Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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Chapter 16, Problem 2PS
A put option on a stock with a current price of
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You are considering purchasing a put on a stock with a current price of $33. The exercise price is $35, and the price of the corresponding call option is $3.25. According to the put-call parity theorem, if the risk-free rate of interest is 4% and there are 90 days until expiration, the value of the put should be:
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A call option has a strike price of $11, and a time to expiration of 0.8 in years. If the stock is trading for $20, N(d1) = 0.5, N(d2) = 0.12, and the risk free rate is 5.40%, what is the value of the call option?
Suppose that a call option with a strike price of $48 expires in one year and has a current market price of $5.17. The market price of the
underlying stock is $46.25, and the risk-free rate is 1%. Use put-call parity to calculate the price of a put option on the same underlying stock
with a strike of $48 and an expiration of one year.
The price of a put option on the same underlying stock with a strike of $48 and an expiration of one year is $. (Round to the nearest cent.)
Chapter 16 Solutions
Essentials Of Investments
Ch. 16 - Prob. 1PSCh. 16 - A put option on a stock with a current price of 33...Ch. 16 - Prob. 3PSCh. 16 - Prob. 4PSCh. 16 - In each of the following questions, you are asked...Ch. 16 - Reconsider the determination of the hedge ratio in...Ch. 16 - Show that Black-Scholes call option hedge ratios...Ch. 16 - We will derive a two-State put option value in...Ch. 16 - a. Calculate the value of a call option on the...Ch. 16 - Prob. 10PS
Ch. 16 - Prob. 11PSCh. 16 - Prob. 12PSCh. 16 - Prob. 13PSCh. 16 - Prob. 14PSCh. 16 - Prob. 15PSCh. 16 - Prob. 16PSCh. 16 - 17. Find the Black-Scholes value of a put option...Ch. 16 - Prob. 18PSCh. 16 - What would be the Excel formula in Spreadsheet...Ch. 16 - Prob. 20PSCh. 16 - Prob. 21PSCh. 16 - Prob. 22PSCh. 16 - Prob. 23PSCh. 16 - Prob. 24PSCh. 16 - Prob. 25PSCh. 16 - Prob. 26PSCh. 16 - Prob. 27PSCh. 16 - Prob. 28PSCh. 16 - Prob. 29PSCh. 16 - Prob. 30PSCh. 16 - Prob. 31PSCh. 16 - Prob. 32PSCh. 16 - Prob. 33PSCh. 16 - Prob. 34PSCh. 16 - Prob. 35PSCh. 16 - Prob. 36PSCh. 16 - Prob. 38CCh. 16 - Prob. 39CCh. 16 - Prob. 40CCh. 16 - Prob. 41CCh. 16 - Prob. 42CCh. 16 - Prob. 43CCh. 16 - Prob. 44CCh. 16 - Prob. 2CP
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- An option has strike price of $9 and 12 months to expiry. The current price of the underlying share is $35 and its volatility (sigma) is 23%. The riskfree rate of interest is 4% per annum. Calculate d2 for this option. [your answer should have at least 2 decimal places]arrow_forwardSuppose a put option is traded at $3. The underlying stock of the option is traded at $105 per share at the same time. The option expires in 3 months and has a strike price of $104. What is the intrinsic value of the option? Is the option in the money, at the money, or out of the money?arrow_forward15. Find the implied volatility (to 2 decimals, for example, σ = 8.23%) of a Put option with a time to expiration of 11 months and a price of $6.13 2 The stock is currently trading at $47. The riskless rate is 2% per annum, and the strike/exercise price of the option is $50. 3 Hint: compute the Put price using the same formula as in exercise 4, as a function of the volatility σ. Then use Solver to change the volatility cell in order to obtain a price of $6.13 4 5 6 d1 = -0.0614997 7 d2 = 8 9 10 N(d1)= 11 N(d2)= 12 13 N(-d1)= 14 N(-d2)= 15 16 17 18 P = 27.41 19 So= 47 K= 50 r = 2% σ = 2.74% T= 0.91666667arrow_forward
- 14. Suppose a call option sells for $2.50, a put option sells for $2.00, both options have a $25.00 striking price, the current stock price is $25.50, and the options both expire in forty-six days. Using the put-call parity model, calculate the rate of interest implied in these numbers. 7arrow_forwardUsing the binomial call option model to find the current value of a call option with a $25 exercise price on a stock currently priced at $26. Assume the option expires at the end of two periods, the riskless interest rate is ½ percent per period. What are the hedge ratios?arrow_forwardConsider a put option written on an underlying security that has a current value of $100 and has a volatility of 25% (i.e. .25). The put has a strike price of $100 and expires in 1 year. The risk-free rate is 3% (.03). If the time to expiration is changed from 1 to 2 to 3 years, what happens to the value of vega (the change in the put value given a percentage point change in the volatility – say from 25% to 26%)? (Note: vega is defined in note N16 on page 8; see ). What is the comparison of the change in vega (given a change from 1 to 2 to 3 years to expiration) if the strike price is $105 (relative to if the strike is $100)?arrow_forward
- A. What is the price of a call option with a strike of $80 and a maturity of 2.5 years? The underlying asset is currently trading at $75. The risk-free rate is 6% and the volatility of the underlying asset is 64% B. What is the price of a put option with an identical strike price? C. Calculate the delta, theta, and vega of the call option. Express theta per month and verga per 1% increase in volatility. D. After 5 months the price has gone up by $10 and the volatility by 10%. Using delta, theta, and vega that you have calculated, what is the total change in value of the option?arrow_forwardAn option has a 40% (actuarial) chance of paying $7.03 when the underlying asset increases by 6.3% and a 60% (actuarial) chance of paying $8.67 if the underlying asset declines by 10.8%. Given that the risk-free rate is 3.6% p.a. and there are 3 months until this option is to expire, what is the risk-neutral price of this option? Answer:arrow_forward4.A put option and a call option with an exercise price of $50 expire in three months and sell for $.84 and $5.10, respectively. If the stock is currently priced at $53.38, what is the annual continuously compounded rate of interest?arrow_forward
- Calculate the elasticity of a call option with a premium of $5.00 and a strike price of $69. The call has a hedge ratio of 0.7, and the underlying stock's price is currently $35. (Round your answer to 2 decimal places.) Elasticity of the call %arrow_forwardA power option pays off [max(S₁ - X),01² at time T where ST is the stock price at time T and X is the strike price. Consider the situation where X = 26 and T is one year. The stock price is currently $24 and at the end of one year it will either $30 or $18. The risk-free interest rate is 5% per annum, compounded continuously. What is the risk- neutral probability of the stock rising to $30? 0.500 0.603 0.450 None of the abovearrow_forwardQuestion 2. You have been asked to value a Arithmetic Lookback option which expires in six months time. At the end of the six months the buyer is paid the arithmetic mean of the underlying stock over the contract period. Using the compressed stock tree presented in Figure 1 and assuming an annual interest rate of 4.5% determine the fair price of the Arithmetic Lookback option. Why are Lookback options considered to he expensive? 182.5 158.7 138 138 120 120 104.4 104.4 90.8 79 Figure 1: Compressed stock treearrow_forward
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