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

a) According to put call parity:

C+X/(1+r)^n=S+P

C=4, S=50, X=50, r=0.10, P=?

X/(1+r)^n=50/1.10^0.25=48.82
4+48.82=50+P
P=$2.82

b) One could enter a short straddle when one thinks that there will be low volatility. Short straddle consists of selling a call and a put option for same strike price and expiration. The gain is achieved when the stock price dosents move much and options expire worthless and the trader recives profit in form of a options premium. The maximum money that can be made is from collecting the option premium. The stock can move to the tune of total option cost in both directions before you start losing money.
Breakeven :
Upside breakeven = strike + premiums received

Downside breakeven = strike - premiums received

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