4. Consider an exchange option. Suppose the initial prices (time 0) of the two stocks areS =S2 = 100 and a =0.40,. Suppose also that the returns on the stocks are uncorrelated.Assume no dividends and final maturity of the option is T = 2 year:(a) Using the closed-form expressions for the price of these options, identify the price ofthe exchange option when o = 0, a2 =0.20, ag =0.40, and @2 =0.60.(b) Is there a trend in the price? Intuitively, why is this the case?

Price of exchange option refers to the value of shares at the time of expiry or when the…

4. Consider an exchange option. Suppose the initial prices (time 0) of the two s - S2 = 100 and a, = 0.40, Suppose also that the returns on the stocks are unc ssume no dividends and final maturity of the option is T = 2 year. %3D (a) Using the closed-form expressions for the price of these options, identify th e exchange option when = 0, z =0.20, a2 =0.40, and ø2 =0.60. (b) Is there a trend in the price? Intuitively, why is this the case?

4. Consider an exchange option. Suppose the initial prices (time 0) of the two s - S2 = 100 and a, = 0.40, Suppose also that the returns on the stocks are unc ssume no dividends and final maturity of the option is T = 2 year. %3D (a) Using the closed-form expressions for the price of these options, identify th e exchange option when = 0, z =0.20, a2 =0.40, and ø2 =0.60. (b) Is there a trend in the price? Intuitively, why is this the case?

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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2. Derive the single - period binomial model for a put option. Include a single - period example where: u = 1.10, d = 0.95, Rf = 0.05, SO = $100, X = $100. 3. Assume ABC stock's price follows a binomial process, is trading at SO = $100, has u 1.10, d = 0.95, and probability of its price increasing in one period is 0.5 (q = 0.5). a. Show with a binomial tree ABC's possible stock prices, logarithmic returns, and probabilities after one period and two periods. . b. What are the stock's expected logarithmic return and variance for 2 periods and 3 periods? c. Define the properties of a binomial distribution.
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?
Consider two put options on different stocks. The table below reports the relevant information for both options: Put optionTime to maturityCurrent price of underlying stockStrike priceVolatility ( )X1 year$27$1830%Y1 year$25$2030%All else equal, which put option has a lower premium? A.Put option Y B.Put option X
Let C be the price of a call option that enables its holder to buy one share of a stock at an exercise price K at time t; also, let P be the price of a European put option that enables its holder to sale one share or the stock for the amount K at time t. Let S be the price of the stock at time 0. Then, assuming that interest is continuously discounted at a nominal rate r, either S+P-C=Ke-rt or there is an arbitrage opportunity. Question: How do I verify that the strategy of selling one share of stock, selling one put option, and buying one call option always results in a positive win if S+P-C>Ke-rt ?
1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.
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.
An 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?
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.
Use the Black-Scholes formula to find the value of a call option based on the following inputs. (Round your final answer to 2 decimal places. Do not round intermediate calculations.) Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value GA $ $ $ 48 60 0.07 0.04 0.50 0.26
Consider a portfolio that consists of the following four derivatives: 1) a put option written(sold) with strike price K − 5, 2) a call option purchased with strike price K − 5, 3) a call option written(sold) with strike price K + 5, and 4) a put option purchased at strike price K + 5. All options are European.The risk-free rate is rf , the time to expiration is T, the initial stock price is S0, and the stock price atmaturity is ST . What are the payoffs at expiration of this portfolio? What must the price of this portfoliobe?
You are evaluating a put option based on the following information: P = Ke-H•N(-d,) – S-N(-d,) Stock price, So Exercise price, k = RM 11 = RM 10 = 0.10 Maturity, T= 90 days = 0.25 Standard deviation, o = 0.5 Interest rate, r Calculate the fair value of the put based on Black-Scholes pricing model. Cumulative normal distribution table is provided at the back.
A call option with X = $50 on a stock currently priced at S = $55 is selling for $10. Using a volatility estimate of σ = .30, you find that N(d1 ) = .6 and N(d2 ) = .5. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than .30? Explain.

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