Question

2 Put-call parity [LO 3] You observe the following prices in a situation in which European pul-call parily ought to apply: Put price $1.95 Call price $1.10 Share price $20.00 Exercise price $22.00 Term to expiry 4 months Risk-free interest rate 1% per month (compound) BUSINESS FINANCE a) Show that pul-coll parity is breached in this case. b) Calculate the payoffs to show that the following strategy is an arbitrage: sell the call, buy the put, buy the shore and borrow the present value of the exercise price for 4 months. Do 31

Answer 1

Assumption: Risk free rate ic compounded MONTHLY

As per put-call parity,

C + PV of Exercise price of call = CMP + P

where, C = Premium on Call, CMP = Current Market Price of Stock & P = Premium on Put

Therefore,

1.1 + [22 × (1/1.01⁴)] = 20 + P

1.1 + [22×0.961] = 20 + P

1.1 + 21.14 - 20 = P

P = 2.24

Therefore, Theoretical Price of Put i.e. 2.24 > Actual Price i.e.1.95

Therefore, Put Option is UNDERVALUED.

Steps for Arbitrage:

Now,

(1) Sell Call Option at 1.1

(2) Borrow 20.85 for 4 months at 1% per month (Put Price 1.95 + Stock Price 20 - Call Price 1.1)

(3) Buy Stock @ 20

(4) Buy Put option @ 1.95

After 4 months,

(i) If Stock Price is > 22,

(5) Exercise Call, Lapse Put

(6) Sell Stock to Call Holder for 22

(7) Repay Borrowal 20.85×1.01⁴ = 21.7

(8) Arbitrage Gain = 22-21.7 = 0.3

(ii) If stock price < 22,

(5) Exercise Put, Lapse Call

(7) Sell stock to Put Writer @ 22

(8) Repay borrowal 20.85×1.01⁴=21.7

(9) Arbitrage Gain = 22-21.7 = 0.3

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