Question

6. Answer the following questions based on the following quotation. On October 1, 2007, S&P 500 closed at 1547 where the quotation of CALL options on S&P 500 was as follows. Those contracts expire in October 2007.

Strike Price	Open	High	Low	Last	Sett
1540	--	--	--	--	31.70
1600	1.70	3.60	1.70	3.00	3.35

(a) Which option is in the money?

(b) Decompose the value of 1540 call, $31.7, into intrinsic value and time value.

(c) Again using the call with exercise price of 1540, what would be your cash proceeds if you exercise the option on October 1 (index options are settled by cash)? Assume that both dividends and transaction costs are small enough to be ignored. Based on this answer and answer on (b), does it make sense to exercise an American call before expiration? Explain.

(d) Assume that put-call parity holds for these options (it does not exactly hold since the above options are all American). What should be the value of a PUT on S&P 500 with exercise price of 1600? Assume that the annual risk-free rate is 5%.

Answer 1

a) Option with Strike price 1540 is in the money because closing price is higher (1547) is higher than strike price.

b) Intrinsic Value = Stock Price - Strike Price

So Intrinsic Value = 1547 - 1540 = 7

Time value = Value of option - intrisic value

So Time value = 31.7 - 7 = 24.7

c) Call option with strike price 1540 is in money by $7, So if buyer of call exercise the option, he will get $7 as his cash proceeds. But there is catch. Buyer has paid $31.7 to buy that option. So technically, buyer is still short of $24.7 when he start making profit. If he exercise the option now, he will loose 24.7 effectively. So he should not exercise this option at this point of time

d) According to Put - Call parity :

C +X/(1+r)^n = P + S

Where C = Call Price, P = Put Price, S = Stock Price, X = Strike Price

r = interest rate for the period

Now this option is expiring in a month,so we need to convert the rate in monthly rate (i.e divide by 12)

So

3.35 + 1600 / (1+0.05/12) = P + 1547

Calculate for P, P = 49.97