10. (15 pts: 4 + 3 + 4 + 4) The European asset-or-nothing call option pays one unit of underlying stock if the stock price at maturity is larger than the strike, and pays 0 otherwise. The European asset-or-nothing put option pays one unit of underlying stock if the stock price at maturity is smaller than the strike, and pays 0 otherwise. (a) Use risk-neutral pricing to find the Black-Scholes value of an asset-or- nothing call option. (b) State the put-call parity for the asset-or-nothing options. Then, use it to find the Black-Scholes value of a asset-or-nothing put option. (c) Assuming the Black-Scholes model for the stock price, derive the formu- lae for the Delta of these asset-or-nothing options. (d) Find the limit of the Black-Scholes values of these options as 0 and as .