Challenging Risk-Neutrality, Reinforcement Learning for Options Pricing in Indian Options market

This thesis aims to challenge the controversial yet common assumption of Risk- Neutrality in much of the Options pricing literature. Traditional Options pricing methods assume perfect hedge portfolio in a risk-neutral world which leads to a paradoxical conclusion that Options themselves are redundant, since Options trading is a trillion dollar market that clearly is not the case. This thesis presents an alternative method using Reinforcement Learning that relaxes the assumption on risk-neutrality and perfect hedging. A risk-sensitive discrete-time Markov Decision Process is created for the hedge portfolio which allows for imperfect hedging. The hedge portfolio consists of cash and position in underlying which is taken to be the action variable for the RL setting. A value function for the RL setting is created as the ask Options price which deviates from the risk-neutral fair price and incorporates risk associated with the option in form of discounted variance of the hedge portfolio. Further steps include calculation of the optimal action and using it to solve the Bellman Optimality condition for the Value function to obtain at the Options price. The model is empirically tested on 37 most liquid Option issuers on NSE with varying strikes and maturities accumulating to a total of 324 different Option contracts. Results show that the Reinforcement Learning model significantly outperforms the Black-Scholes model wrt actual NSE traded prices with an overall scaled RMSE of 8.34% vs 12.28% for the BS model. Also, the RL model shows a better performance in 29 of the total 37 Option issuers.