题目
A one-year European call option has a strike price of $10. The risk-free rate is 4% per annum. What is an estimate of the call price if the stock is $30; i.e., significantly in-the-money?
选项
A.$18.80
B.$20.00
C.$20.39
D.$21.22
答案
C
解析
As the stock price becomes large relative to the strike price, N(d_1) and N(d_2) approach 1.0; in this case, they are 1.000 and 0.9999.In which case, call=S_0 N(d_1 )-Ke^(-rT) N(d_2 ) is approximated by: c = S- K×exp(-rT).In this case,c = 30-10e^(-4%×1)=$20.3921 (the precise value is $20.3922).Please note that, also, as the volatility (sigma) approaches zero, the Black-Scholes similarly approaches the minimum value: S_0-Ke^(-rT).当股票价格和执行价格有很大的关联，N(d_1) 和 N(d_2)接近1/0.那么它们分别为1.000 and 0.9999。根据公式call=S_0 N(d_1 )－Ke^(－rT) N(d_2 )，则 c = 30?10e^(－4%×1)=$20.3921请注意，当波动率(sigma)趋近于零时，BSM也会趋近于最小值S_0－Ke^(－rT)。