Question

Delta Inc. stock currently trades for $30, but you believe the share price will increase over the next six months. Six-month European call options on the stock have an exercise price of $35 and a premium of $.90.  The annual risk free rate is 3%.  You want to create a portfolio that mimics the payoff of writing a 6-month European put on the stock with an exercise price of $35. Which of the following steps must you do in order to achieve this payoff?

A. Buy 100 shares of the stock and pay 3000.

B. Buy a call option and pay $90 for the option premium.

C. Invest the present value of the exercise price ($3447.89) at the risk-free rate of return.

D. None of the above.

What should be the price of 6-month European put option on the stock with an exercise price of $35?

A. 5.83

B. 3.58

C. 5.38

D. 6.43

Suppose that 6-month European put options with an exercise price of $35 are selling for $6. Which of the following statements is true?

A. An arbitrage profit of approximately $17 per put can be made by selling puts in the market and creating a long position in synthetic put options.

B. An arbitrage profit of approximately $62 per put can be made by selling puts in the market and creating a long position in synthetic put options

C. An arbitrage profit of approximately $242 per put can be made by selling puts in the market and creating a long position in synthetic put options

D. An arbitrage profit of approximately $43 per put can be made by buying puts in the market and creating a short position in synthetic put options

E. None of the above

Answer 1

Payoff similar to that of a short put option can be achieved by taking long position in stock and Shorting call option. All the three options mentioned do not give the payoff of writing a put option. Correct answer is D

From Put-call parity

Price of Put option = Call option premium + present value of strike price - spot price of stock

=0.90+35/(1+0.03*6/12)-30

=$5.38 (option C)

If the Put option is priced at $6 , then arbitrage is possible by (per share)

i) Selling the stock and put option for $30 and $6 respectively and buying the call option for $0.9 and taking the remaining amount of $35.1. Out of the same , investing $34.48 at risk free rate. Maturity amount is 34.48*(1+0.03*6/12) = $35 and keeping the $0.62 with oneself as arbitrage profit.

(Buying the call and selling the stock creates synthetic put option)

ii) After 6 months, if stock price > $35 , put option is worthless, so one can buy the stock using call option at $35 and make an arbitrage profit of $0.62

if stock price < $35 , Call option is worthless, so one can buy the stock using sold put option at $35 and make an arbitrage profit of $0.62

For options with lot size of 100 shares , arbitrage profit of $0.62*100 or $62 apx can be made today

(Option B is correct)