The stock of Square Company is currently trading at a market price of $47.04 per
ID: 2706537 • Letter: T
Question
The stock of Square Company is currently trading at a market price of $47.04 per share. During the next year, the price of Square's stock will either increase ( uptick) to $72 or decrease (downtick) to $32. The risk free rate of interest is 2.02% per year compounded continously, so that the PV of a risk free dollar to be received in 1 year is $0.9800. Assuming that Square is not expected to pay a dividend during the next two years, and that the risk-neutral probability of an uptick in the stock price does not change over time, determine
a. the risk - neutral probability of an uptick in the stock price
b. the value of a put option with a $40 strike price having one year to expiration
Explanation / Answer
a. Uptick ratio = 72/47.04 = 1.530612
Downtick ratio = 32/47.04 = 0.680272
Risk neutral probability of uptick in stock price = (e^(2.02%)-0.680272) / (1.530612-0.680272) = 40%
b. Put option payoff on uptick = 0 and on downtick = 40-32 = 8
Value of put option = (40%*0+60%*8)*0.98 = $ 4.704
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