Pricing Vulnerable Options with Market Prices of Common Jump Risks under Regime-Switching Models

Abstract

This paper investigates the valuation of vulnerable European options considering the market prices of common systematic jump risks under regime-switching jump-diffusion models. The way of regime-switching Esscher transform is adopted to identify an equivalent martingale measure for pricing vulnerable European options. Explicit analytical pricing formulae for vulnerable European options are derived by risk-neutral pricing theory. For comparison, the other two cases are also considered separately. The first case considers all jump risks as unsystematic risks while the second one assumes all jumps risks to be systematic risks. Numerical examples for the valuation of vulnerable European options are provided to illustrate our results and indicate the influence of the market prices of jump risks on the valuation of vulnerable European options.

Pricing European Vulnerable Options with Jumps and Stochastic Default Obstacles Barrier under Regime Switching

“…where H T = V T D T . Under the equivalent martingale measure P, the expression of V T and D T are expressed by Equations ( 22)- (24), and the expression of…”

“…The second plan e 2 = (0, 1) can be interpreted as a bad economic state. We refer to relevant literature (such as Han [24]) to choose the initial state of the economy X = X 0 = (1, 0), and the generation matrix of the Markov chain process…”

“…NIU [23] assumes that the value of risk assets is driven by a relevant regime-switching double exponential jump-diffusion model and uses two-dimensional Laplace transforms to obtain a European vulnerable option pricing formula. Han [24] assumes that the value of risk assets is driven by a relevant regime-switching jump-diffusion model and uses the Esscher transform to select an equivalent martingale measure to obtain a European vulnerable option pricing formula and discusses the impact of jump risk on European vulnerable option pricing. Capponi [25] presents an efficient method for pricing vulnerable contingent claims in a regime-switching market using a suitable change of probability measure and a Poisson series representation.…”

“…In addition, we use numerical simulation to explore the impact of default barriers and parameters on option prices and find that stochastic default barriers increase credit risk, leading to lower option prices. We differ from Han [24] in that they assume that the default barrier is constant. We assume that the dynamics of the default barrier are regime-switching geometric Brownian motions related to the underlying assets and counterparty assets.…”

Pricing Vulnerable Options in a Mixed Fractional Brownian Motion with Jumps

“…Wang [12] carried out research into the pricing problem of vulnerable options by assuming that the underlying asset price and the value of counterparty asset both followed jump-diffusion processes and the default barrier was stochastic. Han et al [13] investigated vulnerable options pricing considering the market prices of common systematic jump risks under regimeswitching jump-diffusion models and derived explicit analytic pricing formulae for vulnerable options by risk-neutral pricing theory. Under the reduced-form framework, Niu et al [14] incorporated jump risks and dynamical correlation between the underlying asset and the counterparty asset in vulnerable options to present jump-diffusion pricing models with stochastic correction.…”