Two-State Option Pricing since there is no value associated with maintaining an option position beyond maturity, (4-7)represent the formal specification of the two-state model. Through repeated application of (4), subject to (5-7), one can begin at an option s maturity date and recursively solve for its current price. To illustrate the model, consider a call option on a stock with an exercise price of $100. The current price of the stock is $100 and the possible prices of the stock on the option s maturity date are $110 and $90 implying Hf 1.10 andHi =.90 Assuming that the option is exercised if the stock price rises to $110 and is allowed to expire worthless if the stock price falls to $90, the present prices and the end-of- period payoffs of the stock and option can be represented by the following two-branched tree diagram. Stock Option Stock Option () S10 s9Q$0 Today Option s Maturity Dat If an investor purchases the stock and writes two call options, the end-of-period portfolio value will be $90 in both states. Equivalently, for every $l invested in the stock, a riskless hedge requires that a=(90-1. 10)/(10-0)=-02, or that 02 options are written. Assuming a risk free interest rate of 5%, the present value of the riskless portfolio should be $90/1.05 or $85. 71 to ensure no riskless arbitrage opportunities between the stock-option portfolio and a riskless security. Since he riskless portfolio involves a $100 investment in the stock which is partially offset by the two short options, an option price of $7. 14 is required to obtain an $85.71 portfolio value. The option price can also be obtained directly from(4) Pn=5005-90)+0.10-106 10(15) $7.14. Although this example is unrealistic, it nevertheless illustrates two of the most important features of the TSOPM. We can observe that the option price does not depend upon the probabilities of the up(+)or down (-) states occurring or the risk preferences of the investor. Two investors who agreed that the stock price is n equilibrium, but had different probability beliefs and preferences, would both view $7. 14 as the equilibrium option price. As long as they agreed on the magnitudes of the underlying stock's holding period returns(H*and H),they would agree on the price of the option