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Olinaaaaa · 2024年03月23日

为什么求D1不用foreign- domestic

NO.PZ2020021205000029

问题如下:

The current exchange rate for a currency is 1.2000 and the volatility of the exchange rate is 10%. Calculate the value of a call option to buy 100 units of the currency in two years at an exchange rate of 1.2500. The domestic and foreign risk-free interest rates are 3% and 5%, respectively.

解释:

In this case, S0 = 1.2000, K = 1.2500, r = 0.03,

rf = 0.05, u = 0.1, and T = 2, and Equation (15.10)

gives

d,=ln(1.200/1.2500)  +  (0.03    0.05  +  0.102/2)  X  20.12\frac{\ln(1.200/1.2500)\;+\;(0.03\;-\;0.05\;+\;0.10^2/2)\;X\;2}{0.1\sqrt2}= -0.5008

d2 =ln(1.200/1.2500)  +  (0.03    0.05    0.102/2)  X  20.12\frac{\ln(1.200/1.2500)\;+\;(0.03\;-\;0.05\;-\;0.10^2/2)\;X\;2}{0.1\sqrt2}= -0.6422

C = 1.2OOOe0.052e^{-0.05\ast2}N(-O.5OO8) - 1.25OOe0.032e^{-0.03\ast2}N(-O.6422)= 0.028

This is the value of an option to buy one unit of the currency. The value of an option to buy 100 units is 2.8.

为什么要用0.03-0.05 而不是0.05-0.03 老师给的公式 就是rx-rf

1 个答案

品职答疑小助手雍 · 2024年03月23日

同学你好,因为题目里1.2和1.25的标价方式都是domestic/foreign。所以利率也按这样