7/ Shares of ANA Corp. are trading at $50. The stock does not pay dividends. The

Question

7/ Shares of ANA Corp. are trading at $50. The stock does not pay dividends. The price

of a three-month put with an exercise price of $50 is currently $4 (per share).
a. If the risk-free rate of interest is 10%, calculate the price of an “at the money” call
(with a strike price also of $50)?
b. If you believe that ANA Corp. shares will continue to trade close to $50 for the next
three months, what would be a simple options strategy using a put and a call to profit
from your conviction? What is the most money you could make from it? How far
can the stock move in either direction before you lose money?

Explanation / Answer

1

Put call parity states that S+P=C+Xe^(-rt)

=>C=S+P-Xe^(-rt)=50+4-50*e^(-10%*3/12)=$5.234

2

Short straddle: Sell put and call of the same strike-50 and expiry. Maximum gain is 5.234+4=9.234

S<50 Profit=-Max(S-50,0)-Max(50-S,0)+5.234+4=S-50+9.234

S>50 Profit=-Max(S-50,0)-Max(50-S,0)+5.234+4=50-S+9.234

So, if stock is below 50-9.234=40.766 or above 50+9.234=59.234 you would start losing money

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