Lookback options and dynamic fund protection under multiscale stochastic volatility

This paper investigates the valuation of lookback options and dynamic fund protection under a multiscale stochastic volatility model. The underlying asset price is assumed to follow a geometric Brownian motion with a volatility that is driven by two stochastic processes with one persistent factor and one fast mean-reverting factor. Semi-analytical pricing formulas for lookback options are derived by means of a multiscale asymptotic technique. The effects of stochastic volatility on options with lookback payoffs are examined. By calibrating effective parameters from the volatility smile of vanilla options, our model improves the valuation of options with the lookback feature. We also develop a model-independent parity relation between the price functions of dynamic fund protection and quanto lookback options. This enables us to assess the effect of multiscale stochastic volatility on the price of dynamic fund protection.