Option Pricing Under Jump-Diffusion Processes with Regime Switching

Abstract

We study an incomplete market model, based on jump-diffusion processes with parameters that are switched at random times. The set of equivalent martingale measures is determined. An analogue of the fundamental equation for the option price is derived. In the case of the two-state hidden Markov process we obtain explicit formulae for the option prices. Furthermore, we numerically compare the results corresponding to different equivalent martingale measures.

Numerical approximation of hybrid Poisson-jump Ait-Sahalia-type interest rate model with delay

“…Also for s ∈ [0, t ∧ ς ∆,n ], we obtain from the Lyapunov function in (15) and the mean value theorem that…”

“…The shortcoming of the continuous-time model of Black-Scholes [1] in describing convex phenomena of implied volatility exhibited by most historical financial data led to the underlying assumption of constant volatility to be questioned. Several empirical studies have rather shown that stochastic volatility models with inherent features of past dependency are suitable models for describing convex phenomena of implied volatility against market anomalies (see, e.g., [2,8,9,15]).…”

“…Hybrid models driven by finite-state Markovian chains have also been increasingly employed as suitable models for modelling uncertainty in modern economic or financial systems (see, e.g., [6,14,15,16]). The hybrid models randomly switch between finite number of regimes in anticipation to unexpected abrupt structural changes in underlying economic or financial mechanisms.…”