Quantitative Finance Collector is a blog on Quantitative finance analysis, methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management.
Jan
9
Online option calculator was shared several time before, for example, the post 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:
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.
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.
- 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.
Jul
1
To be honest, I haven't read this paper yet as my research interest has moved gradually from no-arbitrage to arbitrage valuation, however, this paper Adding and Subtracting Black-Scholes:A New Approach to Approximating Derivative Prices in Continuous-Time Models is very interesting from its abstract and may be appealing to some of you.
Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous-Time Models is written by Dennis Kristensen, Antonio Mele, and is accepted by Journal of Financial Economics.
A working paper is available at http://w4.stern.nyu.edu/volatility/docs/Kristensen.pdf
Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous-Time Models is written by Dennis Kristensen, Antonio Mele, and is accepted by Journal of Financial Economics.
Quotation
We develop a new approach to approximating asset prices in the context of continuous-time models. For any pricing model that lacks a closed-form solution, we provide a solution, which relies on the approximation of the intractable model through a known, "auxiliary" one. We derive an expression for the difference between the true (but unknown) price and the auxiliary one, which we approximate in closed-form, and use to create increasingly improved refinements to the initial mispricing induced by the auxiliary model. The approach is intuitive, simple to implement and leads to fast and extremely accurate approximations. We illustrate this method in a variety of contexts, including option pricing with stochastic volatility, volatility contracts and the term-structure of interest rates.
A working paper is available at http://w4.stern.nyu.edu/volatility/docs/Kristensen.pdf
May
3
Read an interesting paper last week "On the Number of State Variables in Options Pricing" by Gang Li, Chu Zhang. As the title suggests, this paper is trying to identify how many state variables are good enough to price an option, ideally the less variables the better.
The authors first review a few popular models for option pricing such as Black Scholes model, GARCH option pricing, and Stochastic volatility models, then they argue two possible sources of model misspecification, one is the omitted state variables, or factors, for instance, should we consider volatility smile? should we include jump into our pricing equation, etc. The other source of model misspecification is the functional form of the process for the state variables, including the specification of risk premiums associated with the state variables, this misspecification may be especially prone to error, or in another term, easily leads to model risk. Square root process or simple mean-reversion? or a combination of these two as some literature suggest.
In order to identify the necessary number of factors, the authors then use a nonparametric approach with state variables approximated by nonlinear principal components extracted from the implied volatilities. Nonparametric approach helps to overcome the problem of function form misspecification, and nonlinear principle component helps to demonstrate the explanatory power of each factor, similar with a typical principle component analysis except the former is able to capture the nonlinear relationship among observation series, which is obviously the case for the implied volatilities.
The authors first review a few popular models for option pricing such as Black Scholes model, GARCH option pricing, and Stochastic volatility models, then they argue two possible sources of model misspecification, one is the omitted state variables, or factors, for instance, should we consider volatility smile? should we include jump into our pricing equation, etc. The other source of model misspecification is the functional form of the process for the state variables, including the specification of risk premiums associated with the state variables, this misspecification may be especially prone to error, or in another term, easily leads to model risk. Square root process or simple mean-reversion? or a combination of these two as some literature suggest.
In order to identify the necessary number of factors, the authors then use a nonparametric approach with state variables approximated by nonlinear principal components extracted from the implied volatilities. Nonparametric approach helps to overcome the problem of function form misspecification, and nonlinear principle component helps to demonstrate the explanatory power of each factor, similar with a typical principle component analysis except the former is able to capture the nonlinear relationship among observation series, which is obviously the case for the implied volatilities.
Aug
31
This guest post is brought to you by Options University.
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John J. Halpin
Dear MathFinance.cn readers,
Options University is giving away $797 worth of Options Education For F.R.E.E. to the next 200 traders.
And trust me. This is not a trick, or a gimmick.
If you are wondering why we are doing this, well, with the economy being in the toilet, Options University wants to show that we're here to help you weather the storm.
So the next 200 students that follow the link below will be armed with some of the most powerful, portfolio-boosting investment education on the planet.
Follow the link below to get your hands on Options 101 and the Advanced Options Home Study Courses (the convenient online editions):
==> Get Your Free Option Trading Course
The only potentially bad news is that the amount of editions released for f.r.e.e. has to be limited to only 200, as these particular home study courses continue to be their best selling education products. But for those of you who are fast enough, please enjoy two of the best selling options education courses for f.r.e.e.
John J. Halpin
Aug
27
VBA week...
Option Pricing Models and Volatility Using Excel-VBA is the best book I have read this year, recommended by a friend of mine couple of days ago. I didn't look positive at it at the beginning as there are dozes of books on similar topics and to be honest, I never heard of the author (now I know he works in industry). However, the more pages I dig, the less willing to stop & happier I feel as the author explains the volatility staff relevant to option pricing SOOOOO well and in plain language. More importantly, there are accompanying VBA codes for almost every example, if that's no enough, the author provides VBA solutions to the exercise as well, which encourage the readers to practice & make our hands dirty, unlike many other books do.
The book starts with complex number, how to write macro code for it; followed by selected root-finding algorithms, and weighted least square regression; then introduces numerical integration, tree-building, black scholes, Heston model, GARCH, implied volatility, parameter estimation, etc. Preview is worth a thousand words, check yourself below:
Option Pricing Models and Volatility Using Excel-VBA is the best book I have read this year, recommended by a friend of mine couple of days ago. I didn't look positive at it at the beginning as there are dozes of books on similar topics and to be honest, I never heard of the author (now I know he works in industry). However, the more pages I dig, the less willing to stop & happier I feel as the author explains the volatility staff relevant to option pricing SOOOOO well and in plain language. More importantly, there are accompanying VBA codes for almost every example, if that's no enough, the author provides VBA solutions to the exercise as well, which encourage the readers to practice & make our hands dirty, unlike many other books do.The book starts with complex number, how to write macro code for it; followed by selected root-finding algorithms, and weighted least square regression; then introduces numerical integration, tree-building, black scholes, Heston model, GARCH, implied volatility, parameter estimation, etc. Preview is worth a thousand words, check yourself below:
