5. What is a lower bound for the price of a one-month European put option on a n

Question

5. What is a lower bound for the price of a one-month European put option on a non-dividend-paying stock when the stock price is $12, the strike price is $15, and the risk-free interest rate is 6% per annum? ____________

6. A four-month European call option on a dividend paying stock is currently selling for $7.25, the stock price is $74, the strike price is $72, and a dividend of $1.80 is expected in one month. The risk-free interest rate is 11.50% per annum for all maturities. What should be the price of a put with the same strike price and time to expiration? ____________

7. The price of a European call that expires in six months and has a strike price of $30 is $2.25. The underlying stock price is $31, and a dividend of $0.90 is expected in two months and again in five months. The term structure is flat, with all risk-free interest rates being 7%. What is the price of a European put option that expires in six months and has a strike price of 30?

Explanation / Answer

1.
Lower bound=Strike price*e^(-r*t)-Spot price=15*e^(-6%*1/12)-12=2.925
2.
Put call parity states that:
S+P=C+Xe^(-rt)+Present Value of Dividends
=>P=C+Xe^(-rt)-S+Present Value of Dividends
Hence, price of Put Option=7.25+72*e^(-11.5%*4/12)-74+1.8*e^(-11.5%*1/12)=$4.325
3.
Put call parity states that:
S+P=C+Xe^(-rt)+Present Value of Dividends
=>P=C+Xe^(-rt)-S+Present Value of Dividends
Hence, price of Put Option=2.25+30*e^(-7%*6/12)-31+0.9*e^(-7%*2/12)=$1.11

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