... 133Black–Scholes formula, 80 82 , 105,131cash-or-nothing, 164–166down-and-out call, 189 European call, 81 , 83 , 89 European put, 81 , 83 , 92geometric average price Asian call, 1 98 up-and-out call, 190Black–Scholes ... formulas, 82 , 83 Black–Scholes PDE, 73, 78, 80 , 81 , 83 , 99, 101–103,165, 166, 239, 251, 257–262American put, 174–176barrier option, 190down-and-out call, 188 , 189 exotic option, 196bottom straddle, ... Indexdividends, 49, 182 double barrier option, 191down-and-in call, 188 , 189 down-and-in put, 190down-and-out call, 187 – 189 , 260–261, 265down-and-out put, 190drift, 54, 105, 1 98 efficient market...