Monte Carlo method for discretization of diffusion processes: part II
Международная лаборатория количественных финансов организовала продолжение мини-курса "Monte Carlo method for discretization of diffusion processes: part II" профессора Emmanuel Lepinette (Paris-Dauphine Universite, France). Прочитано 2 лекции: 5 мая 2015 года - на тему "Milshtein scheme, a method to increase the convergence rate" и 12 мая 2015 года - на тему "Barrier options, the bridge simulation method based on Brownian bridges"
(Paris-Dauphine Universite, France)
Since the pioneering work of Black-Scholes-Merton in 1973, diffusion processes have been extensively used when modeling financial market models. When the market is complete, the replicating price of an European claim is the discounted expectation of the payoff. If the asset dynamics is modeled by a diffusion process, this price is then explicitly given and the question of interest is how to compute it. Contrarily to the Black and Scholes model, Call option price does not admit an analytic expression in local volatility models. The very idea is therefore to `` compute '' independent trajectories of the underlying asset many times so that we deduce an approximation of the discounted expectation (average) of the payoff when applying the law of large numbers. The goal of this lecture is to introduce the so called Monte Carlo methods which provide approximations of the trajectory of a diffusion process. We study the convergence rate of the proposed approximation schemes and then deduce applications to pricing in complete markets. Moreover, two practical works are proposed where implementation of Monte Carlo methods are done on Scilab software. This course assumes a basic understanding of probability theory and Ito calculus.
Тема: "Milshtein scheme, a method to increase the convergence rate"
Вторник, 12 мая 18:10−19:40
Тема: "Barrier options, the bridge simulation method based on Brownian bridges"