Question

Portfolio of options on shares of a non-dividend paying stock. The portfolio consists of:

1. Long call with a strike price of 50
2. Short call with a strike price of 55
3. Long put with a strike price of 55
4. Short put with a strike price of 50

All options expire in 2 months.The current price of one share of stock is 48.00. The risk-free interest rate is 3%.

1. Determine the cost of the portfolio?

2. Determine the maximum and minimum profit obtained at the end of 2 months?

Please show work

Answer 1

Part (1)

Recall the call put parity equation:

C(K) - P(K) = S0 - Ke-rt

the cost of the portfolio

= C(K1) - C(K2) + P(K2) - P(K1)

= [C(K1) - P(K1)] - [C(K2) - P(K2)]

= [S0 - K1e-rt] - [S0 - K2e-rt]

= (K2 - K1)e-rt

= (55 - 50)e-3% x 2/12

= 4.98

Part (2)

Long Call and short put position is similr to a forward contract with payoff = S - K at the time of expiration. Hence, the payoff at expiration = K2 - K1

Profit = Payoff - Cost of the portfolio x ert = (K2 - K1) - (K2 - K1)e-rt x ert = 0

Hence, after taking into account the time value of money, there will no profit at the end of 2 months.