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seven-zhu · 2023年02月26日

如题

NO.PZ2018122701000087

问题如下:

The market price of a European call is $3.00 and its Black-Scholes price is $3.50.The Black-Scholes price of a European put option with the same strike price and time to maturity is $2.00.What should the market price of this put option be?

选项:

A.

$1.50

B.

$2.00

C.

$1.00

D.

$0.50

解释:

A is correct.

考点: Volatility Smile

解析:Based on the put-call parity, Cbs+KerT=Pbs+S0eqTC_{bs}+Ke^{-rT}=P_{bs}+S_0e^{-qT} and Cmkt+KerT=Pmkt+S0eqTC_{mkt}+Ke^{-rT}=P_{mkt}+S_0e^{-qT}

we can know that CbsCmkt=PbsPmktC_{bs}-C_{mkt}=P_{bs}-P_{mkt}

And Cbs =$3.50, Cmkt =$3.00, Pbs =$2.00, so Pmkt =$1.50

The market price of a European call is $3.00 and its Black-Scholes price is $3.50.The Black-Scholes price of a European put option with the same strike price and time to maturity is $2.00.What should the market price of this put option be?


C+K = P + S,K是option的折现,S是stock的折现。题目里面能清晰的判断出C = 3, K = 2, S = 3.5, 所以P = 1.5 我想确认下所以Black-Scholes price在这里就是指的stock的折现价格对吧。

1 个答案
已采纳答案

DD仔_品职助教 · 2023年02月27日

嗨,爱思考的PZer你好:


同学你好,

不是的哦,题目说的是call option的市场价格是3,通过BS模型得出的合理价格是3.5,put通过BS模型得出的合理价格是2,求put的市场价格是多少。

因为call和put都是针对同一个股票,执行价格都一样,所以基于买卖权平价可以写出两个公式:

一个是关于市场价格的:C mkt + PV(K) = P mkt + S

一个是关于BS 模型的:C bs + PV(K) = P bs + S

K和S都一样就可以消掉,最后的公式是C bs​−C mkt​=P bs​−P mkt,代入数据即可反求出P mkt价格。​


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