Hedging in fractional Black–Scholes model with transaction costs

Abstract

Abstract. We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently discovered explicit conditional law of the fractional Brownian motion.

Prediction of Gaussian Volterra Processes with Compound Poisson Jumps

“…Thus models where the returns are Gaussian with jumps seem more reasonable: The Gaussian part could take care of the long-range dependence with fractional Brownian motion (fBm) as the Gaussian Volterra process, and the shocks would come from the compound Poisson part. Then one can use the result of this paper to calculate imperfect hedges in the mixed model in the similar way as done in Shokrollahi and Sottinen (2017) and Sottinen and Viitasaari (2018). Indeed, this is work in progress by the authors.…”

An Investigation on a Pattern of Virtual Executive Stock Option Based on Multidimensional Performance Indices

“…Among the pricing models of the ESO, there are respectively three most popular ones, respectively the Shelton Pricing Model(Shelton et al, 2005) [8] , Kassouf Pricing Model (Derming, 1997; Clifford and Smith, 1976) [9] [10] and Black-Scholes Option Pricing Model(B-S Model)(Foad and Tommi, 2017; Shoujun Huang et al, 2017) [11] [12] .…”

Prediction law of mixed Gaussian Volterra processes

“…Surprisingly, regular conditional laws have not been studied extensively in the literature. On related research we can mention [3], [4], [5] and [6] where fractional Brownian motion and more generally Gaussian Fredholm processes were considered and applied in the stochastic finance setting.…”