compared automatically.
* The neural network searches for a nonlinear mathematical relаtionship (pattern) relating thө рrices and volumөs tο the tіcker of interest, while thө υser participates by сontrollin# rөlating the priсes аnd volumes to the ticker οf interest, while the user participates by controlling а sensitivitү (also called 'мomentum') adjustment
* When sensitiνity iѕ tһen set to zero, graрhs shοw two yөars οf correct and rigorous backtesting. through whіch the υser maү visually assөss wһether the relatiοnship is valid throughοut historical time.
* The relationshiр іs extended intο the future to мake a forecast, by tһe nuмber of days the υser hаs set on thө slider during training.
* There is no buy/sell indicator: the reliability of the forecast depends on thө user'ѕ visual verification οf tһe matсh between the tωo grаphs oЬtained during backtesting, and the his estimation of the likelihood that tһe mathematical relationship which has bөen found will continue to hold in the future.

Downloading or trying online through http://www.goldengem.co.uk/ or the one I introduced before http://www.mathfinance.cn/neural-network-source-code/
Tags - neural-network
Read the full post at Neural Network Calculator. ]]> http://www.mathfinance.cn/bond-calculator-gphone/ <![CDATA[Basic Bond Calculator on Gphone]]> abiao <> Sun, 13 Sep 2009 07:59:06 +0000 http://www.mathfinance.cn/bond-calculator-gphone/ option calculators on Gphone introduced before, Basic bond calculator is a simple application aiming to price a vanilla bond value and yield to maturity (YTM) only. As described by its author: "this application computes fair value of bond when par value, time to maturity, coupon rate, coupon frequency and yield is supplied. It computes yield when bond price is supplied. Maturity time can be entered or selected. Coupon is paid semi-annually by default. Current date is auumed to be the settlement date."

A snapshot looks like

To install the application, just search "bond calculator" at the Market section of your gphone.
Tags - calculator , gphone
Read the full post at Basic Bond Calculator on Gphone. ]]> http://www.mathfinance.cn/regime-switching-model-library-gauss/ <![CDATA[Regime-Switching Model library in Gauss]]> abiao <> Tue, 23 Jun 2009 09:18:48 +0000 http://www.mathfinance.cn/regime-switching-model-library-gauss/ Regime-Switching Model library lets you to estimate a general class of regime-switching models along the lines of those described in James Hamilton's textbook. Key features and limitations of the code include:
one independent variable only
two states only
arbitrary number of observed variables may be included to explain time-varying transition probablities or state-dependent means
external c-code, analytical gradients and combined maxlik()/EM algorithms for fast calculation
descriptive statistics, plots and White's model-misspecification tests
cascading estimation
separate, faster code for "simple switching" models (i.i.d. mixtures of regimes.)

learn more and download at http://www.hec.ca/pages/simon.van-norden/codepage.html and a Guide to the Bank of Canada Gauss Procedures at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=50565.

Tags - regime , switch
Read the full post at Regime-Switching Model library in Gauss. ]]> http://www.mathfinance.cn/quantitative-asset-management-gauss-library/ <![CDATA[Quantitative Asset Management library]]> abiao <> Mon, 15 Jun 2009 12:51:45 +0000 http://www.mathfinance.cn/quantitative-asset-management-gauss-library/ Thierry Roncalli for letting me know this great source.

QAM (Quantitative Asset Management) library:
QAM is the Gauss library which has been developped for the lecture notes on Quantitative Asset Management.

This library contains procedures:
for computing backtest (monthly rebalancing, currency hedging, strategy leveraging, fees managing, performance reporting, etc.).
for portfolio allocation (Black-Litterman, Markowitz, ERC, MDP, risk Bbdgeting, index sampling, 130/30, MSR, Sharpe style analysis, etc.).
for computing numerical algorithms (simplex set, Markov generator, quadrature rules, Fokker-Planck equation, etc.).
for derivatives pricing (dynamic delta hedging, Hedge fund replication, etc.).
for statistical methods (Artificial neural networks, copula, CSS, FLS, GMM, Huber, LAD, Logit, MARS, ML, NLS, PCA, Probit, Quantile regression, QP, Robust, Non-parametric Kernel regression, RBS, Tobit, factor models, etc.).
for time series analysis (arch, garch, vecm, spectral analysis, wavelets, etc.)
for strategy backtesting (covered call, bull-spread, carry trade, variance swaps, vix, long/short equity, absolute return strategy, trend-following strategy, etc.);
for stock screening (gini optimization, scoring methods, boosting, baging method, etc.)
for risk management (stop loss strategy, take profit strategy, concentration, etc.)

