The stock of Square Company is currently trading at a market price of $47.04 per

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

Hope this helped ! Let me know in case of any queries.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.