Mr Pareto wants to try his hand at applying the binominal model to option pricin

Question

Mr Pareto wants to try his hand at applying the binominal model to option pricing so that he may compare theoretical prioes with empirical ones. He desides to price ar S&P; 500 index put option for this purpose. Suppose that the index is currently 1912 and has a volatility of 27%, while the risk-free rate is 1%. Compute the price of a 3-month ATM option by using a one-step binomial model if the up factor u and the down factor d are given by the following formulas: du = e-07 (a) 130 (b) 131 (o) 132 (d) 133 (5 marks)

Explanation / Answer

we have the formulas for u and d given in the question

so using them we get u = e^(.27)*(3/12)^1/2 = 1.144

d= 1/u = 0.874

Risk neutral probability = (e^(r*t)-d)/u-d = 1.0025-0.874/.27 = 0.475

I think to proceed further, stock price and strike price would be required.

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