3. For a derivative security we have payout at maturity a 1 V(T) = S(T) We will assume that this security is on an asset that follows geometric Brownian motion in a market with a constant risk-free interest rate r. (a) Derive a formula for the value of this instrument at time t. (b) Determine an initial position and a replicating strategy to repro- duce this security. 3. For a derivative security we have payout at maturity a 1 V(T) = S(T) We will assume that this security is on an asset that follows geometric Brownian motion in a market with a constant risk-free interest rate r. (a) Derive a formula for the value of this instrument at time t. (b) Determine an initial position and a replicating strategy to repro- duce this security