Homework Answers
21. B. Have to first calculate the value of call and use put call parity for calculation of put option value
22. E. Theta measure the relationship between option price and time to expiration
23. D. Increase; Increase (standard deviation (volatility is positive correlation with both call and put option prices)
24. B. Increase; Decrease (Increase in interest rate has positive impact on call option while it is negatively correlated with put option price.
25. E. multiplied by delta (as Delta is calculated change in option price / change in stock price))
26. E. Decrease; Increase (Stock price is positively correlated with call option and negatively correlated with put option price. Hence decrease in stock price will decrease call option price and increase the put option price)
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To compute the value of a put using the Black-Scholes option pricing model, you: A) subtract...
3.5 In the Black-Scholes option pricing model, value of an option decreases, all else equal, as...
3.5 In the Black-Scholes option pricing model, value of an option decreases, all else equal, as it nears expiration. (True / False) 3.6 The Black-Scholes option pricing model assumes which of the following? a. Jumps in the underlying price b. Constant volatility of the underlying c. Possibility of negative underlying price d. Interest rate increasing as option nears expiration 3.7 Which Greek shows how sensitive option delta is to the price of the underlying asset? a. Vega b. Gamma c....
B. decreases by approximately 4.3%. C. decreases by approximately $1.72. Answer C The put option will...
B. decreases by approximately 4.3%. C. decreases by approximately $1.72. Answer C The put option will decrease in value as the underlying stock price increases: -0.43 x S4 S1.72. 100,000 Stocks Call Option sold has the following details. The stock price is $49, the strike price is $50, the risk-free rate is 5%, the stock price volatility is 20%, and the time to exercise is 20 weeks or 20/52 year. Table below shows Delta, Gamma, Vega, Theta and Rho for...
In the use of the Black-Scholes option valuation model to determine the value of a European...
In the use of the Black-Scholes option valuation model to determine the value of a European call option, which one of the following relationships is NOT correct? A. An increase in the risk-free rate increases the value of the European call option. B. An increase in the exercise price of the European call option increases the value of the option. C. An increase in the price of the underlying stock increases the value of the European call option. D. An...
d. $5.00 According to put-call parity for European options, purchasing a put option on ABC stock...
d. $5.00 According to put-call parity for European options, purchasing a put option on ABC stock would be equivalent to: a. Buying a call, buying ABC stock, and buying a zero-coupon bond. b. Buying a call, selling ABC stock, and buying a zero-coupon bond. Selling a call, selling ABC stock, and buying a zero-coupon bond. d. Buying a call, selling ABC stock, and selling a zero-coupon bond. C. te 1C Tha riek feee.
d. $5.00 According to put-call parity for...
Question 1 Consider the derivation of the Black-Scholes model of option pricing. Let S=S(t) be the...
Question 1 Consider the derivation of the Black-Scholes model of option pricing. Let S=S(t) be the underlying stock price at time t and let f=f(S, t) be the option price at time t. a) Write down the value P of the portfolio defined in the Black-Scholes model. [2 marks] b) Use Itô’s lemma to find an expression for the change Δf in the discrete time Δt. [5 marks] c) Use the expression you have found in point b) to find...
Problem 1: - Using the Black/Scholes formula and put/call parity, value a European put option on...
Problem 1: - Using the Black/Scholes formula and put/call parity, value a European put option on the equity in Amgen, which has the following characteristics. Expiration: Current stock price of Amgen: Strike Price: Volatility of Amgen Stock price: Risk-free rate (continuously compounded): Dividends: 3 months (i.e., 60 trade days) $53.00 $50.00 26% per year 2% None If the market price of the Amgen put is actually $2.00 per share, is the above estimate of volatility higher or lower than the...
5. Suppose that you sold an American put option P on the underlying stock ABC. You...
5. Suppose that you sold an American put option P on the underlying stock ABC. You calculated the delta and gamma of the put option and found Ap = -0.4 and Ip= 0.3. Suppose you want a position which is both delta and gamma neutral. Determine the hedge in the following two cases: (a) Use the underlying stock itself and a call option C on the stock (with different strike and maturity as the put), with Ac 0.25 and Io...
From the Black-Scholes-Merton model, N(d1) = 0.42 for a 3-month call option on Panorama Electronics common...
From the Black-Scholes-Merton model, N(d1) = 0.42 for a 3-month call option on Panorama Electronics common stock. If the stock price falls by $1.00, the price of the call option will: Decrease by less than the increase in the price of the put option. Increase by more than the decrease in the price of the put option. Decrease by the same amount as the increase in the price of the put option.
A call option on a stock has a delta of 0.40 and a gamma of 0.10....
A call option on a stock has a delta of 0.40 and a gamma of 0.10. A $0.10 rise in the price of the underlying stock will: (a) reduce the price of the call option by $0.04 (b) reduce the delta of the call option by 0.04 (c) raise the price of an equivalent put option by $0.06 (d) raise the delta of the call option by 0.01.
Use the Black-Scholes model to find the value for a European put option that has an...
Use the Black-Scholes model to find the value for a European put option that has an exercise price of $62.00 and four months to expiration. The underlying stock is selling for $64.00 currently and pays an annual dividend of $1.17. The standard deviation of the stock’s returns is 0.09 and risk-free interest rate is 2.5%. (Round intermediary calculations to 4 decimal places. Round your final answer to 2 decimal places.) Put value $
3.5 In the Black-Scholes option pricing model, value of an option decreases, all else equal, as it nears expiration. (True / False) 3.6 The Black-Scholes option pricing model assumes which of the following? a. Jumps in the underlying price b. Constant volatility of the underlying c. Possibility of negative underlying price d. Interest rate increasing as option nears expiration 3.7 Which Greek shows how sensitive option delta is to the price of the underlying asset? a. Vega b. Gamma c....
B. decreases by approximately 4.3%. C. decreases by approximately $1.72. Answer C The put option will decrease in value as the underlying stock price increases: -0.43 x S4 S1.72. 100,000 Stocks Call Option sold has the following details. The stock price is $49, the strike price is $50, the risk-free rate is 5%, the stock price volatility is 20%, and the time to exercise is 20 weeks or 20/52 year. Table below shows Delta, Gamma, Vega, Theta and Rho for...
d. $5.00 According to put-call parity for European options, purchasing a put option on ABC stock would be equivalent to: a. Buying a call, buying ABC stock, and buying a zero-coupon bond. b. Buying a call, selling ABC stock, and buying a zero-coupon bond. Selling a call, selling ABC stock, and buying a zero-coupon bond. d. Buying a call, selling ABC stock, and selling a zero-coupon bond. C. te 1C Tha riek feee.
d. $5.00 According to put-call parity for...
Problem 1: - Using the Black/Scholes formula and put/call parity, value a European put option on the equity in Amgen, which has the following characteristics. Expiration: Current stock price of Amgen: Strike Price: Volatility of Amgen Stock price: Risk-free rate (continuously compounded): Dividends: 3 months (i.e., 60 trade days) $53.00 $50.00 26% per year 2% None If the market price of the Amgen put is actually $2.00 per share, is the above estimate of volatility higher or lower than the...
5. Suppose that you sold an American put option P on the underlying stock ABC. You calculated the delta and gamma of the put option and found Ap = -0.4 and Ip= 0.3. Suppose you want a position which is both delta and gamma neutral. Determine the hedge in the following two cases: (a) Use the underlying stock itself and a call option C on the stock (with different strike and maturity as the put), with Ac 0.25 and Io...
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