Consider the following contingent claim whose value at maturity date T is given by f(T.ST) = min(ST. ST) where To is some intermediate between t (current time) and T (maturity date). ST, and ST denote the prices of the underlying asset at time To and time T respectively. We assume that the asset is non-dividend paying and its asset price satisfies ds, = us,dt + os dWt with μ = 0.05, a = 0.2. The riskfree interest rate is 6% per annum. Take t = 0, To = 0.5 and T = 1.5. The current price of the asset is So = $25. (a) Calculate the price of the contingent claim at time To using replication technique. Express your answer in terms of ST (Hint: The value of ST is known at time To. To find the price, treat To as the "current time"). (b) Using the result of (a), find the current price of this contingent claim using risk neutral valuation principle
Consider the following contingent claim whose value at maturity date T is given by f(T.ST) = min(ST. ST) where To is some intermediate between t (current time) and T (maturity date). ST, and ST denote the prices of the underlying asset at time To and time T respectively. We assume that the asset is non-dividend paying and its asset price satisfies ds, = us,dt + os dWt with μ = 0.05, a = 0.2. The riskfree interest rate is 6% per annum. Take t = 0, To = 0.5 and T = 1.5. The current price of the asset is So = $25. (a) Calculate the price of the contingent claim at time To using replication technique. Express your answer in terms of ST (Hint: The value of ST is known at time To. To find the price, treat To as the "current time"). (b) Using the result of (a), find the current price of this contingent claim using risk neutral valuation principle
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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Transcribed Image Text:Consider the following contingent claim whose value at maturity date T is given by
f(T,Sp) = min(Sr S;)
where T, is some intermediate betweent (current time) and T (maturity date). Sr, and Sr
denote the prices of the underlying asset at time To and time T respectively.
We assume that the asset is non-dividend paying and its asset price satisfies
dS; = uS,dt + oS,dW,
with u = 0.05, a = 0.2. The riskfree interest rate is 6% per annum. Take t = 0, T, = 0.5
and T = 1.5. The current price of the asset is So = $25.
(a) Calculate the price of the contingent claim at time Ta using replication technique.
Express your answer in terms of ST..
(©Hint: The value of S, is known at time To. To find the price, treat T, as the
"current time").
(b) Using the result of (a), find the current price of this contingent claim using risk
neutral valuation principle
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