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 and price of the Asian option as an analytic, that is closed form, expression. Numerical computations whi...

Substantial progress has been made in developing more realistic option pricing models. Empirically, however, it is not known whether and by how much each generalization improves option pricing and hedging. We ll this gap by rst deriving an option model that allows volatility, interest rates and jumps to be stochastic. Using S&P 500 options, we examine several alternative models from three persp...

This article attempts to extend the complete market option pricing theory to incomplete markets. Instead of eliminating the risk by a perfect hedging portfolio, partial hedging will be adopted and some residual risk at expiration will be tolerated. The risk measure (or risk indifference) prices charged for buying or selling an option are associated to the capital required for dynamic hedging so...

As the core of option transaction, price changing with supply and demand in market is a variable which affects profit loss both trading sides directly. In 20th century, multitudinous econometric pricing models proposed lacked universal recognition until Black Scholes Merton model came out. This paper focuses on stocks options from Visa Inc. to do article consisting calibration, hedging using fu...

We consider a financial market with liquidity cost as in Çetin, Jarrow and Protter [3] where the supply function S(s, ν) depends on a parameter ε ≥ 0 with S(s, ν) = s corresponding to the perfect liquid situation. Using the PDE characterization of Çetin, Soner and Touzi [6] of the super-hedging cost of an option written on such a stock, we provide a Taylor expansion of the super-hedging cost in...

We compare the dynamic hedging performance of the deterministic local volatility function approach with the implied/constant volatility method. Using an example in which the underlying price follows an absolute diffusion process, we illustrate that hedge parameters computed from the implied/constant volatility method can have significant error even though the implied volatility method is able t...