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4 of 18 3 if the stock price at time t is s k but

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Unformatted text preview: th an increase in D (true for both American and European style options). Table 3. INTEL STOCK OPTIONS (finance.yahoo.com) Expiration Strike 20/11/07: St = $25.52 22/11/07: St = $24.65 T K C P C P $20 $5.25 $0.14 $5.00 $0.16 JAN ‘08 $25 $1.71 $1.11 $1.29 $1.46 $30 $0.18 $4.80 $0.15 $5.15 $20 $6.20 $0.49 $5.50 $0.51 APR ‘08 $25 $2.59 $1.93 $2.17 $2.20 $30 $0.74 $5.13 $0.60 $5.20 $20 $6.30 $0.85 $6.10 $0.96 JUL ‘08 $25 $3.20 $2.25 $3.08 $2.63 $30 $1.29 n/a $1.18 n/a e) Table 3 confirms assertions with regard to stock price St, strike price K, and maturity T. 1) Intel stock price fell from $25.62 to $24.65 over the two days shown in Table 3. At given K and T, C fell and P rose when St fell. For JAN 08 and K = $20: • C fell from $5.25 to $5.00 • P rose from $0.14 to $0.16 2) At given St and T, C is lower and P higher as K rises. For APR 08 and St = $25.52: • For K = $20, C = $6.20 and P = $0.49 • For K = $25, C = $2.59 and P = $1.93 3) At given St and K, both C and P increase with T. For St = $24.65 and K = $25: • For T = APR 08, C = $2.17 and P = $2.20 • For T = JUL 08 , C = $3.08 and P = $2.63 4. Early Exercise (at τ < T) of American Options: {Hull §10.5 - 10.7; BKM §21.2} a) In general, American options give an investor more latitude than European options, and should therefore be worth more and trade at higher premiums. 1) By this line of reasoning, we would expect that C ≥ c and P ≥ p. 2) For put options, the latitude to exercise early is valuable, and P ≥ p is surely valid. 3) An exception might be American calls on no- dividend stock. For these, freedom to exercise early is virtually worthless, so we might expect that C = c. b) American- style call options (no- dividend stocks). 1) It is never optimal to exercise this option early, so C = c. Consider an American call with strike price K, premium C, and expiration T. 2) If the call option holder exercises early, he will buy stock for K. If he intends to keep the stock at least thru time T, then he should wait until T to exercise. • If he exercises early (at time τ < T) and buys the stock at K, then holds it unti...
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