2. Let 0 < Ki < K2. In the Black Scholes market, consider the contingent claim X that pays one unit of the currency, pro

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2 Let 0 Ki K2 In The Black Scholes Market Consider The Contingent Claim X That Pays One Unit Of The Currency Pro 1 (607.27 KiB) Viewed 33 times

2. Let 0 < Ki < K2. In the Black Scholes market, consider the contingent claim X that pays one unit of the currency, provided Si(T), the price of a share of stock at the maturity time T, belongs to the interval (K1, K2). For te [0, T), find the fair price II(t) of the claim X. Write down II(t) by using the function N(d). Hint. Denote by X{K1,K2)(x) the indicator function of the interval [K1, K2), i.e., ſi, if ze [K1, K2]. € X[K1,K2) (2) = 10, otherwise , . Use that X = X[K1,K3(Si(T)), and note that 1 La dy = L. 126*dy - L v2c * dy = N(6) – N(a). 270 / Recall that N(d) denotes the distribution function of the standard normal distribution, 1 = V 2T J- N(N) - .