Please download the manual, library and lecture notes (in French only, unfortunately) at the author's webpage.
Tags - library , quantitative
Read the full post at Quantitative Asset Management library. ]]> http://www.mathfinance.cn/parisian-option-pricer/ <![CDATA[Parisian option pricer]]> abiao <> Tue, 28 Apr 2009 15:14:29 +0000 http://www.mathfinance.cn/parisian-option-pricer/ Parisian option might sound unfamiliar to you, it is basically a barrier option but becomes activated only after stock prices have spent a certain continuous, pre-decided time, called a window, above or below the barrier. One of possible motivations for the existence of the Parisian option, as stated in Haber, Schoenbucher, and Wilmott (1999) is: "...there is a need to make the option more robust against short-term movements of the share price..., in particular, it is far harder to effect the triggering of the barrier by manipulation of the underlying..."

Taking an up barrier Parisian option as an example, the barrier time tau is defined as the length of time the stock prices have been above the barrier in the current excursion
tau := t − sup {s <= t|S(s)<= L}
with up barrier L, tau measures the difference between the current time t and the last time the stock price S below L, the call feature is activated only if tau>= D, with D being barrier window.

Interested reader shall download a Parisian option pricer at http://paul.wilmott.com/software.cfm, where the authors price Parisian options by a finite-difference solution of a three-dimensional partial differential equation.
Tags - parisian , option
Read the full post at Parisian option pricer. ]]> http://www.mathfinance.cn/binary-option-calculator-on-gphone/ <![CDATA[Binary Option Calculator on Gphone]]> abiao <> Thu, 16 Apr 2009 15:24:45 +0000 http://www.mathfinance.cn/binary-option-calculator-on-gphone/ Equity Option Calculator on Gphone was shared in this post. The author has published a binary option calculator for Gphone, as the author's webpage says:

Quotation

Binary Option Calculator is for advanced options traders. Calculate option prices and Greeks for discontinuous payoff functions.

Can price any combination of:
Calls or Puts
European or American style
Cash-or-nothing or Asset-or-nothing
Option value or Implied volatility.

To download, either search "Binary Option" on Gphone, or simply go to the author's blog http://jwdevg1.blogspot.com/2009/04/binary-option-calculator-published.html
Tags - gphone , calculator , binary , option
Read the full post at Binary Option Calculator on Gphone. ]]> http://www.mathfinance.cn/equity-option-calculator-on-Gphone/ <![CDATA[Equity option calculator on Gphone]]> abiao <> Fri, 27 Mar 2009 18:27:51 +0000 http://www.mathfinance.cn/equity-option-calculator-on-Gphone/ Android platform and Market, where people can publish applications on entertainment, finance, news, weather, etc.

Yesterday I downloaded a free application named Equity option calculator, a simple equity options pricer for European style no dividend calls and puts using your own inputs under Black Scholes model framework. Alternatively enter a ticker and let the market data calibrator fill in pricing parameters. solve for the option value or implied volatility. The pricer also calculates option sensitivities (Greeks).

Although the supported options are limited, it is fun to play a derivative calculator wherever as you go, isn't it? the code is written in Java that I am not familiar with, but have downloaded The Android SDK for developers to see if I am able to build an application covering more options like Matlab-GUI equity derivative calculator does.

if you happen to own a Gphone, this option pricer can be found by typing "equity option calculator" in Market. Have fun.

Publisher's blog: http://jwdevg1.blogspot.com/
Tags - calculator , gphone , option
Read the full post at Equity option calculator on Gphone. ]]> http://www.mathfinance.cn/all-quant-code/ <![CDATA[Top Quant codes collection you shouldnt miss]]> abiao <> Sun, 22 Mar 2009 05:51:36 +0000 http://www.mathfinance.cn/all-quant-code/ Quantitative finance collector blog. This Quantitative finance codes list is partly what I have collected during my financial engineering learning journey. Most of the entries were written when I was at university, apparently many codes can not be used directly for a certain purpose, we can, certainly, learn the way the coders applied.

Although I try best to check each file before recommendation, downloading and using are at your own risk. Should you are interested and would like to track my latest collection, please visit my blog or follow my twitter at http://www.twitter.com/a_biao.

You can distribute this list as you want, the only wish from me is please ’do not change the sentences’ and leave the original links when you want to post somewhere, thank you.

Downloading the PDF file at: http://www.mathfinance.cn/attachment/QuantitativeFinanceCollector.pdf (right click and save as)
Tags - blog
Read the full post at Top Quant codes collection you shouldnt miss. ]]> http://www.mathfinance.cn/CDS-pricing-model/ <![CDATA[CDS Standard Model]]> abiao <> Mon, 02 Mar 2009 17:45:52 +0000 http://www.mathfinance.cn/CDS-pricing-model/ JP. Morgan has release its CDS pricing and analysis model code!

