Research Area: Computational Finance
Thesis Supervisor: Dr. Siddhartha P. Chakrabarty
Research Description: Computational finance is a branch of applied computer science that deals with problems of practical interest in finance. Some slightly different definitions are the study of data and algorithms currently used in finance and the mathematics of computer programs that realise financial models or systems. Computational finance emphasises practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. It is an interdisciplinary field between mathematical finance and numerical methods. Two major areas are efficient and accurate computation of fair values of financial securities and the modelling of stochastic price series.
Currently, I am working on pricing of "Passport Option". This specific financial instrument is a call option on the balance of trading account. The fundamental purpose of a passport option is to protect a trading accounts. Holder should buy the passport option because wrong trading strategy is already covered by the insurance and writer of the option will gain when holder will not choose the optimal trading strategy. The pricing partial differential equation for passport option is a non-linear parabolic (HJB type) with non-smooth diffusion coefficient as well as non-smooth payoff.