2. Consider the following one-period model for the asset class S, where the interest rar = 0 Asset Binary 9 SU 1 S(0) -S/U 0 If the risk-neutral probability q = 1/a calculate the value for U in terms of a. Construct the replicating portfolio for a binary option B(t) which has a payoff with value 1 if S > S(0) and 0 otherwise. Use the replicating portfolio to show that 1 B(0) a (6) Now extend the model in part (a) to a multi-period model with T time steps where for all time steps the asset is multiplied by U for an up move with risk-neutral probability q = 1/a and for down moves the asset is multiplied by 1/U. Assume interest rates r = 0. Woch B(t) is again a binary option with payoff 1 if S > S(0) and 0 otherwise. Let n represent the number of up moves. Show that the price of B(t) at time 0 is given by (1) - E () (a 1)T-n an n>n for some that you need to find. (1) Explain why we use risk-neutral probabilities to value derivatives. How does a market-maker make money trading derivatives? 2. Consider the following one-period model for the asset class S, where the interest rar = 0 Asset Binary 9 SU 1 S(0) -S/U 0 If the risk-neutral probability q = 1/a calculate the value for U in terms of a. Construct the replicating portfolio for a binary option B(t) which has a payoff with value 1 if S > S(0) and 0 otherwise. Use the replicating portfolio to show that 1 B(0) a (6) Now extend the model in part (a) to a multi-period model with T time steps where for all time steps the asset is multiplied by U for an up move with risk-neutral probability q = 1/a and for down moves the asset is multiplied by 1/U. Assume interest rates r = 0. Woch B(t) is again a binary option with payoff 1 if S > S(0) and 0 otherwise. Let n represent the number of up moves. Show that the price of B(t) at time 0 is given by (1) - E () (a 1)T-n an n>n for some that you need to find. (1) Explain why we use risk-neutral probabilities to value derivatives. How does a market-maker make money trading derivatives