We use Malliavin calculus and the Clark–Ocone formula to derive the hedging strategy of an arithmetic Asian Call option in general terms. Furthermore we derive an expression for the density of the integral over time of a geometric Brownian motion, which allows us to express hedging strategy...

We use Malliavin calculus and the Clark–Ocone formula to derive the hedging strategy of an arithmetic Asian Call option in general terms. Furthermore we derive an expression for the density of the integral over time of a geometric Brownian motion, which allows us to express hedging strategy...

We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore we...

The Samp;P 500 index return interacts negatively with its volatility. This paper traces the negative interaction to three distinct economic channels and proposes to disentangle the relative contribution of each channel using Samp;P 500 index options. First, equity volatility increases...

The risk-neutral process is modeled by a four parameter self-similar process of independent increments with a self-decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models...

Vanilla (standard European) options are actively traded on many underlying asset classes, such as equities, commodities and foreign exchange (FX). The market quotes for these options are typically used by exotic options traders to calibrate the parameters of the (risk-neutral) stochastic process...