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• W2073676254 abstract "Empirical evidence has shown that subordinated processes represent well the price changes of stocks and futures. Using either transaction counts 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 information-time. This contention has also been supported later in theoretical models. In this paper we investigate the implication of this contention to option pricing.First we price the option in calendar-time where the return of the underlying asset follows a jump subordinated process. We extend Rubinstein's Rubinstein, M. 1976. The valuation of uncertain income streams and the valuation of options. Bell J. Econom. Management Sci.7 407-425. and Ross's Ross, S. 1989a. Information and volatility: The no-arbitrage martingale approach to timing and resolution irrelevancy. Finance44 1-17. martingale valuation methodology to incorporate the pricing of volatility risk. The resulting equilibrium formula requires estimating seven parameters upon implementation. We then make a stochastic time change, from calendar-time to information-time, in order to obtain a stationary underlying asset return process to price the option. We find that the isomorphic option has random maturity because the number of information arrivals prior to the option's calendar-time expiration date is random. We value the option using Dynkin's Dynkin, E. B. 1965. Markov Processes, Vols. I and II. Springer-Verlag, Berlin and New York. version of the Feynman-Kac formula that allows for a random terminal date. The resulting information-time formula requires estimating only one additional parameter compared to the Black-Scholes's in practical application. In this regard, the time change has reduced the computational complexity of the option pricing problem. Simulations show that the formula may outperform the Black-Scholes Black, F., M. Scholes. 1973. The pricing of options and corporate liabilities. Political Econom.81 637-659. and Merton Merton, Robert C. 1976a. Option pricing when underlying stock returns are discontinuous. Financial Econom.3 125-143. models in pricing currency options.As a first attempt to derive valuation relationships in the information-time 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." @default.
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• W2073676254 date "1996-07-01" @default.
• W2073676254 modified "2023-09-24" @default.
• W2073676254 title "Option Pricing with Stochastic Volatility: Information-Time vs. Calendar-Time" @default.
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• W2073676254 doi "https://doi.org/10.1287/mnsc.42.7.974" @default.
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