EBK INVESTMENTS
11th Edition
ISBN: 9781259357480
Author: Bodie
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 21, Problem 17PS
Summary Introduction
To comment:
On the right choice of the options given in the question. For this we have to elaborate the definition of delta and its characteristics.
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Describe the five variables (Assets price, Strick price or Exercise Price, Risk- Free- Rate, Time to Expiration, Volatility) that Black-Scholes-Merton Formula uses to calculate the price of call and put options. Explain how the change in these variables (Assets price, Strick price or Exercise Price, Risk- Free- Rate, Time to Expiration, Volatility) affects the price of the option.
a) discuss the relationship between the up-factor (u), down-factor (d), risk-free rate (r), and binomial probability (p) in the binomial model.
b) discuss the assumptions in Black-Scholes-Merton model (BSM) from memory.
c) discuss the variables in the BSM formula and explain how they affect call option pricing.
d) define historical volatility and implied volatility.
e) demonstrate how to reduce risk with gamma hedging.
a)explain the concept of the delta normal method for calculating VAR when options are present in the portfolio.
b)explain the basic concepts of the historical method and the Monte Carlo simulation method of calculating VARs.
c)discuss the benefits and limitations of VAR.
d)define credit risk (default risk).
e)explain how option pricing theory can be used in valuing default risk.
Chapter 21 Solutions
EBK INVESTMENTS
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- 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_forwardDescribe how a risk-free portfolio can be created using stocks and options. How cansuch a portfolio be used to help estimate a call option’s value?arrow_forwardIdentify the key parameters that influence option price. Discuss the impact of a rise and fall in the value of each parameter on the prices of put and call options.arrow_forward
- 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.arrow_forwardDraw the profit diagram (profit not payoff) 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. Clearly state any assumptions made. Is the cost of the portfolio positive?arrow_forwardDescribe the effect of a change in each of the following factors on the value of a calloption:1. Stock price2. Exercise price3. Option life4. Risk-free ratearrow_forward
- What impact does each of the followingparameters have on the value of a call option?(1) Current stock pricearrow_forwardi) Calculate the expected return for each stock assuming the Capital Asset Pricing Model (CAPM) is valid, and explain if they are correctly priced. Show your calculations.arrow_forwardDescribe the five variables like Stock Price, Exercise Price, Risk-Free Rate, Volatility or Standard Deviation, and Time to Expiration that the Black-Scholes-Merton Formula uses to calculate the price of call and put options. Explain with some examples for having detail justifications. (Note: Your explanations should be at least 500 words)arrow_forward
- Discuss the risks and payoffs of the following positions, accompanied by payoff graphs. Buy a stock. Buy a call. Buy stock and sell a call option on the stock (covered call).arrow_forwardBoth 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.arrow_forwardWe showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity theorem as well as a numerical example to prove your answer.arrow_forward
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