Pricing Vulnerable Options in a Mixed Fractional Brownian Motion with Jumps

Abstract

A new framework for pricing European vulnerable options is developed in the case where the underlying stock price and firm value follow the mixed fractional Brownian motion with jumps, respectively. This research uses the actuarial approach to study the pricing problem of European vulnerable options. An analytic closed-form pricing formula for vulnerable options with jumps is obtained. For the purpose of understanding the pricing model, some properties of this pricing model are discussed in the paper. Finally, we compare and analyze the pricing results of different pricing models and discuss the influences of basic parameters on the pricing results of our proposed model by using numerical simulations, and the corresponding economic analyses about these influences are given.

An Imex-Based Approach for the Pricing of Equity Warrants Under Fractional Brownian Motion Models

“…For example, Almani et al introduced a new FBM with a two-variable Hurst exponent, and found that the model is more precisely matched to the real values of the rate of the stock price [2]. Cheng and Xu considered the pricing of vulnerable options under a mixed FBM model with jumps [9]. By introducing an FBM to the constant elasticity of variance (CEV) model, Araneda and Bertschinger proposed a sub-fractional CEV model and considered the pricing of options underneath [3].…”