A Finite Element Differential Equations Analysis Library
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2010/01/15 14:22 | by abiao ]
2010/01/15 14:22 | by abiao ]
Attended a training of NAG Toolbox for MATLAB today (NAG is short for Numerical Algorithms Group), nice presentation and persuasive performance against Matlab toolbox. I will soon get a licence and start to experience myself.
Anyway, I got to know two sites after the training, first one is deal.II, which is a finite element differential equations analysis library aiming to enable rapid development of modern finite element codes, using among other aspects adaptive meshes and a wide array of tools classes often used in finite element program. As stated on its webpage: "deal.II is a C++ program library targeted at the computational solution of partial differential equations using adaptive finite elements. It uses state-of-the-art programming techniques to offer you a modern interface to the complex data structures and algorithms required." It should be very useful for those people playing often with PDE numerical solution.
The other site is Walking randomly, a blog where the author randomly collects things including mathematics, physics, vintage computing, Linux, pocket PCs, Android, music and programming. I am especially interested in its Matlab, R, NAG, and statistics categories.
Have a nice weekend.
Anyway, I got to know two sites after the training, first one is deal.II, which is a finite element differential equations analysis library aiming to enable rapid development of modern finite element codes, using among other aspects adaptive meshes and a wide array of tools classes often used in finite element program. As stated on its webpage: "deal.II is a C++ program library targeted at the computational solution of partial differential equations using adaptive finite elements. It uses state-of-the-art programming techniques to offer you a modern interface to the complex data structures and algorithms required." It should be very useful for those people playing often with PDE numerical solution.
The other site is Walking randomly, a blog where the author randomly collects things including mathematics, physics, vintage computing, Linux, pocket PCs, Android, music and programming. I am especially interested in its Matlab, R, NAG, and statistics categories.
Have a nice weekend.
Friday reading list 01/08/2010
[ 2010/01/09 01:11 | by abiao ]
2010/01/09 01:11 | by abiao ]
1, Yes, the Choice of Performance Measure Does Matter for Ranking of US Mutual Funds, "Recent literature in performance evaluation has focused on preferences and characteristics of returns’ distribution that go beyond mean and variance world. However, Eling (2008) compared the Sharpe ratio with some of these performance measures, and found virtually identical rank ordering using mutual fund data. This paper compares 13 performance measures with the traditional Sharpe Ratio using a sample of US Fixed-Income, Equity and Asset Allocation Mutual Funds. Results show that performance measures based on absolute reward-risk ratios have similar rankings, when the numerator (mean excess return) is the same. However, when we move to other types of performances measures, results may be significantly different. " http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1403916
2, The Augmented Black-Litterman Model: A Ranking-Free Approach to Factor-Based Portfolio Construction and Beyond, "The Fama and French (1992 and 1993 etc.) factor ranking approach is very popular among quantitative fund managers. However, this approach suffers from hidden factor view, loss of information, etc. issues. Based on the Black-Litterman model (Black and Litterman, 1992; as explained in Cheung, 2009A), we design a technique that endogenises the ranking process and elegantly resolves these issues. This model explicitly seeks forward-looking factor views and smoothly blends them to deliver robust allocation to securities. Our numerical experiments show this is an intuitive and practical framework for factor-based portfolio construction, and beyond." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1347648
3, Transparent Augmented Black-Litterman Allocation: Simple and Unified Framework for Strategy Combination, Factor Mimicking, Hedging, and Stock-Specific Alphas, "You have some factor, strategy, and/or stock-specific alpha ideas. Without an optimiser, some straightforward linear algebra gives you the diversified and efficient Bayesian allocation that allows greater performance accountability. All you need is just a factor risk model. How does this sound? This paper derives a transparent version of the ABL model (Cheung, 2009B) with an explicit allocation expression, including components for all the needed functionalities. In addition to further insights, it allows more tangible implementation of strategy combination, factor mimicking, hedging, and stock-specific bets in a unified framework." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1347663
4, Homogeneous Volatility Bridge Estimators, "We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge, corresponding to given log-price stochastic process, and in its close value, for a given time interval. The efficiency of the new proposed estimators is favorably compared with that of the Garman-Klass and Parkinson estimators." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1523225
5, A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives, "We propose a general framework for efficient pricing via a Partial Differential Equation (PDE) approach of cross-currency interest rate derivatives under the Hull-White model. In particular, we focus on pricing long-dated foreign exchange (FX) interest rate hybrids, namely Power Reverse Dual Currency (PRDC) swaps with Bermudan cancelable features." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1502302
Have a nice weekend.
