题目
Hull (equation 17.4) shows that the relationship between theta, delta and gamma is given by: theta + (Rf × S × delta) + (0.5×variance(S)×S^2×gamma) = Rf×Value(option portfolio), where (Rf) is the risk-free rate and (S) is the stock price. The price of a one-year European call option with a strike price of $100 is $13.75 when the stock price is also $100. The volatility is 30.0% and the risk-free (Rf) rate is 4.0% per annum. The option's (percentage) delta is 0.612 and gamma is 0.0128. What is the option's theta?
选项
A.-5.333
B.-7.658
C.-9.112
D.-11.115
答案
B
解析
「huixue_img/importSubject/1564170387531632640.png」应用等式，在算出theta rf=theta＋rS_0×delta＋1/2 σ^2 〖S_0〗^2×gamma theta=4%×13.75 －(4%×100×0.612) － (0.5×〖30%〗^2×〖100〗^2×0.0128)=－7.658