Suppose you are an option trader and are now considering the options on the shar
ID: 2790730 • Letter: S
Question
Suppose you are an option trader and are now considering the options on the shares of HSBC.
The HSBC share price and its January futures price closed at $58.3 and $58.5 on 3 January 2017, respectively. The HSBC January call option price was $3 with a strike price $60 on 3 January 2017. The call and put options are of European style. The Hong Kong Interbank Offer Rate was 0.3% per annum with continuous compounding.
Required:
a Calculate the HSBC January put option price with a strike price $60 using the put-call parity. (7 marks)
b Determine the arbitrage profit if the market price of the put option is $5 by the end of January. Show your steps. (16 marks)
c Calculate the HSBC January put option price with a strike price $60 using the put-call-futures parity. (7 marks)
Explanation / Answer
1)
P + S = C + X*EXP(-r*T)
T = 28 days = 28/365
P = 3 + 60*EXP(-0.3%*28/365) - 58.3 = 4.69
2)
left side = P + S = 5 + 58.3 = 63.3
right side = C + X*EXP(-r*T) = 62.99
there is an arbitrage, hence long on right side and short on left side
long on right side = buy call option and invest in bond
short on left side =Write a put option and short the stock.
Profit = 63.3 - 62.99 = 0.31
3)
P + S = C + X*EXP(-r*T)
T = 28 days = 28/365
P = 3 + 60*EXP(-0.3%*28/365) - 58.5 = 4.49