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Exercise 4.2.3. Use the Black-Scholes methodology to nd, by direct calculation, an explicit formula for the fair price (at time t) of the following contingent claims (European type options) where the price of the underlying (stock) at time t is denoted by 3(t); the time of maturity by T; the risldess interest rate by r; the volatility of the underlying by or: (a) The stock or nothing call option: A claim that will pay exactly the price of the underlying in all cases where the price of the underlying at time T is larger or equal to K (and 'l] in all other cases). (b) The stock or nothing put option: A claim that will pay exactly the price of the underlying in all cases where the price of the underlying at time T is smaller or equal to K (and U in all other cases). 'ce of cases). (6} A money or nothing put option: this claim that will pay exactly the xed amount Y in all cases where the price of the underlying at time T is larger or equal to K (and 0 in all other cases). Hint: You should use the socalled characteristic or indicator functions in your calcula- tions. The indicator function of the interval [0, b} is dened as follows: 1 ifagzcgb 0 otherwise Mahdi) = {