2, The Augmented Black-Litterman Model: A Ranking-Free Approach to Factor-Based Portfolio Construction and Beyond, "The Fama and French (1992 and 1993 etc.) factor ranking approach is very popular among quantitative fund managers. However, this approach suffers from hidden factor view, loss of information, etc. issues. Based on the Black-Litterman model (Black and Litterman, 1992; as explained in Cheung, 2009A), we design a technique that endogenises the ranking process and elegantly resolves these issues. This model explicitly seeks forward-looking factor views and smoothly blends them to deliver robust allocation to securities. Our numerical experiments show this is an intuitive and practical framework for factor-based portfolio construction, and beyond." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1347648
3, Transparent Augmented Black-Litterman Allocation: Simple and Unified Framework for Strategy Combination, Factor Mimicking, Hedging, and Stock-Specific Alphas, "You have some factor, strategy, and/or stock-specific alpha ideas. Without an optimiser, some straightforward linear algebra gives you the diversified and efficient Bayesian allocation that allows greater performance accountability. All you need is just a factor risk model. How does this sound? This paper derives a transparent version of the ABL model (Cheung, 2009B) with an explicit allocation expression, including components for all the needed functionalities. In addition to further insights, it allows more tangible implementation of strategy combination, factor mimicking, hedging, and stock-specific bets in a unified framework." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1347663
4, Homogeneous Volatility Bridge Estimators, "We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge, corresponding to given log-price stochastic process, and in its close value, for a given time interval. The efficiency of the new proposed estimators is favorably compared with that of the Garman-Klass and Parkinson estimators." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1523225
5, A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives, "We propose a general framework for efficient pricing via a Partial Differential Equation (PDE) approach of cross-currency interest rate derivatives under the Hull-White model. In particular, we focus on pricing long-dated foreign exchange (FX) interest rate hybrids, namely Power Reverse Dual Currency (PRDC) swaps with Bermudan cancelable features." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1502302
Have a nice weekend.
Google Quant Staff
[ 2010/01/07 21:07 | by abiao ]
2010/01/07 21:07 | by abiao ]
Sharing a Google Quant Staff page I created initially for myself, the motivation was to make the job more convenient since I had to search in Google too many times per day, what's worse is sometimes I prefer video results, while sometimes what I need is just PDF documents or Matlab files. Adjusting frequently with Google advanced search makes me feel silk.
Google Quant Staff is by no means an invention, I just put several searching filters in one page, that's it.
For example, to find pdf documents about "Asian option", simply type "Asian option" in the form and click the PDF icon
Similarly each icon stands for one filter:
Searching results will be openned in a new browser window in Google as what I did was creating a page to filter results. You can also choose to search books in Amazon below.
PS: the page can also be used for keywords nothing to do with Quant staff as long as google catches them.
Anyway, hope you find it somehow useful: Google Quant Staff, bookmark if you like.
Google Quant Staff is by no means an invention, I just put several searching filters in one page, that's it.
For example, to find pdf documents about "Asian option", simply type "Asian option" in the form and click the PDF icon
Similarly each icon stands for one filter:
Searching results will be openned in a new browser window in Google as what I did was creating a page to filter results. You can also choose to search books in Amazon below.
