OPTION PRICING WITH STOCHASTIC VOLATILITY - INFORMATION-TIME VS CALENDAR-TIME

Empirical evidence has shown that subordinated processes represent wel l the price changes of stocks and futures. Using either transaction co unts or trading volume as a proxy for information arrival, it supports the contention that volatility is stochastic in calendar-time because of random information arrival, and thus becomes stationary in informa tion-time. This contention has also been supported later in theoretica l models. In this paper we investigate the implication of this content ion to option pricing. First we price the option in calendar-time wher e the return of the underlying asset follows a jump subordinated proce ss. We extend Rubinstein's (1976) and Ross's (1989a) martingale valuat ion methodology to incorporate the pricing of volatility risk. The res ulting equilibrium formula requires estimating seven parameters upon i mplementation. We then make a stochastic time change, from calendar-ti me to information-time, in order to obtain a stationary underlying ass et return process to price the option. We find that the isomorphic opt ion has random maturity because the number of information arrivals pri or to the option's calendar-time expiration date is random. We value t he option using Dynkin's (1965) version of the Feynman-Kac formula tha t allows for a random terminal date. The resulting information-time fo rmula requires estimating only one additional parameter compared to th e Black-Scholes's in practical application. In this regard, the time c hange has reduced the computational complexity of the option pricing p roblem. Simulations show that the formula may outperform the Black-Sch oles (1973) and Merton (1976a) models in pricing currency options. As a first attempt to derive valuation relationships in the information-t ime economy, this investigation may suggest that the information-time approach is a functional alternative to the current calendar-time norm . It is especially suitable for deriving ''volatility-free'' portfolio insurance strategies.