Risk-minimizing pricing and hedging foreign currency options under regime-switching jump-diffusion models

Abstract

This article mainly investigates risk minimizing European currency option pricing and hedging strategy when the spot foreign exchange rate is driven by a Markov-modulated jumpdiffusion model. We suppose the domestic and foreign money market floating interest rates, the drift and the volatility of the exchange rate dynamics all depend on the state of the economy, which is modeled by a continuous-time hidden Markov chain. The model considered in this paper will provide market practitioners with flexibility in characterizing the dynamics of the spot foreign exchange rate. Using the minimal martingale measure, we obtain a system of coupled partialdifferential-integral equations satisfied by the currency option price and find the corresponding hedging strategies and the residual risk. According to simulation of currency option prices in the special case of double exponential jump diffusion regime switching model, we will further discuss and show the effects of the parameters on the prices.

Pricing and Hedging Performance on Pegged FX Markets Based on a Regime Switching Model

“…where i, j ∈ {0, 1} and Λ ij is a consecutive left closed right open intervals of the real line with length q ij (q ij is the element in Q), see [2] and [19]. We further define v(dy) as the Lévy measure and m(dy, dt) as the compensator measure of the Poisson random measure M (dy, dt).…”

“…These models while self contained for pricing within a band, do not apply for real data calibration on pegged markets as they do not allow for strikes outside of the band. Starting with Naik [24], continuous time regime switching processes in the context of option pricing have been widely studied from empirical and theoretical viewpoint, see [3,8,15,16,19,23,27] among others and the references therein. In contrast to the usual frameworks, the regime switch in this specific model is not independent of the underlying process but triggered by the jump of which.…”

“…In contrast to the usual frameworks, the regime switch in this specific model is not independent of the underlying process but triggered by the jump of which. To our knowledge, the closest form to this model is the one in [19] which is more general. However, the focus of [19] is on local risk-minimizing hedging portfolio.…”

“…To our knowledge, the closest form to this model is the one in [19] which is more general. However, the focus of [19] is on local risk-minimizing hedging portfolio. As for Fourier and FFT methods in finance, they too has been widely studied starting with Heston [17] and [4].…”

Optimal Combination of Currency Assets and Algorithm Simulation under Exchange Rate Risk

“…e two most important assets held by residents are stocks and real estate. e high-yield characteristics of stocks attract more and more investors to enter the market [18]. With the continuous appreciation of real estate, a large amount of capital is attracted to the real estate market.…”