Question

A four-month European call option on a dividend-paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.80 is expected in one month. The risk-free interest rate is 12% per annum for all maturities. What opportunities are there for an arbitrageur

Answer 1

The PV gain is 0.56 for an arbitrageur.

Explanation:

PV of the strike price is 60e-(12 $\times$ 4/12) = $57.65

PV of dividend is 0.80e-(12 $\times$ 1/12) = $0.79

where 5 < 64 - 57.65 - 0.79

• The arbitrageur should buy the option and short stock, this above condition is missing in 10.8 condition.

• The arbitrageur ought to contribute $ 0.79 of this at 12% for one month to deliver a profit of $0.80 in one month and the remaining $ 58.21 is put resources into four months in 12%, without considering the benefit that figures it out.  

• If the stock price declines below $ 60 of every four months, the arbitrageur loses $ 5 spent on the choice however gains on an extremely short position, the arbitrageur shorts when the stock price is in $ 64 and deliver profit with PV of $ 0.79 and closes the short position when the stock price is $ 60 or less because $ 57.65 is the PV of $ 60 the short position generates at least 64-57.65-0.79 = 5.56

The PV gain at least 5.56-5.00  

0.56

• If the stock price is above $60 at option when exercised and arbitrageur buys stock for $60 for four months and closes the short option. The PV of 60 is $57.65 and the dividend is 0.79 and gain in a short position and exercise the short option it results in 64-57.65-0.79= 5.56 and gains on PV is 5.56-5.0 = 0.56