A four month (120 day) call option on a certain stock has an exercise (strike) p
ID: 2731323 • Letter: A
Question
A four month (120 day) call option on a certain stock has an exercise (strike) price of $62 and is currently selling for $10. If the corresponding put option for this same stock (with the same $62 strike price and four month expiration length) is selling for $15.40, what is the underlying stock’s current market price? Use the put/call parity model to determine your answer. (Assume the current risk-free rate is 4%, and that the stock pays no dividends.)
Put/Call Parity Formula(s). pt = ct – St + X e^ -r T
Where:
ct - pt = St – X e^ -r T
St = ct – pt + X e^ -r T
Xe^ –r T = St + pt - ct
Can someone please solve for me using the provided formulas and explain how the answer is derived. Thanks. The answer is 55.78 but i need to know hwo to solve.
Explanation / Answer
Put-Call Parity:-
Price of call option + Present value of strike price = Price of put option + Stock's current market price
10 + 62 * 1 / 1 + 0.0133(NOTE) = 15.40 + Stock's current market price
10 + 62 * 1 / 1.0133 = 15.40 + Stock's current market price
10 + 62 * 0.9868 = 15.40 + Stock's current market price
10 + 61.18 (approx) = 15.40 + Stock's current market price
Stock's current market price = 71.18 - 15.40
Stock's current market price = 55.78 (approx)
(NOTE):- Discount rate = 4 * 4 / 12 = 1.33 % or 0.0133.
Conclusion:- Stock' Current market price = $ 55.78
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