The Black-Scholes model is often used to price financial options. (The model ass

Question

The Black-Scholes model is often used to price financial options. (The model assumes that the stock price is a random walk with drift, or more precisely is a geometric Brownian motion process. The Black-Scholes equation is a partial differential equation that describes the price of the option over time.) It provides a method to construct a riskless portfolio using hedging. Although the model uses simplifying assumptions, the model works well enough to provide guidance in option pricing. One of the assumptions made by the model is that the logarithm of the stock price at a future time is normally distributed which means that stock prices are lognormally distributed. The lognormal model for stock prices is reasonable because stock prices have limited liability and cannot become negative. S at a future time is normally distributed with mean = 3 and standard deviation = 1 as Suppose the log stock price log shown in the figure below Lognormal DIstrlbutlon for Stock Price S 0.030 0.025 0.020 0.015 0.010 0.005 0.000 50 100 150 Stock Price S (US$

Explanation / Answer

log (S) follows normal distribution with mean 3 and standard deviation 1.

So, S follows log normal distribution .

Mean of log normal distribution is given by,

E( S) = e µ+ (1/2) 2 = 33.11545

Rounding off the expected value we get,

E(S) = 33

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