Recall that an asset-or-nothing call option has payoff function A(S(T)) of the form I for >...

 

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Recall that an asset-or-nothing call option has payoff function A(S(T)) of the form I for > E, A(x) = x/2 for x = E, 0 for x < E. Sketch the payoff diagram. Recall that denotes the expected drift rate of the as- set and r denotes the interest rate. The risk-neutral approach of setting e-r(T-E (A(S(t)) produces the asset-or-nothing call option value = r in exp e-7(T-1) (log(1/S)-(r-2/2)(T-1))2 20(T-1) 2(T-t) dr. Show that this expression simplifies to SN(d). Define the payoff function for an asset- or-nothing put option, and, using the no-arbitrage assumption, or otherwise, show that this put option has the value SN(-d). (2,4,2 marks) Recall that an asset-or-nothing call option has payoff function A(S(T)) of the form I for > E, A(x) = x/2 for x = E, 0 for x < E. Sketch the payoff diagram. Recall that denotes the expected drift rate of the as- set and r denotes the interest rate. The risk-neutral approach of setting e-r(T-E (A(S(t)) produces the asset-or-nothing call option value = r in exp e-7(T-1) (log(1/S)-(r-2/2)(T-1))2 20(T-1) 2(T-t) dr. Show that this expression simplifies to SN(d). Define the payoff function for an asset- or-nothing put option, and, using the no-arbitrage assumption, or otherwise, show that this put option has the value SN(-d). (2,4,2 marks)