On pricing and optimal hedging of path-dependent financial derivatives

  • Vijaysekhar Chellaboina
  • Sanjay P. Bhat
  • Deep Shikha

Abstract

In this paper, we consider the problems of pricing and hedging discretely monitored pathdependent European contingent claims (ECCs), that is, European-type derivatives whose payoff depends on underlying asset value observed at a discrete set of times. Such derivatives include cliquet
option (options with strike reset feature), Asian option, and chooser option. First, assuming that the underlying asset follows a geometric Brownian motion (Black-Scholes) model, we provide a general expression for arbitrage-free price of discretely monitored ECCs. We then provide a closed-form
expression (in terms of the derivative price) for dynamic hedging. The proposed dynamic hedging strategy is restricted to a set of discrete-times (as opposed to a continuous-time hedging strategy) and minimizes the variance of the hedging error. Finally, we specialize the pricing and hedging expression
to the case of a cliquet option.

Published
2014-05-25
Section
Articles