PS: the page can also be used for keywords nothing to do with Quant staff as long as google catches them.
Anyway, hope you find it somehow useful: Google Quant Staff, bookmark if you like.
Vanna Volga Method
[ 2010/01/05 22:11 | by abiao ]
2010/01/05 22:11 | by abiao ]
The vanna volga method is a popular pricing model for implied volatilities, especially for foreign exchange options, it is an empirical procedure that can be applied to "draw" an implied volatility smile curve from three given quotes (reversal, ATM and butterfly) for a certan time to maturity. Empirical research shows the vanna volga method has a comparable pricing performance with some stochastic volatility model, for example, Castagna and Mercurio (2007) show the implied volatility curve of vanna volga method outperforms that of Malz (1997), and performs equally well as of SABR (2002).
By building a self-financing portfolio consisting a unit of option at strike K, -delta1 units of underlying asset, and -xi units of options at strike ki, Castagna and Mercurio (2007) calculate the weight xi for three given quotes with the help of Ito's lemma and then approximate the European option value under vanna volga method, as stated in the paper, VV pricing model has several advantages: "it has a clear financial rationale supporting, based on the hedging argument...; it allows for an automatic calibration to the main volatility data...; ... it can be extended to any European-style derivative..."
Below is a simple Matlab code to price a call option based on Castagna and Mercurio (2007):
where Vega is a function to compute vega under black scholes formula
Implied volatilities curve is therefore easily achieved by inverting VV pricing model. Interested ppl please refer to http://www.risk.net/risk/technical-paper/1506580/the-vanna-volga-method-implied-volatilities or an advanced one www.mathfinance.de/wystup/papers/wystup_vannavolga_eqf.pdf
By building a self-financing portfolio consisting a unit of option at strike K, -delta1 units of underlying asset, and -xi units of options at strike ki, Castagna and Mercurio (2007) calculate the weight xi for three given quotes with the help of Ito's lemma and then approximate the European option value under vanna volga method, as stated in the paper, VV pricing model has several advantages: "it has a clear financial rationale supporting, based on the hedging argument...; it allows for an automatic calibration to the main volatility data...; ... it can be extended to any European-style derivative..."
Below is a simple Matlab code to price a call option based on Castagna and Mercurio (2007):
% option price under Vanna volga model for any strike k
% sigma2 is ATM implied vol, k2 is ATM strike
s = 1.205;
t = 94/365;
r = -log(0.9902752)/t;
rf = -log(0.9945049)/t;
sigma1 = 0.0979;
sigma3 = 0.0929;
sigma2 = 0.09375;
k1 = 1.172;
k3 = 1.2504;
k2 = 1.2115;
k = 1.24;
Vega1 = Vega(s,k1,r,t,sigma2,rf);
Vega3 = Vega(s,k3,r,t,sigma2,rf);
Vegak = Vega(s,k,r,t,sigma2,rf);
x1 = Vegak*log(k2/k)*log(k3/k)/(Vega1*log(k2/k1)*log(k3/k1));
x3 = Vegak*log(k/k1)*log(k/k2)/(Vega3*log(k3/k1)*log(k3/k2));
price = blsprice(s,k,r,t,sigma2,rf)+x1*(blsprice(s,k1,r,t,sigma1,rf)...
-blsprice(s,k1,r,t,sigma2,rf))+x3*(blsprice(s,k3,r,t,sigma3,rf)...
-blsprice(s,k3,r,t,sigma2,rf));
% sigma2 is ATM implied vol, k2 is ATM strike
s = 1.205;
t = 94/365;
r = -log(0.9902752)/t;
rf = -log(0.9945049)/t;
sigma1 = 0.0979;
sigma3 = 0.0929;
sigma2 = 0.09375;
k1 = 1.172;
k3 = 1.2504;
k2 = 1.2115;
k = 1.24;
Vega1 = Vega(s,k1,r,t,sigma2,rf);
Vega3 = Vega(s,k3,r,t,sigma2,rf);
Vegak = Vega(s,k,r,t,sigma2,rf);
x1 = Vegak*log(k2/k)*log(k3/k)/(Vega1*log(k2/k1)*log(k3/k1));
x3 = Vegak*log(k/k1)*log(k/k2)/(Vega3*log(k3/k1)*log(k3/k2));
price = blsprice(s,k,r,t,sigma2,rf)+x1*(blsprice(s,k1,r,t,sigma1,rf)...
