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yolanda · 2020年03月13日

问一道题：NO.PZ2020021205000028 [ FRM I ]

  1. FRM I
  2. Financial Markets And Products

问题如下：

A stock price is USD 50 with a volatility of 22%. The risk free rate is 3%. Use the Black-Scholes-Merton formula to value (a) a European call option and (b) a European put option when the strike price is USD 50, and the time to maturity is nine months.

解释：

In this case:

d, =ln⁡(5O/5O)  +  (0.03  +  0.222/2)  x  0.750.22X0.75\frac{\ln(5O/5O)\;+\;(0.03\;+\;0.22^2/2)\;x\;0.75}{0.22X\sqrt{0.75}}= 0.2134

d2 =ln⁡(5O/5O)  +  (0.03  −  0.222/2)  x  0.750.22X0.75\frac{\ln(5O/5O)\;+\;(0.03\;-\;0.22^2/2)\;x\;0.75}{0.22X\sqrt{0.75}}= 0.0228

and the call option price is

50 N(0.2134) - 50 e−0.03∗0.75e^{-0.03\ast0.75}N(O.O228) = 4.3

The put option price is

50 e−0.03∗0.75e^{-0.03\ast0.75}N(O.O228)N(-O.O228) - 50N(-O.2134) = 3.2

put option的答案多了一个N（0.0228）
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1 个答案

袁园_品职助教 · 2020年03月14日

是的同学，这里是个typo，谢谢提醒，我们尽快修改！

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NO.PZ2020021205000028 问题如下 A stopriis US50 with a volatility of 22%. The risk free rate is 3%. Use the Black-Scholes-Merton formula to value (a Europecall option an(a Europeput option when the strike priis US50, anthe time to maturity is nine months.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463f44}span.s1 {color: #695147}span.s2 {color: #303c61}span.s3 {color: #4363} In this case:p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #555255} =ln⁡(5O/5O)  +  (0.03  +  0.222/2)  x  0.750.22X0.75\frac{\ln(5O/5O)\;+\;(0.03\;+\;0.22^2/2)\;x\;0.75}{0.22X\sqrt{0.75}}0.22X0.75​ln(5O/5O)+(0.03+0.222/2)x0.75​= 0.2134p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 5.5px Helveticcolor: #504b4e}span.s1 {font: 8.5px Helvetica}span.s2 {font: 8.0px Helvetica} =ln⁡(5O/5O)  +  (0.03  −  0.222/2)  x  0.750.22X0.75\frac{\ln(5O/5O)\;+\;(0.03\;-\;0.22^2/2)\;x\;0.75}{0.22X\sqrt{0.75}}0.22X0.75​ln(5O/5O)+(0.03−0.222/2)x0.75​= 0.0228p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #504b4e}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #555255}anthe call option priis50 N(0.2134) - 50 e−0.03∗0.75e^{-0.03\ast0.75}e−0.03∗0.75N(0.0228) = 4.3The put option priisp.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #413b3f}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464047}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #555255}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #504a51}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 5.5px Helveticcolor: #504b4e}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #504b4e}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #433f45}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #484045}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f45}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a4348}span.s1 {color: #5a4f}span.s2 {color: #303c63}span.s3 {color: #737279}span.s4 {font: 5.0px Helvetica}span.s5 {color: #5a5a63}span.s6 {color: #757479}span.s7 {font: 8.5px Helvetica}span.s8 {font: 8.0px Helvetica}span.s9 {color: #466b}span.s10 {color: #675248}span.s11 {color: #797777}span.s12 {color: #7a7879}span.s13 {color: #5e6b7b}span.s14 {color: #615455}span.s15 {color: #3f353a}50 e−0.03∗0.75e^{-0.03\ast0.75}e−0.03∗0.75N(-0.0228) - 50N(-0.2134) = 3.2 算出,后，是不是需要查表，还是有不查表的方法，，？

2022-09-12 08:13 1 · 回答