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Information about stock price, its up or down movements, risk-free rate and strike price is given below.

What is the value of a six-month American put option?

In general, when are American options exercised early and why?

Should the put-call parity hold for American options? Explain

Estimate at what minimum risk-free interest rate it would be optimal to exercise the American put option immediately.

H I J K L . D D E F G 1 2 Information about stock price, its up or down movements, risk-free rate and strike price is given below. a) What is the value of a six-month American put option? 3 b) In general, when are American options exercised early and why? 4 c) Should the put-call parity hold for American options? Explain 5 d) (BONUS question) Estimate at what minimum risk-free interest rate it would be optimal to exercise 6 the American put option immediately. 7 8 9 10 11 K K $21.00 12 s $20.00 13 S $22.00 14 Sa $18.00 15 2.00% 16 Trading period 3 months 17 Maturity 6 months 18 19 20 a) What is the value of a six-month American put option? 21 22 23 Current Price $20.00 24 Strike Price $21.00 25 Risk free 2.00% 26 Trading period 3/12 years 27 u 1.10 28 d d 0.90 29 30 Risk-neutral probability 31 32 Time 0 0 3/12 33 $24.20 34 34 25 35 20 36 27 37 37 $22.00 30 38 39 39 40 40 40 41 40 42 Underlying $20.00 $19.80 20 23 43 Intrinsic AX 44 Quasi-European 45 American AC 46 19 47 $18.00 40 40 48 40 49 50 50 51 52 53 $16.20 54 55 56 American Option Price 57 58 6/12 H I J K L . D D E F G 1 2 Information about stock price, its up or down movements, risk-free rate and strike price is given below. a) What is the value of a six-month American put option? 3 b) In general, when are American options exercised early and why? 4 c) Should the put-call parity hold for American options? Explain 5 d) (BONUS question) Estimate at what minimum risk-free interest rate it would be optimal to exercise 6 the American put option immediately. 7 8 9 10 11 K K $21.00 12 s $20.00 13 S $22.00 14 Sa $18.00 15 2.00% 16 Trading period 3 months 17 Maturity 6 months 18 19 20 a) What is the value of a six-month American put option? 21 22 23 Current Price $20.00 24 Strike Price $21.00 25 Risk free 2.00% 26 Trading period 3/12 years 27 u 1.10 28 d d 0.90 29 30 Risk-neutral probability 31 32 Time 0 0 3/12 33 $24.20 34 34 25 35 20 36 27 37 37 $22.00 30 38 39 39 40 40 40 41 40 42 Underlying $20.00 $19.80 20 23 43 Intrinsic AX 44 Quasi-European 45 American AC 46 19 47 $18.00 40 40 48 40 49 50 50 51 52 53 $16.20 54 55 56 American Option Price 57 58 6/12