-blsprice(s,k1,r,t,sigma2,rf))+x3*(blsprice(s,k3,r,t,sigma3,rf)...
-blsprice(s,k3,r,t,sigma2,rf));
where Vega is a function to compute vega under black scholes formula
function VegaValue = Vega(s,k,r,t,sigma,rf)
d1 = (log(s/k)+(r-rf+0.5*sigma^2)*t)/(sigma*sqrt(t));
VegaValue = s*exp(-rf*t)*sqrt(t)*normpdf(d1,0,1);
d1 = (log(s/k)+(r-rf+0.5*sigma^2)*t)/(sigma*sqrt(t));
VegaValue = s*exp(-rf*t)*sqrt(t)*normpdf(d1,0,1);
Implied volatilities curve is therefore easily achieved by inverting VV pricing model. Interested ppl please refer to http://www.risk.net/risk/technical-paper/1506580/the-vanna-volga-method-implied-volatilities or an advanced one www.mathfinance.de/wystup/papers/wystup_vannavolga_eqf.pdf
Post your article on this blog
[ 2010/01/01 13:52 | by abiao ]
2010/01/01 13:52 | by abiao ]
Happy new year!
I have got few emails and messages recently asking for the possibility to write an article and post on Quantitative finance collector blog, for example, "I have come across finance sites and am willing to contribute with an article. Please do let me know if you are interested to do so", "I love to write unique finance articles & after seeing ur site I have written one unique article for ur site. Will u be interested to publish it in ur site along with my link"...
Forgive me if I didn't reply individually, the general answer is: YES, you can, but subject to the following criteria:
1, the content of the article must be relevant to quantitative finance in general, specifically, any article about quantitative trading, quantitative risk analysis, derivative pricing code and software, etc., is highly welcomed;
2, the article must be unique and writen only for Quantitative finance collector blog, instead of a copy from sites;
3, the site linked to must be healthy.
The benefits of posting artiles on this blog:
1, as a sign of gratitude, we will put a link back to your site in the post, which will increase the exposure and traffic of your site;
2, the link is do-follow, which means the link will be better recoganized by search engines;
3, more opinions on this blog is always good for our readers.
How to post an article:
simply send your article to abiao @ mathfinance.cn (remove space). Posting an article is totally free as we believe it will be a win-win strategy.
I have got few emails and messages recently asking for the possibility to write an article and post on Quantitative finance collector blog, for example, "I have come across finance sites and am willing to contribute with an article. Please do let me know if you are interested to do so", "I love to write unique finance articles & after seeing ur site I have written one unique article for ur site. Will u be interested to publish it in ur site along with my link"...
Forgive me if I didn't reply individually, the general answer is: YES, you can, but subject to the following criteria:
1, the content of the article must be relevant to quantitative finance in general, specifically, any article about quantitative trading, quantitative risk analysis, derivative pricing code and software, etc., is highly welcomed;
2, the article must be unique and writen only for Quantitative finance collector blog, instead of a copy from sites;
3, the site linked to must be healthy.
The benefits of posting artiles on this blog:
1, as a sign of gratitude, we will put a link back to your site in the post, which will increase the exposure and traffic of your site;
2, the link is do-follow, which means the link will be better recoganized by search engines;
3, more opinions on this blog is always good for our readers.
How to post an article:
simply send your article to abiao @ mathfinance.cn (remove space). Posting an article is totally free as we believe it will be a win-win strategy.
