Abstract:

In financial market an investor can either directly trade in stocks or trade in derivative securities such as options. An option is a contact which gives the buyer the right, but not obligation to buy or sell a stock at a specified strike price, on or before a specified date, depending on the form of the of the option. Hence the pricing of options is a very important problem encountered in financial markets.

The most popular approach for option pricing is by driving a governing partial differential equation, called ”Black Scholes Partial Differential Equation” and solving it. BSPDE has an explicit solution for vanilla options. However solving BSPDE, is not a trivial task for options that can be exercised early (e.g American Option) , the ones that are path dependent(e.g Asian Option), or the ones that have multiple underlying options(e.g Rainbow Option). The existing ways to price more complicated options include numerical discretization methods like Finite Difference Scheme and Monte Carlo approximation.

Artificial neural networks(ANN) and deep learning algorithms(DNN) have achieved a lot of success in various applications in recent years. Computer vision, language processing are examples of those applications. Despite such success in a lot of fields, so far deep learning does not find much use in scientific computing. However recently solution of PDEs using ANNs/DNN has emerged as a sub-field. The idea is to basically replace Numerical discretization methods with ANNs/DNN. The key advantages of using ANNs to solve PDEs being that ANNs is a mesh free approach and it can break the curse of dimensionality.

Proposal Defense Committee   

Dr. Mian Muhammad Awais (CS - co-supervisor)

Dr. Adnan Khan (supervisor)

Dr. Sultan Sial

Dr. Zahra Lakhdawala