Markov Chain Monte Carlo and Sequential Monte Carlo for Derivatives
Summary
The document collects suggested reading for someone implementing option pricing with Markov chain Monte Carlo methods. One cited paper applies MCMC to continuous-time option models, including constant-volatility, stochastic-volatility, price jump-diffusion, and volatility jump-diffusion settings. It also describes a Bayesian approach to estimation and model selection using a mixture-model MCMC algorithm. Other recommendations cover sequential Monte Carlo applications to option pricing, credit risk, commodity models, and American options under stochastic volatility.
The material is a bibliography-style answer rather than a tutorial or implementation guide. It names research directions and points readers toward references and a scientific computing library for implementation, but provides no algorithm details, performance comparisons, or pricing results. The suggested papers span related derivative and risk applications, so readers still need to determine which methods suit their product, model, and computational goals. The text does not establish that MCMC is preferable to other pricing approaches.
Key ideas
- MCMC research addresses option models with constant or stochastic volatility and jump components.
- A mixture-model MCMC approach is cited for Bayesian estimation and model selection.
- Sequential Monte Carlo references cover options, credit risk, and commodity models.
- One suggested application concerns American options under stochastic volatility.
- The document points to literature but does not explain implementation or compare performance.
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Full text
# Reference on Markov chain Monte Carlo method for option pricing? # Reference on Markov chain Monte Carlo method for option pricing? I have to implement option pricing in c++ using Markov chain Monte Carlo. Is there some paper which describes this in detail so that I can learn from there and implement? ## Answer by Alchemist (score 9) https://quant.stackexchange.com/a/2139 I believe this is a nice paper for you to start with. Check out what references it cited and who cited it. Markov Chain Monte Carlo Analysis of Option Pricing Models "Use the Markov Chain Monte Carlo (MCMC) method to investigate a large class of continuous-time option pricing models. These include: constant-volatility, stochastic volatility, price jump-diffusions and volatility jump-diffusions. We propose a new Bayesian method for estimation and model selection, the “Mixture Model MCMC” algorithm." ## Answer by GKED (score 7) https://quant.stackexchange.com/a/2140 Check this document out: link to pdf file Also, if you are concerned with actual performance of your code and want to implement efficient code then gsl libraries would be the first place look at: link. It's got everything you need. ## Answer by TheBridge (score 5) https://quant.stackexchange.com/a/2142 Here are a few more papers about MCMC and alike methods for derivative pricing and co. : Blanchet-Scalliet, Patras - Counterparty risk valuation for CDS Jasra, Del Moral - Sequential Monte Carlo Methods for Option Pricing Frey, Schmidt - Filtering and Incomplete Information in Credit Risk Peters, Briers, Shevchenko, Doucet - Calibration and Filtering for Multi Factor Commodity Models with Seasonality, Incorporating Panel Data from Futures Contracts Rambharat, Brockwell - SMC Pricing of American-style Options under Stochastic Volatility Models Most of those papers are available online (mostly on Arxiv) Regards
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