Calculate the Black&Scholes&Merton call and put premiums S = 29.50, K = 32.5, T - t...

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Calculate the Black&Scholes&Merton call and put premiums S = 29.50, K = 32.5, T - t = 53 days, the annual risk-free rate with continuous compounding r = 4.736% and VOL is a = 50%. In calculating N(d1) and N(d2), use the interpolation explained above the Normal tables and in my slides. Q2. Consider Europen call and a put on a non dividend paying stock; both for K = $45 and T = 1yr. The stock price is $45/share. The Call premium is equal to the put premium c = p = $7/share/share. The annual risk-free rate is 10%. Use the put-call parity and show that there exists an arbitrage opportunity. Q3. Show the complete table of cash flows and P/L at the options expiration date, T, of a strategy which is based on your result in Q2. and is an arbitrage profit strategy. Q4. Consider three strike prices: K< K₂ <K, such that K₂ = (.5) (K The cost of opening a long calls Butterfly is: c₁ -2c₂ + + K, ). C₁. The cost of opening a long puts Butterfly with the corresponding puts is given by: P₁ -2p ₂ + P3. (the calls and the puts are all on the same non dividend paying stock, the same strike prices and the same expiration date T.) Prove that these costs are the same. For the proof you must use the put-call parity for European options on a non dividend paying stock t), C₁ - P,= S, - Ke-T- Calculate the Black&Scholes&Merton call and put premiums S = 29.50, K = 32.5, T - t = 53 days, the annual risk-free rate with continuous compounding r = 4.736% and VOL is a = 50%. In calculating N(d1) and N(d2), use the interpolation explained above the Normal tables and in my slides. Q2. Consider Europen call and a put on a non dividend paying stock; both for K = $45 and T = 1yr. The stock price is $45/share. The Call premium is equal to the put premium c = p = $7/share/share. The annual risk-free rate is 10%. Use the put-call parity and show that there exists an arbitrage opportunity. Q3. Show the complete table of cash flows and P/L at the options expiration date, T, of a strategy which is based on your result in Q2. and is an arbitrage profit strategy. Q4. Consider three strike prices: K< K₂ <K, such that K₂ = (.5) (K The cost of opening a long calls Butterfly is: c₁ -2c₂ + + K, ). C₁. The cost of opening a long puts Butterfly with the corresponding puts is given by: P₁ -2p ₂ + P3. (the calls and the puts are all on the same non dividend paying stock, the same strike prices and the same expiration date T.) Prove that these costs are the same. For the proof you must use the put-call parity for European options on a non dividend paying stock t), C₁ - P,= S, - Ke-T-

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Q1 Calculation of BlackScholesMerton Call and Put Premiums Given Stock price S 2950 Strike price K 3250 Time to expiration Tt 53 days or 53365 years A... View the full answer