Question

DES shares are currently trading at $38 per share. The stock pays no dividends. A one-year European put option on DES with an exercise price of $40 is currently trading at $3.10.

1. If the risk-free interest rate is 5% per year, what is the price of a one-year European option to buy DES with an exercise price of $40?

2. Is there an arbitration opportunity:
a. If the option to purchase on DES is trading at $2.50? If so, what do you need to do to exploit this arbitration opportunity?

b. If the option to purchase DES is trading at $3? If so, what do you need to do to exploit this arbitration opportunity?

c. If the option to purchase des DES is trading at $3.50? If so, what do you need to do to exploit this arbitration opportunity?

Answer 1

1. One - year european option price of DES = current price of DES option *(1+ risk free rate/100)^time period

= 3.10(1+5/100)1

= $3.255

2. a. Yes arbitration opportunity is there.

if option price is $2.50 we can take short position on this option & buy equal number of DES share in current market, in this way we can get benifit from market movemnt.

b. if option price is $ 3.0 then we can sell & buy equal number of put to cover both side of volatility.

c. if option is $3.50 then we will take long position on put option & sell in current market. in this way we can make money in both the market.