Monday, March 5, 2018 | 2:00pm-3:30pm | Room 337, HSBC Business School Building

Abstract

Continuous time Markov chain (CTMC) approximation is an intuitive and powerful method for pricing and hedging options in general Markovian models. This talk is a summary of recent developments in this direction, from both perspectives of applications and theoretical analysis. Our works in this line begin with algorithm developments for option pricing in a family of non-Levy jump models. Later on, this algorithm is extended to hedging VIX derivatives in our new developed pure jump models and it shows very good performance. For the theoretical issues, we established the sharp convergence rates of Markov chain approximation for pricing options with nonsmooth payoff functions. The analysis is then extended to nonuniform grid case, as well as option delta and gamma which are important quantities for option hedging and risk management. Inspired by these theoretical results, we propose a simple nonuniform grid construction method to achieve the optimal convergence behaviours, i.e., smooth second order convergence that enables extrapolation to further speed up the convergence. To conclude the talk, I will introduce some interesting future research topics to explore.