3%和5%如何进行对应呢？

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.

选项：

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

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

C = 1.2OOO $e^{-0.05\ast2}$ N(-O.5OO8) - 1.25OO $e^{-0.03\ast2}$ 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.

想请问一下为什么5%对应的是1.2而3%对应的1.25呢？

感谢解答~

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1 个答案

李坏_品职助教 · 2022年02月21日

嗨，从没放弃的小努力你好：

国内利率是3%，国外利率是5%，汇率的现价是1.2，期权的行权价格是1.25。由于这里的期权是外汇期权，把外汇类比股票，外汇的红利（外币利率，5%）就像是股票的红利，是要对汇率现价（字母S）进行折现的。而国内利率(3%) 是无风险利率，对期权的行权价（字母K）进行折现。

套用期权定价的BSM公式：

c = S * exp(-rf * t)* N(d1) - K* exp(-r * t) * N(d2)，这里rf是国外利率5%，r是国内无风险利率3%。S是1.2，K是1.25.

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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