Consider the following contingent claim whose value at maturity date T is given byf(T,Sp) = min(Sr S;)where T, is some intermediate betweent (current time) and T (maturity date). Sr, and Srdenote 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 satisfiesdS; = uS,dt + oS,dW,with u = 0.05, a = 0.2. The riskfree interest rate is 6% per annum. Take t = 0, T, = 0.5and 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 riskneutral valuation principle

(a) To calculate the price of the contingent claim at time T using replication technique, we first…

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

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter6: Fixed-income Securities: Characteristics And Valuation

Section: Chapter Questions

Problem 7QTD

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