Final answer:
Put-call parity does not hold for the given options and stock prices, indicating an arbitrage opportunity. The arbitrage strategy involves selling the call, buying the put, buying the stock, and borrowing funds, which results in an approximate $5 profit in 3 months.
Step-by-step explanation:
When assessing whether put-call parity holds for a European option, the following condition must be met:
C + PV(X) = P + S
where:
- C is the call option price
- PV(X) is the present value of the strike price (X)
- P is the put option price
- S is the stock price
Given the call option price (C) is $5, the put option price (P) is $2, the strike price (X) is $28, the stock price (S) is $30, and the risk-free rate is 10%, the put-call parity can be checked as follows:
PV(X) = $28 / (1 + 0.10)^(3/12)
PV(X) = $27.30 approximately
Now checking the condition:
$5 + $27.30 = $2 + $30
$32.30 = $32
Since the LHS does not equal the RHS, put-call parity does not hold, which indicates an arbitrage opportunity.
To exploit this opportunity, the arbitrage strategy would include selling the call, buying the put, buying the stock and borrowing the present value of the strike price to finance these transactions. The net cash flow today would be:
$5 + $30 - $2 - $27.30 = $5.70
In 3 months, if the stock is above $28, the put option expires worthless, and the short call option is exercised. You sell the stock for $28, repay the borrowed amount (PV of strike price), and the profit is any money left over.
If the stock is below $28, you exercise the put, selling the stock for $28, and the same repayment happens. Either way, you realize an arbitrage profit of approximately:
$5.70 - ($28 - $27.30) = $5