Consider a Russian option with value function V(S, J) in the case where thereare continuous dividends paid on the underlying asset S at rate D. Define thevariable J for this option. A similarity reduction of the form W(n) = V/J withn S/J leads to110²² W +(r− D)nW' rW = 0,which must be solved subject to-W(1) W'(1) = 0, W(no) = 1, W'(no) = 0,where n = ŋo is the optimal exercise boundary in similarity coordinates. Thecurrent value of the underlying is S = 3. What is the current value of theRussian option assuming that σ = 0.3, r = 0.1 and D = 0.05? Present yourresults to a minimum of 4 decimal places.

1. Understand the Problem SetupWe are given a Russian option whose value V(S, J) depends on the…

Answered: Consider a Russian option with value…

Financial Management: Theory & Practice

16th Edition

ISBN:9781337909730

Author:Brigham

Publisher:Brigham

Chapter25: Portfolio Theory And Asset Pricing Models

Section: Chapter Questions

Problem 4P

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Consider a Stop-loss option with value function V(S, J) in the case where there are continuous dividends paid at rate D. A similarity reduction of the form W(n) =V/J with n = S/J leads to ¹o²³n²W" + (r = D)nW' − rW = 0, which must be solved subject to - W (1) W'(1)=0 and W(A) = X. - The current value of the underlying is S = 1. What is the current value of the Stop-loss option assuming What is the value of a Stop-loss option with r = 0.25, σ = 0.4, D = 0.2 and λ = 0.9. Present your results to a minimum of 4 decimal places.
A forward contract has an underlying asset which, in Cox-RossRubenstein notation, has S=22,u=1.2 and d=0.9. This forward contract matures in one time step and the return over this time step is R=1.02. Assuming the forward price is calculated rationally, what is the value of the forward at node (1,1)? (Give your answer as a positive number.)
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We believe that the single factor model can predict any individual asset’s realized rate of return well. Both Portfolio A and Portfolio B are well-diversified: ri = E(ri) + βiF + Ei, where E(ei) = 0 and Cov(F, i) = 0 A B β 1.2 0.8 E(r) 0.1 0.08 (1) What is the rate of return of the risk-free asset? (2) What is the expected rate of return of the well-diversified portfolio C with βC = 1.6, which also exists in the market? (3) A fund constructs a well-diversified portfolio D. Studies show that βD = 0.6. The expected rate of return of D is 0.06. Is there an arbitrage opportunity? If so, construct a trading strategy to earn profits with no risk. If not, why?
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Consider the Black-Scholes equation for the option price V(S, t) if the underlying does not pay out dividends. (i) Show that V(S,t) = AS, where S is the underlying price, t is time, and A is a constant, is a solution to the Black-Scholes equation. (ii) For the solution V(S,t) = AS, define the value A (Delta) used for hedging.
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The CAPM states that the expected (required) return on an asset is : E(Ri)=Rf+βi[E(RM)−Rf] where the term in square brackets is the risk-premium earned by the market portfolio. Therefore, the beta of the market portfolio (βM) must be equal to __________ . A) zero B) 0.5 C) 1.0 D) an unknown estimate
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 S0 = (1 + r)T..

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