Question: 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

Consider the following contingent claim whose value at maturity date T is

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 = s,dt + os,dW with = 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 Sto (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

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