Markov Chain Monte Carlo and Finance ?

SPAAGG · January 14th, 2004, 12:26 pm

Hi, thanks for your answer concerning Monte Carlo in the future !!! Great to have feedbacks.Now a new question, regarding Markov Chain Monte Carlo. May someone explain me what exactly is MCMC, the difference with usual Monte Carlo, and applications, in particular wrt Finance.Thanks !

pjotr314 · January 14th, 2004, 12:56 pm

Here is a short explanaion of MCMC:In Monte Carlo you simulate from a know underlying process.In Markov Chain Monte Carlo you don't know the excact distribution of the underlying process. But you can get it by drawing from a Markov chain with the desired distribution.

ScilabGuru · January 14th, 2004, 1:16 pm

Marcov process is the process whose conditional distribution P(X_t|F_s) is completely defined by the state X_s. Thus defining P(X_t|X_s) and initial value X_0, you can simulate path (pathes) X_i, with P(X_i | X_{i-1}) predefined.

SPAAGG · January 14th, 2004, 4:25 pm

thanks pjotr314 and scilabguru,can u give me an example. Hence, you don't know the diffusion process of the underlying.dX_t=mu(t,x)*dt+sigma(t,x)*dW where mu and sigma are unknown.What can u do now ?

ScilabGuru · January 14th, 2004, 6:37 pm

MC cannot solve all problems in our life, you know. If you don't know any spec of the process and you don't have any real data to get parameters for your simualtion, what .... you are going to simulate?

SPAAGG · January 15th, 2004, 6:21 am

of course....do you have any reference in MCMC's field (papers, websites, etc)thanks

pjotr314 · January 15th, 2004, 6:49 am

have you ever heard of google.comif you try +introduction +"markov chain monte carlo" +pdfyou will get for exampleThis oneand this one.the last book reference in the last presentation is a good starting book in MCMC.Good luck!

SPAAGG · January 15th, 2004, 10:51 am

Thanks for these answers!of course I know google... but I wanted examples and papers on MCMC applications in Finance.If someone has an idea, thanks

PeteJ · January 15th, 2004, 3:15 pm

QuoteOriginally posted by: SPAAGGThanks for these answers!but I wanted examples and papers on MCMC applications in Finance.If someone has an idea, thanksWell, Johannes & Polson is probably the most famous paper on MCMC in finance and is has also been mentioned at these forums often. The paper also has a lot of nice references to various financial MCMC applications (mainly by Johannes, Polson and Eraker).

Alphabet · January 16th, 2004, 5:06 pm

It sounds closely related to Simulated Annealing, which I've always found to be (i) useful, and (ii) suspicious.