Statistical Methods in Finance 2016

Abstract

Pricing Derivatives in a Regime Switching Market with Time Inhomogeneous Volatility

by Milan Kumar Das

In the geometric Brownian motion model of asset prices, the drift and the volatility coeficients of the prices are constants. On the other hand, the regime switching model, allows those coeficients to be Markov pure jump processes. We consider a financial market where the asset price dynamics follow a regime switching model in which the coeficients depend on a more general, possibly non-Markov pure jump stochastic processes. We further allow the volatility coeficient to depend on time explicitly, to capture periodic uctuations like Monday efects etc. Under this market assumption we study locally risk minimizing pricing of vanilla options. It is shown that the price function can be obtained by solving a non-local degenerate parabolic PDE. We establish existence and uniqueness of a classical solution of at most linear growth of the PDE. We further show that the PDE is equivalent to a Volterra integral equation of second kind. Thus one can find the price function by solving the integral equation which is computationally more eficient. We finally show that the corresponding optimal hedging can be computed by performing a numerical integration.

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