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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What is the implied volatility of a European call option with the following parameters? c = $3 s0 = $40 k = 41 r = 10% T = 0.5 years (Enter 11.51% as 0.1151. Required precision +/- 0.0002)
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Assume interest rate is zero. In a shout call option the strike price is $30. The holder shouts when the asset price is $40. What is the payoﬀ from the option if the ﬁnal asset price is $35? A. $0 B. $5 C. $10 D. $15
A European call option on the stock which expires at time 2 with strike price 6. a two-period binomial model with u = 2, d =1/2, r =1/4 and S0 = 4.
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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.
Suppose that the current price of an asset is $100. After three months, there are two possible values for the asset price, and after six months there are three, as follows: S++ = 121 s+ = 110 So = 100 st- = 92 S- = 90 S-- = 81 The annual risk-free rate of interest is 2%.
i need the answer quickly
2. Calculate the put premium according to put-call parity which gives no arbitrage opportunity. Explain what transaction would you do if the put premium is below/above the put premium you calculated. European call option premium: c = $2 Stock price today: So- $30 Life of option: T=0.5 Risk-free rate for maturity T with continous compounding: r= 8% Strike price: K= Decide on the K value yourself (carefully). No dividends paid during life of option.
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.
Data: S0 = 120; X = 126; 1 + r = 1.05. The two possibilities for ST are 150 and 102. Required: a-1. The range of S is 48 while that of C is 24 across the two states. What is the hedge ratio of the call? Note: Round your answer to 2 decimal places. a-2. Calculate the value of a call option on the stock with an exercise price of 126. (Do not use continuous compounding to calculate the present value of X in this example because we are using a two-state model here; the assumed 5% interest rate is an effective rate per period.) Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Assume an interest rate of zero. A Call option and a Put option with the same exercise price, X = 100p are priced at 9p for the Call and 4p for the Put. What is the price of the synthetic share?

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