Assume the price, S, of a non-dividend paying stock follows geometric Brownian motion withdrift r and volatility o. Consider a perpetual call option on S. The option is exercised whenS = Ŝ, and the payoff on the option is Ŝ– X, where X is the exercise price of the option.Assume all investors are risk-neutral and the instantaneous risk-free rate of interest is aconstant, r. Note that the drift of the stock the instantaneous rate of return on the stock-isequal to r. Of course, this makes sense, since the return on all traded assets in a risk-neutralworld must be the risk-free rate of interest. Compute the value of the call option C(S;$) andthe optimal exercise policy S = arg max[C(S; $)].

A call option gives the right to the buyer to buy a stock at an exercise price X. An option is a…

Answered: Assume the price, S, of a non-dividend…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Use the put-call parity relationship to demonstrate that an at-the-money call option on a nondividend-paying stock must cost more than an at-the-money put option. Show that the prices of the put and call will be equal if So = (1 + r)^T
The Capital Asset Pricing Model (CAPM) says that the risk premium on a stock is equal to its beta times the market risk premium. ..... True False
Theta measures an option's: Multiple Choice O O intrinsic value. volatility. rate of time decay. sensitivity to changes in the value of the underlying asset. sensitivity to changes in the risk-free rate.
Assume a security follows a geometric Brownian motion with volatility parameter = 0.2. Assume the initial price of the security is 21 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 19 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price.
4. Valuation of a Derivative Consider a derivative on a stock with the time to expiration T and the following payoff: 0 K₁ 0 if ST K₁. What is the present value of the derivative? Provide an analytic expression of the price using N(), the cumulative probability distribution function of a standard normal random variable.
Assume that the CAPM assumptions hold. Consider the following statements:i. A stock with a beta below zero will tend to move in the same direction as the market but will tend to move less aggressively in that direction than the market does.ii. Alpha measures the additional risk we take on top of the risk of the market portfolio.
2. In the capital asset pricing model, what does the stock beta stand for? (a) The volatility of the security (b) The joint volatility of any two securities in a portfolio (c) The relative co-movement of a security with respect to the market portfolio (d) The volatility of a security divided by the volatility of the market index
Stocks A and B have the same price and are in equilibrium, but Stock A has the higher required rate of return. Which of the following statements is CORRECT? a. Stock B must have a higher dividend yield than Stock A. b. Stock A must have a higher dividend yield than Stock B. c. If Stock A has a higher dividend yield than Stock B, its expected capital gains yield must be lower than Stock B's. d. Stock A must have both a higher dividend yield and a higher capital gains yield than Stock B. e. If Stock A has a lower dividend yield than Stock B, its expected capital gains yield must be higher than Stock B's.
The premium on a call option is primarily a function of the difference in spot price S relative to the strike price X, the length of time until expiration T, and the volatility of the currency o. C = f(S-X, T, o) For each characteristic of a call option, use the table to indicate whether that would lead to a higher call option premium or a low call option premium (all else equal). Characteristic A lower spot price relative to the strike price A shorter time before expiration A higher level of volatility for the currency Higher Call Option Premium O Lower Call Option Premium When using a call option to hedge payables in an international currency, a U.S. based MNC can lock in the to obtain the needed foreign currency. maximum minimum amount of dollars needed
Question 1. Let St be the current price of a stock that pays no dividends. a)Let rbid be the interest rate at which one can invest/lend money, and roff be theinterest rate at which one can borrow money, rbid≤roff. Both rates are continuously compounded. Using arbitrage arguments, find upper and lower bounds for the forwardprice of the stock for a forward contract with maturity T > t. b)How does your answer change if the stock itself has bid price St,bid and offer price St,off?
Assume that F, and Fy are the futures prices of two contracts on the same non-dividend-paying investment asset, with times to maturity T, and Tz, Tz > T1. Prove that therelationship between the two prices must be see image

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