CRSC Projects: Financial Mathematics

Financial Mathematics

This project concerns the derivation of formulas for pricing options in the context of stochastic volatility models. Option pricing consists in finding the fair price of a contract written on the future random evolution of a risky asset. These options represent now a large part of the market, largely due to growing hedging funds, and their pricing is an extremely important problem. This problem is mathematically modeled by second order partial differential equaations with random coefficients which require heavy computations. Our study consists in deriving simple and practical formulas which approximate their solutions using a separation of scales. Free boundary value problems associated to American style options are also investigated as well as models for interest rates. The original techniques that we propose to use are generral and relevant to the theory of stochastic processes and their numerous applications.