Question

Option pricing (LO 3] You observe the following prices in a situation in which call options should sell for at least their minimum theoretical price of Max [0, current share price - present value of the exercise price): Call price $0.33 Share price $17.50 Exercise price $18.00 Term to expiry 6 months Risk-free interest rate 10% p.a. (simple, i.e.5% for a 6-month period) What should the minimum call price be? Calculate the payoffs to show that the following strategy is an arbitrage: buy the call, short sell the share and lend $17.17 at the risk-free interest rate for 6 months.

Answer 1

B D E F G H I J K L Put call parity Hm+ Call price = Spot price - present value of exercise price 5 a) Minimum call price 0.36 9 b) 11 12 13 Buy call Short share Lend 17.17 Cash flow Cash flow 0.33 -17.50 17.17 0.00 Arbitrage profit 15 16 19 18 At maturity Spot price Payoff call Cover short share Receive borrowing Cash flow 17 o -17 18.03 1.03 18 o -18 18.03 0.03 20 1 2 -20 18.03 0.03 -19 18.03 0.03 21 3 -21 18.03 0.03 22 4 -22 18.03 0.03 23 5 -23 18.03 0.03 19 20 22.

E F G H I J Put call parity Hnm + Call price = Spot price - present value of exercise price =17.5 - 18/(1+5%) 5 a) Minimum call price 6 7 D b) 9 10 11 12 Buy call Short share Lend 17.17 Cash flow Cash flow 0.33 -17.5 17.17 =SUM(C10:C12) 13 Arbitrage profit 14 15 16 17 18 At maturity Spot price Payoff call Cover short share Receive borrowing Cash flow 17 =C16+1 =D16+1 =E16+1 =F16+1 =G16+1 =H16+1 =MAX(C16-18,0) =MAX(D16-18,0) =MAX(E16-18,0) =MAX(F16-18,0) =MAX(G16-18,0) =MAX(H16-18,0) =MAX(116-18,0) --C16 --D16 --E16 --F16 --G16 --H16 =-116 =17.17*(1+5%) =17.17*(1+5%) =17.17*(1+5%) =17.17*(1+5%) =17.17*(1+5%) =17.17*(1+5%) =17.17*(1+5%) =SUM(C17:019) SUM(D17:019) =SUM(E17:E19) =SUM(F17:F19) =SUM(G17:619) =SUM(H17:H19) =SUM(117:119) 19 20 21 22