(b) Consider two options on the same stock and same time to maturity but with different strike prices. For option A, the strike price (K1) is equal to 10 USD, while for option B, the strike price (K2) is equal to 9.5 USD. The current stock price (S) is equal to 10 USD. There are no dividends and the risk - free is 3% p.a. In calculating the arbitrage - free option prices an investor's volatility estimate is 15% p.a. Yet option A trades for 0.8 USD and option B for 1 USD. i. Compare the implied volatilities of both options A and B to the investor's estimate of 15% ii. ii. Identify the optimal strategy in the two options. Using the investor's volatility estimate, derive the delta - neutral position of your call option portfolio.

(b) Consider two options on the same stock and same time to maturity but with different strike prices. For option A, the strike price (K1) is equal to 10 USD, while for option B, the strike price (K2) is equal to 9.5 USD. The current stock price (S) is equal to 10 USD. There are no dividends and the risk - free is 3% p.a. In calculating the arbitrage - free option prices an investor's volatility estimate is 15% p.a. Yet option A trades for 0.8 USD and option B for 1 USD. i. Compare the implied volatilities of both options A and B to the investor's estimate of 15% ii. ii. Identify the optimal strategy in the two options. Using the investor's volatility estimate, derive the delta - neutral position of your call option portfolio.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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D3) Finance What is the probability that the put option is OTM at maturity if: the Stock is S = $195.00, no dividend is paid, the risk-free rate is r = 2.40%, the strike price is K = 209.00, the maturity is T = 23 months and the parameters are d1 = 0.2328 and d2 = -0.3175?
You are attempting to value a call option with an exercise price of $108 and one year to expiration. The underlying stock pays no dividends, its current price is $108, and you believe it has a 50% chance of increasing to $136 and a 50% chance of decreasing to $80. The risk-free rate of interest is 10%. Calculate the call option's value using the two-state stock price model. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places.
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You are attempting to value a call option with an exercise price of $108 and one year to expiration. The underlying stock pays no dividends, its current price is $108, and you believe it has a 50% chance of increasing to $136 and a 50% chance of decreasing to $80. The risk-free rate of interest is 10%. Calculate the call option's value using the two-state stock price model. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. > Answer is complete but not entirely correct. Value of the call option $ 12.73 x
Consider a bearish option strategy of buying one $50 strike put for $7, selling two $42 strike puts for $4 each, and buying one $37 put for $2. All options have the same maturity. Calculate the final profit per share of the strategy if the underlying is trading at $33 at expiration. 1. $1 per share 2. $2 per share 3. $3 per share 4. $4 per share
Suppose that a European call option to buy a share for $ 90.00 costs a . Under what circumstances will the SELLER of the option make a profit ? \$4.00 and is held until maturity . ( DRAW the GRAPH to show ALL answers ) b . when will the option be exercised ( at what price , show on graph ) ? c . What is the Maximum profit for SELLER and at what stock price ? d . What is the Maximum loss for SELLER and at what stock price ? e . What will be profit / loss for SELLER if St is 150 ?
Please show step by step work (not in excel): What is the call option premium given the following information? What would happen to the call price if the company initiated and paid a dividend before the expiration of the option? What would happen to the call premium if the expiration of the option expanded beyond the current 9 months? Stock price $36.00 Strike price $30.00 Volatility 16% Dividend Yield 0.00 Time 0.75 Riskfree Rate 2.70%
Suppose there is also a 1-year European put option on the same stock as in Question 3 with exercise price $30. The current stock price is also $25 and the stock price, in 1 year, will be either $35 (up by 40%) or $20 (down by 20%). The interest rate is 8%. This stock does not pay dividend. What is the value of the put option? Please use risk neutral probability method and assume discrete discounting. (2) What is put-call parity in option pricing? What needs to be true in order for put-call parity to hold?
You are attempting to value a put option with an exercise price of $108 and one year to expiration. The underlying stock pays no dividends, its current price is $108, and you believe it has a 50% chance of increasing to $130 and a 50% chance of decreasing to $86. The risk-free rate of interest is 10%. Calculate the value of a put option with exercise price $108. Note: Do not round intermediate calculations. Round your answer to 2 decimal places. X Answer is complete but not entirely correct. Value of a put option $ 107.50
2. Calculate the put premium according to put-call parity which gives no arbitrage opportunity. Explain what transaction would you do if the put premium is below/above the put premium you calculated. European call option premium: c = $2 Stock price today: So- $30 Life of option: T=0.5 Risk-free rate for maturity T with continous compounding: r= 8% Strike price: K= Decide on the K value yourself (carefully). No dividends paid during life of option.
The profit (loss) experienced on option B is $ ? (Round to the nearest dollar. Enter a negative number for loss.) The profit (loss) experienced on option C is $ ? (Round to the nearest dollar. Enter a negative number for loss.) The profit (loss) experienced on option D is $ ? (Round to the nearest dollar. Enter a negative number for loss.) The profit (loss) experienced on option E is $ ? (Round to the nearest dollar. Enter a negative number for loss.) How do I find the calculations for these questions?
H2. Using the Black-Scholes model (BSOPM), compute the standard deviation that is implied by the following call option data as: the time to the option's maturity is 0.25 years, the price of the underlying option asset is RM30, the continuously compounded risk-free interest rate is 0.12. the exercise or striking price is RM30, and the cost or premium of the call is RM1.90.

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