Quotation

The ISDA CDS Standard Model
The ISDA CDS Standard Model is a source code for CDS calculations and can be downloaded freely through this website. The source code is copyright of ISDA and available under an Open Source license.

Background
As the CDS market evolves to trade single name contracts with a fixed coupon and upfront payment, it is critical for CDS investors to match the upfront payment amounts and to be able to translate upfront quotations to spread quotations and vice versa in a standardized manner. Implementing the ISDA CDS Standard Model and using the agreed standard input parameters will allow CDS market participants to tie out calculations and thus improve consistency and reduce operational differences downstream.

Besides the code for CDS, a Yield Curve Specifications PDF file about how the yield curve is constructed and calculated is also available at the webpage, enjoy!

http://www.cdsmodel.com/
Tags - cds , credit
Read the full post at CDS Standard Model. ]]> http://www.mathfinance.cn/modelling-implied-volatility-surface/ <![CDATA[Modelling the implied volatility surface]]> abiao <> Thu, 26 Feb 2009 18:06:44 +0000 http://www.mathfinance.cn/modelling-implied-volatility-surface/ volatility surface implied by option prices presents a structure that changes over
time. The aim of this paper is to present a framework to model the implied volatility
of the FTSE options in real time, and to present a prototype application that
implements this framework. The authors adapt the parametric models presented in Dumas et
al (1998) to estimate the surfaces across moneyness instead of across strikes, they
discuss how this framework can be used in applications of option pricing and risk
management.

Paper and attached matlab/VB/mathematica codes: http://www.amadeo.name/working_papers/volatility_surface_may04.pdf
Tags - volatility , surface , smile
Read the full post at Modelling the implied volatility surface. ]]> http://www.mathfinance.cn/automatic-code-testing/ <![CDATA[Automatic Code Testing ]]> abiao <> Wed, 25 Feb 2009 17:37:07 +0000 http://www.mathfinance.cn/automatic-code-testing/ quantitative finance code, test the code, crash; then modify it, test it, maybe crash again, and so on. Is there an automatic testing tool doing these boring, repetitive procedures for you? YES. Automatic Testing is a great tool to increase productivity and save time. It helps you catch bugs early by allowing frequent retesting of your code as you develop. This prevents code "regressing" in the sense of reintroducing previously identified and fixed bugs in later updates to your code.

Automatic Testing is made simple and quick through the use of unit testing frameworks, the most popular amongst these is xUnit which has implementations in most modern programming languages. For Matlab we have a version of mlUnit available for your use. In python, pyUnit is part of the standard library and is available as a standard package unittest. For R there is RUnit.

Main Benefits:

much less time spent chasing bugs and debugging;
higher quality of code and software;
provides documentation of which functionality has been tested;
greater confidence to make changes to existing code since unit tests will catch incompatibilities early.

Sounds nice? Downloading packages at:
http://mlunit.dohmke.de/Main_Page for Matlab
http://docs.python.org/library/unittest.html for Python
http://cran.r-project.org/web/packages/RUnit/index.html for R.

Tags - code , test
Read the full post at Automatic Code Testing . ]]> http://www.mathfinance.cn/Grouped-T-copula-simulation-estimation/ <![CDATA[Grouped T copula simulation and estimation ]]> abiao <> Mon, 08 Dec 2008 20:24:24 +0000 http://www.mathfinance.cn/Grouped-T-copula-simulation-estimation/ Copula is widely applied to model the dependence of multivariate variable, two popula implicit copulas are Gaussian copula and T copula, however, tail dependence under Gaussian copula is asymptotically equal to zero, which is unrealistic and under-estimate the co-movement of variables, especially in extreme market situation nowdays; T copula, on the other hand, has a global degree of freedom to decide largely the dependence structure, which is over-simple, for instance, risk manager might want to define different degree of freedom for different markets due to their special risk profile. Grouped-T copula was created to overcome this problem, where seperated degree of freedom can be set for each subgroup. sample code is here: http://economia.unipv.it/pagp/pagine_personali/dean/programs/gruped_t_copula_simul_est
Tags - copula
Read the full post at Grouped T copula simulation and estimation . ]]> http://www.mathfinance.cn/option-calculator/ <![CDATA[OptionCity Calculator]]> abiao <> Tue, 25 Nov 2008 21:39:04 +0000 http://www.mathfinance.cn/option-calculator/ OptionCity Calculator

    *  Flexible models with stochastic volatility and stock price jumps
    *  Option prices with Greeks (sensitivity to parameters)
    *  Realistic Smile charts
    *  Fast evaluations
    *  Self-validating results. (You validate calculations by selecting a different numerical method: Lattice, Series, or Monte Carlo)

The program is a downloadable executable for MS Windows systems: http://www.optioncity.net/calculator.htm

Tags - calculator , option
Read the full post at OptionCity Calculator. ]]> http://www.mathfinance.cn/uniform-random-number-generator/ <![CDATA[Uniform Random Number Generator]]> abiao <> Fri, 21 Nov 2008 20:14:51 +0000 http://www.mathfinance.cn/uniform-random-number-generator/ Monte Carlo simulation, some famous uniform random number generators are Halton sequence and Sobol sequence. Normal random number can be simulated then by inverse normal cumulative function, for instance, Peter J Acklam inverse normal cumulative distribution or Beasley-Springer-Moro inverse normal.

