Dr. Leunglung Chan

Pricing Volatility Swaps Under Heston's Stochastic Volatility Model with Regime Switching

1 February 2007 in Applied Mathematical Finance

Journal Article

Pricing Options Under a Generalized Markov-Modulated Jump-Diffusion Model

A model is developed for pricing volatility derivatives, such as variance swaps and volatility swaps under a continuous‐time Markov‐modulated version of the stochastic volatility (SV) model developed by Heston. In particular, it is supposed that the parameters of this version of Heston's SV model depend on the states of a continuous‐time observable Markov chain process, which can be interpreted as the states of an observable macroeconomic factor. The market considered is incomplete in general, and hence, there is more than one equivalent martingale pricing measure. The regime switching Esscher transform used by Elliott et al. is adopted to determine a martingale pricing measure for the valuation of variance and volatility swaps in this incomplete market. Both probabilistic and partial differential equation (PDE) approaches are considered for the valuation of volatility derivatives.

19 June 2007 in Stochastic Analysis and Applications

Journal Article

We consider the pricing of options when the dynamics of the risky underlying asset are driven by a Markov-modulated jump-diffusion model. We suppose that the market interest rate, the drift and the volatility of the underlying risky asset switch over time according to the state of an economy, which is modelled by a continuous-time Markov chain. The measure process is defined to be a generalized mixture of Poisson random measure and encompasses a general class of processes, for example, a generalized gamma process, which includes the weighted gamma process and the inverse Gaussian process. Another interesting feature of the measure process is that jump times and jump sizes can be correlated in general. The model considered here can provide market practitioners with flexibility in modelling the dynamics of the underlying risky asset. We employ the generalized regime-switching Esscher transform to determine an equivalent martingale measure in the incomplete market setting. A system of coupled partial-differential-integral equations satisfied by the European option prices is derived. We also derive a decomposition result for an American put option into its European counterpart and early exercise premium. Simulation results of the model have been presented and discussed.

1 January 2014 in Journal of Computational and Applied Mathematics

Journal Article

On pricing barrier options with regime switching

OPTION PRICING FOR GARCH MODELS WITH MARKOV SWITCHING

1 September 2006 in International Journal of Theoretical and Applied Finance

Journal Article

Robert J. Elliott

A PDE approach for risk measures for derivatives with regime switching

12 January 2007 in Annals of Finance

Journal Article