4 (1) Explain what is meant by a "replicating portfolio". [2] (ii) Explain what is meant by a "risk-neutral probability measure" and state mathematically what it implies about the pricing of derivatives relative to the price of the underlying asset. [2] (iii) Consider a one-period model of a non-dividend paying-stock, currently priced at S, and which may move up or down to give S, = Sou or $1 =Sod. Consider a derivative that pays cy or co following an up or down event. The risk-free rate of return (continuously compounded) is r. (a) Use a replicating portfolio to derive an equation for the price of the derivative at time t =0. (b) Hence find the price of a derivative whose payoff is defined as | $1 -So , assuming d 1. (c) Explain how to synthesise the derivative in (iii)(b) from simpler options. [8] [ Total 12] .5 Using the Black-Scholes formula for the value of a European call option on a non-dividend-paying stock, show that the call price, c, tends to the maximum of S-ke and zero (depending on the strike price) as a tends to zero. [9] 6 The price of a non-dividend-paying stock at time 1, S, , is related to the price at time 0, So , as follows: 51 = Sou with probability p Sod with probability 1-p The continuously compounded rate of return on a risk-free asset is r. (i) (a) Determine the replicating portfolio for a European call option written on the stock that expires at time 1 and has a strike price of k, where do