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I'd recommend M. Joshi and T. Leung "Using Monte Carlo simulation and importance sampling to rapidly obtain jump-diffusion prices of continuous barrier options". Though it assumes jump-diffusion process for the returns it is straightforward to obtain the scheme for a diffusion process. Also Paul Glasserman's [book][2] [2]: ...


The first book that comes to mind that is written in the style of Definition - Proposition - Proof is: Bjork - Arbitrage Theory in Continuous Time It's pretty well written and can get quite technical. Probably a more common reference is the two-volume set: Shreve - Stochastic Calculus for Finance I & II The first part deals with the binomial ...

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