Principles of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
12th Edition
ISBN: 9781259144387
Author: Richard A Brealey, Stewart C Myers, Franklin Allen
Publisher: McGraw-Hill Education
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Chapter 21, Problem 18PS
Option delta Suppose you construct an option hedge by buying a levered position in delta shares of stock and selling one call option. As the share price changes, the option delta changes, and you will need to adjust your hedge. You can minimize the cost of adjustments if changes in the stock price have only a small effect on the option delta. Construct an example to show whether the option delta is likely to vary more if you hedge with an in-the-money option, an at-the-money option, or an out-of-the-money option.
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Students have asked these similar questions
Both call and put options are affected by the following five factors: the exercise price, the underlying stock price, the time to expiration, the stock’s standard deviation, and the risk-free rate. However, the direction of the effects on call and put options could be different.
Use the following table to identify whether each statement describes put options or call options.
Statement
Put Option
Call Option
1. When the exercise price increases, option prices increase.
2. An option is more valuable the longer the maturity.
3. The effect of the time to maturity on the option prices is indeterminate.
4. As the risk-free rate increases, the value of the option increases.
Both call and put options are affected by the following five factors: the exercise price, the underlying stock price, the time to expiration, the stock’s standard deviation, and the risk-free rate. However, the direction of the effects on call and put options could be different.
Use the following table to identify whether each statement describes put options or call options.
Statement
Put Option
Call Option
1. An option is more valuable the longer the maturity.
2. A longer maturity in-the-money option on a risky stock is more valuable than the same shorter maturity option.
3. When the exercise price increases, option prices increase.
4. As the risk-free rate increases, the value of the option increases.
Which of the following strategy would you adopt if you expect the fall in prices of a stock?
A. Buy a call
B. Sell a call
C. Sell a put
D. Buy a future
Chapter 21 Solutions
Principles of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Ch. 21 - Prob. 1PSCh. 21 - Option delta a. Can the delta of a call option be...Ch. 21 - Prob. 4PSCh. 21 - Binomial model Over the coming year, Ragworts...Ch. 21 - BlackScholes model Use the BlackScholes formula to...Ch. 21 - Option risk A call option is always riskier than...Ch. 21 - Prob. 8PSCh. 21 - Prob. 9PSCh. 21 - Binomial model Suppose a stock price can go up by...Ch. 21 - American options The price of Moria Mining stock...
Ch. 21 - Prob. 12PSCh. 21 - American options Suppose that you own an American...Ch. 21 - Prob. 14PSCh. 21 - Prob. 15PSCh. 21 - American options The current price of the stock of...Ch. 21 - Option delta Suppose you construct an option hedge...Ch. 21 - Prob. 19PSCh. 21 - American options Other things equal, which of...Ch. 21 - Option exercise Is it better to exercise a call...Ch. 21 - Prob. 22PSCh. 21 - Option delta Use the put-call parity formula (see...Ch. 21 - Option delta Show how the option delta changes as...Ch. 21 - Dividends Your company has just awarded you a...Ch. 21 - Prob. 27PSCh. 21 - Prob. 28PSCh. 21 - Prob. 29PS
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- Black-Scholes Model Assume that you have been given the following information on Purcell Industries call options: According to the Black-Scholes option pricing model, what is the option’s value?arrow_forwardAccording to the Black-Scholes formula, what will be the hedge ratio (delta) of a call option as the stock price becomes infinitely large? Explain briefly.arrow_forwardSelect all that are true with respect to the Black Scholes Option Pricing Model (BSOPM) Group of answer choices When using BSOPM to value a stock option, the BSOPM assumes that stock prices follow a normal distribution. When using BSOPM to value a stock option, the BSOPM assumes that stock returns follow a normal distribution. Half of the observations in a normal distribution are above the mean and half are below the mean. Fisher Black and Myron Scholes were awarded the Nobel Prize in 1997 for their work in Option Pricing.arrow_forward
- In the Black-Scholes option pricing model, the value of a call is inversely related to: a. the risk-free interest stock b. the volatility of the stock c. its time to expiration date d. its stock price e. its strike pricearrow_forwardD3) Finance a) What does the option delta refer to? For a standard European put option, draw the graph of the delta as a function of the price of the underlying asset. b) You have delta hedged a long call position on a stock. The stock price drops. Explain how you would adjust your hedgearrow_forwardMy question is for a synthetic call option why do we need to borrow the present value of the strike price and what does it mean in a simple language explanation. Similarly why do we need to lend the present value of the stock at risk-free rate and what does it mean in simple language explanation? Please also clarify the significance of risk free rate? Why is it used in put call parity. Synthetic Call Option: If an investor believes that a call option is over-priced, then he/she can sell the call on the market and replicate a synthetic call. Borrow the present value of the strike price at the risk free rate and purchase the underlying stock and a put. Synthetic Put Option: Similar to the synthetic call option. A synthetic put can be created by re-arranging the put-call parity relationship, if the trader believes the put is overvalued. Synthetic Stock: A synthetic stock can also be created by rearranging the put-call parity identity. In this case, the investor will buy the…arrow_forward
- A) Assume that you have some shares of stock in ABC Inc. Why do we say that if you also purchase a put option on the same stock, the price paid to buy the put option is like paying an insurance premium? B) We understand standard deviation of returns as a measure of risk and rational investors would like to minimize risk. Notwithstanding this, you may have read that as the standard deviation of returns of the underlying asset increases the value of an option rises. If standard deviation is a measure of risk and investors do not particularly like it, why does it lead to an increase in an option's value?arrow_forwardIf you are creating an option play that benefits from a VOLATILITY strategy, you expect the stock price to do what? ○ Go down Go up OR down, by a lot Go up O Remain right around its current pricearrow_forwardFor each of the statements below, determine if they are TRUE/FALSE and briefly explain why. a) Delta hedging is most difficult for at-the-money options just before their expiration. b) A protective put with a higher strike price provides greater downside protection but lower upside gains. c) A covered call with a lower strike price provides greater downside protection but a lower maximum gain on the upside. d) It is possible to change the Gamma of a portfolio of options by adding the underlying assets to your position. e) You have delta hedged a long call position on a stock. The stock price drops. To maintain your hedge, you need to buy back some shares.arrow_forward
- Suppose that put options on a stock with strike prices $66 and $75 cost $3 and $5, respectively. How can the options be used to create (a) a bull spread and (b) a bear spread? For what range of future stock prices will the bear spread strategy be profitable. Is the profit for the bear spread strategy limited? If so, how much and at what price range? At what price range will you exercise the long position from the bear spread strategy? At what range of future stock prices will the bear spread strategy lead to a loss? What is the maximum loss that you can incur from bear spread strategy and at what price range?arrow_forwardExplain in your own words what dynamic hedging is, and how a trader could profit by dynamically hedging an option if they have a forecast of volatility that is different to implied volatility.arrow_forwardVolatility smile” is referred to as evidence against the Black-Scholes model. Why is that? A) Black-Scholes model assumes that different options on a given stock have different values for implied volatility b.) Volatility of returns on one and the same stock, over one and the same future period of time, can only take one value C) Black-Scholes model generates option premium close to the observed premium if the observed stock volatility is usedarrow_forward
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