最后一步算Call option价格的公式是不是有问题

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

汇率互换不是要把外国的利率当时分红来处理，S0应该*e的-（r-q）T吧？为什么是5%呢

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1 个答案

DD仔_品职助教 · 2022年02月25日

嗨，爱思考的PZer你好：

同学你好，

这里只是类比，把国外的利率当做分红来处理，并不是说公式和之前有分红比率q的完全一样。

具体的公式如下图，rx代表外币利率，rf代表本国利率，视频在17章倒数第二个，1.5倍速2‘30s左右，老师有具体讲解，同学可以再听一下。

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NO.PZ2020021205000029问题如下The current exchange rate for a currenis 1.2000 anthe volatility of the exchange rate is 10%. Calculate the value of a call option to buy 100 units of the currenin two years exchange rate of 1.2500. The mestic anforeign risk-free interest rates are 3% an5%, respectively.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463e45}span.s1 {color: #495566}span.s2 {color: #695147}span.s3 {color: #303c63}In this case, S0 = 1.2000, K = 1.2500, r = 0.03,rf = 0.05, u = 0.1, anT = 2, anEquation (15.10)p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464248}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #484045}span.s1 {font: 10.0px Helvetica}span.s2 {font: 6.5px Helvetica}span.s3 {color: #757475}span.s4 {font: 9.5px Helvetica}span.s5 {color: #466b}givesp.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 13.0px Helveticcolor: #4e4a4=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}0.12ln(1.200/1.2500)+(0.03−0.05+0.102/2)X2= -0.5008p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #484449}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474b} =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}0.12ln(1.200/1.2500)+(0.03−0.05−0.102/2)X2= -0.6422p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474045}span.s1 {color: #6b6767}span.s2 {font: 5.0px Helvetica}span.s3 {color: #777777}C = 1.2OOOe−0.05∗2e^{-0.05\ast2}e−0.05∗2N(-O.5OO8) - 1.25OOe−0.03∗2e^{-0.03\ast2}e−0.03∗2N(-O.6422)= 0.028This is the value of option to buy one unit of the currency. The value of option to buy 100 units is 2.8.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474045}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474044}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4632}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4432}span.s1 {color: #6b5547}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

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