In this paper, we derive a closed from solution for the value of a perpetual American option when the logreturn of a stock is driven by a fractional Brownian motion, with Hurst parameter H ↦ (0,1). A special case of our model would be the model driven by standard Brownian motion

This paper evaluates the prices of European-style options when dynamics of the underlying asset is assumed to follow a Markov-switching Heston's stochastic volatility model. Under this framework, the expected return and the long-term mean of the variance of the underlying asset rely on states of...

We consider a regime-switching HJB approach to evaluate risk measures for derivative securities when the price process of the underlying risky asset is governed by the exponential of a pure jump process with drift and a Markov switching compensator. The pure jump process is flexible enough to...

In this paper we develop a method for pricing derivatives under a Markov switching version of the Heston-Nandi GARCH (1, 1) model by using a well known tool from actuarial science, namely the Esscher transform. We suppose that the dynamics of the GARCH process switch over time according to one...

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...

The behavior of the optimal exercise price of American puts near expiry has been well studied under the Black-Scholes model as a result of a series of publications. However, the behavior of the optimal exercise price under a stochastic volatility model, such as the Heston model, has not been...