INVESTMENTS (LOOSELEAF) W/CONNECT
11th Edition
ISBN: 9781260465945
Author: Bodie
Publisher: MCG
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Chapter 21, Problem 18PS
Summary Introduction
Case summary:
Mr. M is considering preparing delta-hedge strategy for safeguarding the portfolio against uncertainties of market volatility. Mr. M. is taking long on put options which has delta of -0.65.
Character in this case: Mr. M
Adequate information:
Delta of put option is -0.65
Stock price falls by 6
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A. An option is trading at $5.03. If it has a delta of -.56, what would the price of the option be if the underlying increases by $.75? What would the price of the option be if the underlying decreases by $.55?
B. What type of option is this and how?
C. With a delta of -.56, is this option ITM, ATM or OTM and how?
With all other variables being equal (the same excerise price, underlying asset, implied volatility, interest rate, etc.), an at-the-money option with 30 days to expiration will tpyically have a gamma that is higher than an at-the-moeny option with 180 days to expiration (hint: think of the different shapes of the associated probability distribution and the change in delta)
True or False?
1. An option is trading at $5.26, has a delta of .52, and a gamma of .11. what would the delta of the option be if the underlying increases by $.75? What would the delta of the option be if the underlying decreases by $1.05? Explain.
Chapter 21 Solutions
INVESTMENTS (LOOSELEAF) W/CONNECT
Ch. 21 - Prob. 1PSCh. 21 - Prob. 2PSCh. 21 - Prob. 3PSCh. 21 - Prob. 4PSCh. 21 - Prob. 5PSCh. 21 - Prob. 6PSCh. 21 - Prob. 7PSCh. 21 - Prob. 8PSCh. 21 - Prob. 9PSCh. 21 - Prob. 10PS
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Similar questions
- Consider a call option whose maturity date is T and strike price is K. At any time t < T, is it always the case that the call option's price must be greater than or equal to max(St – K,0), where St is the stock price at t? (Your answer cannot be more than 30 words. Answers with more than 30 words will not be graded.)arrow_forwardAn option is trading at $3.45. If it has a delta of .78, what would the price of the option be if the underlying increases by $.75? A. What would the price of the option be if the underlying decreases by $.55? B. What makes this a call option? C. With a delta of .78, is this option ITM, ATM or OTM and how?arrow_forwardWhat does it mean to assert that the delta of a call option is 0.7? How can a short position in 1,000 options be made delta neutral when the delta of each option is 0.7?arrow_forward
- A put option has a strike price of MYR3.00/SGD. If the option is exercised before maturity, what price in the followings would maximize gain? a. MYR3.00/SGD. b. MYR2.90/SGD. c. MYR3.05/SGD. d. MYR2.95/SGD.arrow_forwarda) The cost of a portfolio consisting of a long position in a call option with strike price 50 and a short position in a call option with strike price 80 is zero (both call options are on the same stock and have the same maturity date). True or false? Explain. b) Carefully draw the payoff diagram of a portfolio consisting of a long position in two call options with exercise price ?, a short position in five call options with exercise price 2? and a long position in four call options with exercise price 3?. All options have the same maturity date and the same underlying stock. What reasons could a speculator have for holding such a portfolio (explain in detail)?arrow_forwardIn a binomial model, a call option and a put option are both written on the same stock. The exercise price of the call option is 30 and the exercise price of the put option is 40. The call option’s payoffs are 0 and 5 and the put option’s payoffs are 20 and 5. The price of the call is 2.25 and the price of the put is 12.25. a. What is the riskless interest rate? Assume that the basic period is one year. b. What is the price of the stock today?arrow_forward
- A European call option has a strike price of K and maturity of T. If the stock price at the maturity is ST, what is the payoff from a short position in this call option (without considering the option price)? Group of answer choices: Max(K - ST, 0) -Max(ST - K, 0) -Max(K - ST, 0) Max(ST - K, 0)arrow_forwardConsider the model of Black and Scholes. Consider the cash=or-nothing put option V (T) = 1{S(T)<= K} It pays out one unit of cash if the spot is below the strike at maturity. Evaluate the price of the option.arrow_forwardConsider a call and a put options with the same strike price and time to expiry. Given that the strike price is exactly equals to the forward price, then: A. Put and call have same premium B. The premium of the put is equal to the forward price C. The premium of the put is equal to the premium of the call plus the present value of the strike D. The premium of the call is equal to the forward pricearrow_forward
- An up-and-out barrier call option with barrier B, strike price K and exercise time T has payoff H(T) = (S(T) − K) + if max {S(t)| 0 ≤ t ≤ T} < B, 0 otherwise, that is, the payoff is that of a call option if the underlying stock price does not reach or exceed the barrier B at any time up to and including time T, and 0 otherwise. For an up-and-out barrier call option with barrier B = 140, strike price K = 90 and exercise time T = 3 in the binomial model with parameters U = 0.2, D = −0.1, R = 0.1 and S(0) = 100 compute the following. (a) The option price at time 0;arrow_forwardI was asked to repost the question. It is as follows: Assume a security follows a geometric Brownian motion with volatility parameter sigma=0.2. Assume the initial price of the security is $25 and the interest rate is 0. It is known that the price of a down-and-in barrier option and a down-and-out barrier option with strike price $22 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price. In regards to the above question, I had this follow up question: I am working with the following equation: The risk neutral present value of a "down-and-in" option PLUS the present value of a "down-and-out" option is EQUAL to the risk neutral price of a traditional call option (using Black-Scholes formula). I have calculated the call option to be $3.00 using the Black-Scholes formula. If I am being asked to find the "common risk neutral price", given that the price of a down-and-in barrier option and a down-and-out barrier option are equal, would my answer…arrow_forwardThe cost of a portfolio consisting of a long position in a call option with strike price 50 and a short position in a call option with strike price 80 is zero (both call options are on the same stock and have the same maturity date). True or false? Explain.arrow_forward
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