Option Valuation Under a Double Regime‐Switching Model

Abstract

This paper is concerned with option valuation under a double regime‐switching model, where both the model parameters and the price level of the risky share depend on a continuous‐time, finite‐state, observable Markov chain. In this incomplete market set up, we first employ a generalized version of the regime‐switching Esscher transform to select an equivalent martingale measure which can incorporate both the diffusion and regime‐switching risks. Using an inverse Fourier transform, an analytical option pricing formula is obtained. Finally, we apply the fast Fourier transform method to compute option prices. Numerical examples and empirical studies are used to illustrate the practical implementation of our method. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:451–478, 2014

Pricing annuity guarantees under a double regime-switching model

“…Comparatively little attention has been paid to regime-switching models with the assumption that both model parameters and the price level of the reference investment fund may change when the modulating Markov chain switches from one state to another. Using the terminology in Shen et al (2014), when a regime switch occurs, the model with only model parameters changing is called the single regime-switching (SRS) model, while the other kind of regime-switching model is denoted as the double regime-switching (DRS) model. The DRS models are more flexible than their SRS counterparts to describe the stochastic movements of the reference investment fund due to the fact that a jump in the investment fund price level occurs in the former, rather than the latter, when there is a regime switch (see Naik, 1993, Yuen and Yang, 2009.…”

“…Our paper extends the results of Lin et al (2009) in the following aspects. Firstly, we consider the valuation of EIAs and VAs under a double regime-switching model in Shen et al (2014). In addition to the assumption that model parameters are governed by the modulating Markov chain adopted in Lin et al (2009), we also assume that a jump in the price level of the reference investment fund may occur when the modulating Markov chain switches from one state to another.…”

“…In this paper, we adopt the DRS model proposed in Shen et al (2014) to investigate the valuation of the equity-linked products with mortality risk. Various designs including the point-to-point EIAs, the annual ratchet EIAs and the GMDB in variable annuities are considered.…”

“…Here, we present two approaches to selecting pricing kernels. Firstly, we use the generalized version of the regime-switching Esscher transform introduced in Shen et al (2014) to select an equivalent martingale measure (i.e. risk-neutral probability measure).…”

R&D Project Valuation Considering Changes of Economic Environment: A Case of a Pharmaceutical R&D Project

“…We propose a new real option valuation model which simultaneously employs mean-reverting stochastic process and time-varying parameters based on a binomial lattice approach. The mean-reversion assumption and a regime switching technique can more realistically capture the characteristics of R&D projects and the structural changes of economic conditions [17,27]. Additionally, as Mun [28] indicated, a lattice-based approach is relatively intuitive and can therefore be accepted easily.…”