Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion

Abstract

The pricing problem of a kind of European vulnerable option was studied. The mixed fractional Brownian motion and the jump process were used to characterize the evolution of stock prices. The closed-form solution to European option pricing was obtained by applying martingale measure transformation method. At the end of this paper, some numerical experiments were adopted to compare the new pricing formula introduced in this paper with the classical Black-Scholes pricing formula. The result showed that the new pricing formula conformed to the actual financial market. In fact, the option value is positively correlated with the underlying asset price and the company’s asset price and the jump process has significant influence on the value of option.

Variable annuities valuation under a mixed fractional Brownian motion environment with jumps considering mortality risk

“…Sun 18 priced European currency options using the MFBM model. Ouyang et al 23 studied the pricing problem of vulnerable European options using the MFBM model. Valuation of options using the MFBM model with jumps is proposed by Murwaningtyas et al 24 Wang et al 22 considered the pricing problem of one asset and three assets European call option and Greeks under the FBM model.…”