Option pricing and perfect hedging on correlated stocks

Abstract

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process. With a modified portfolio consisting in calls, secondary calls and bonds we achieve a riskless strategy which results in a closed expression for the European call price which is always lower than Black-Scholes price. We also obtain a partial differential equation for the option price and study the sensitivity to several parameters and the risk of the dynamics of the call price.

36 pages, 8 figures, 2 tables

References in corpus (4)

• A correlated stochastic volatility model measuring leverage and other stylized facts
• Stochastic volatility and leverage effect
• The effect of non-ideal market conditions on option pricing
• Option Pricing and Hedging with Temporal Correlations

Cited by in corpus (5)

• Extreme times for volatility processes
• Quantum extension of European option pricing based on the Ornstein-Uhlenbeck process
• Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model
• Partial Derivative Approach for Option Pricing in a Simple Stochastic Volatility Model
• Market memory and fat tail consequences in option pricing on the expOU stochastic volatility model