THE JOURNAL OF FINANCE. VOL XXXIV. NO 5. DECEMBER 1979 The fournal of finance VOL. XXXIV DECEMBER 1979 Two-State Option Pricing RiChard J, RENDLEMAN, JR, and brIt. barttER' I. Introduction IN THIS PAPER WE present an elemental two- state option pricing model (TSoPM) which is mathematically simple, yet can be used to solve many complex option pricing problems. In contrast to widely accepted option pricing models which require solutions to stochastic differential equations, our model is derived alg braically. First we present the mathematics of the model and illustrate its application to the simplest type of option pricing problem. Next, we discuss the statistical properties of the model and show how the parameters of the model can be estimated to solve practical option pricing problems. Finally, we apply the model to the pricing of European and American put and call options on both non-dividend and dividend paying stocks. Elsewhere, we have applied the model to the valuation of the debt and equity of a firm with coupon paying debt in its capital structure [9], the valuation of options on debt securities [7], and the pricing of fixed rate bank loan commitments[1, 2]. In the Appendix we derive the Black-scholes [3] model using the two-state approach I. The Two-State Option Pricing Model Consider a stock whose price can either advance or decline during the next period Let Hi and Hi represent the returns per dollar invested in the stock if the price rises(the state)or falls(the - state), respectively, from time t-l to time t and Vi and Vi the corresponding end-of-period values of the option. With the assumption that the prices of the stock and its option follow a two-state process it is possible to form a riskless portfolio with the two securities. [See Black and Scholes [3] for the continuous time analog of riskless hedging. Since the end-of- period value of the portfolio is certain, the option should be priced so that the portfolio will yield the riskless interest rate The riskless portfolio is formed by investing one dollar in the stock and Both Assistant Professors of Finance, Graduate School of Management, Northwestern University Since the original writing of this paper, the authors have learned that a similar procedure has been suggested by Rubinstein [10], Sharpe [11], and Cox, Ross, and Rubinstein[5]