MAXIMA AND MINIMA Sample Clauses

MAXIMA AND MINIMA. A standard call has a payoff of the form max[0, ST − K ] and a standard put has a payoff of max[0, K − ST ] . If an exotic option has a payoff of the form max [ g ( ST ) , f ( ST )] or min[ g (ST ) , f (ST )] , where g and f are linear functions, then the price of the option can be expressed in terms of a put or a call by using the following rules: • max [ A , B] = B + max [ A − B , 0 ] = A + max [ 0, B − A] • min[ A , B] = B + min [ A − B , 0 ] = A + min[ 0, B − A] • max [ k A, k B] = k max [ A , B] if k > 0 • min[ k A , k B] = k min[ A , B ] if k > 0 • max [− A , −B ] = −min[ A , B] • max [ A , B] + min [ A , B ] = A + B , and so min[ A , B] = A + B − max [ A, B ] Assume the Black-Scholes framework applies. The current price of a nondividend-paying stock is 25. The stock has a volatility of 40%. The continuously compounded risk-free rate of interest is 4%. Consider an option that pays the owner the smaller of the following two values at the end of two years: 200, or 10 times the price of the stock at that time. Calculate the price of this option.
Sample 1
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