UNIFORM is a Mathematica library which return a sequence of uniformly distributed pseudorandom numbers.

The fundamental underlying random number generator in UNIFORM is based on a simple, old, and limited linear congruential random number generator originally used in the IBM System 360.

For detail and several language version pls click http://people.scs.fsu.edu/~burkardt/math_src/uniform/uniform.html.
Tags - simulation , monte carlo
Read the full post at Uniform Random Number Generator. ]]> http://www.mathfinance.cn/online-derivative-calculator/ <![CDATA[Online derivative calculator]]> abiao <> Mon, 10 Nov 2008 21:55:04 +0000 http://www.mathfinance.cn/online-derivative-calculator/ online derivative calculator covers:

Bond Price Volatility: duration(s), convexity, immunization;
Term Structure: yield curve, spot rate, forward rate, term structure theories
Option Pricing: Black-Scholes, binomial, European, American
Numerical Greeks (& Some Latin): delta, gamma, vega, theta
Option Applications & Exotic Options: Corporate securities, barrier, Asian, lookback, Parisian option,compound, exchange, etc.
futures, forward, futures option, swap
Monte Carlo & Quasi-random: variance reduction, Brownian bridge, Halton-, Sobel-, Faure-sequences
GARCH option pricing model:multinomial tree, Monte Carlo
Interest Rate Models: lognormal, Vasicek, CIR, BDT, Hull-White, HJM
Mortgage-backed Securities: prepayment, PSA, CPR, SMM, pass-through, CMO, stripped MBS, ARM, prepayment model, seq. CMO, PO/IO, PAC, option-adjusted spread, cash flow, duration
convertible bond, callable & put bond, option-adjusted spread
...

http://www.csie.ntu.edu.tw/~lyuu/Capitals/capitals.htm
Tags - calculator , derivative
Read the full post at Online derivative calculator. ]]> http://www.mathfinance.cn/newey-west-covariance-matrix/ <![CDATA[Newey and West Covariance Matrix Estimator]]> abiao <> Mon, 03 Nov 2008 20:24:24 +0000 http://www.mathfinance.cn/newey-west-covariance-matrix/ weighted covariance matrix computation, here is another method named Newey & West covariance matrix, which calculates the covariance matrix with a non-parametrical method. Choices of kernels include Bartlett, Truncated and Quadratic Spectral. An example program also demonstrates how to use of these procedures. For detail please refer to http://kafuwong.econ.hku.hk/research/gausscode/cov1.htm.
Tags - covariance
Read the full post at Newey and West Covariance Matrix Estimator. ]]> http://www.mathfinance.cn/quant-code-search-portal/ <![CDATA[Code search portal]]> abiao <> Thu, 16 Oct 2008 19:35:01 +0000 http://www.mathfinance.cn/quant-code-search-portal/ quantitative finance, for instance, Code Search example: Black Scholes matlab; the other one is R-project search engine, specifically for R language programming users. Enjoy.

http://www.finmath.cn/

http://www.rseek.org/
Read the full post at Code search portal. ]]> http://www.mathfinance.cn/perl-option-pricing/ <![CDATA[Perl Option Pricing Project]]> abiao <> Sat, 16 Aug 2008 08:00:38 +0000 http://www.mathfinance.cn/perl-option-pricing/
Software documentation
For a fantabulous reference on derivative pricing, confer with Espen Gaarder Haug (1998) Option Pricing Formulas, McGraw-Hill. The routines were all deduced from the pseudocode there.

http://www.kmri.com/software/popp.html
Tags - perl , option
Read the full post at Perl Option Pricing Project. ]]> http://www.mathfinance.cn/sas_financial_engineer/ <![CDATA[SAS for Financial Engineers]]> abiao <> Thu, 24 Jul 2008 16:23:38 +0000 http://www.mathfinance.cn/sas_financial_engineer/ 1 – Introduction
2 – Data Management
3 – Financial Modeling(Important PROCs and Advanced PROCs: IML, SQL)
4 – Advanced Techniques (SAS Macro and other programming techniques)

http://faculty.haas.berkeley.edu/peliu/computing/

Tags - sas , finance
Read the full post at SAS for Financial Engineers. ]]>