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xiaobaicp3 · 2025年03月23日

为什么现价用期货折现时,T也等于0.5,而不是等于18/12呢

NO.PZ2023091802000210

问题如下:

A derivatives dealer actively trades options on various underlying assets with its clients. The firm wants to apply the Black-Scholes-Merton (BSM) model to price a call option on a futures contract. Relevant data is provided below:

· Current futures price: EUR 63

· Strike price of the option: EUR 68

· Time to expiration of the option: 6 months

· Time to maturity of the underlying futures contract: 18 months

· Continuously compounded annual risk-free interest rate: 3%

· N(d1): 0.4678

· N(d2): 0.3449

Which of the following is closest to the value of this option estimated using the BSM model?

选项:

A.

EUR 5.75

B.

EUR 5.93

C.

EUR 6.36

D.

EUR 6.81

解释:

B is correct:

The option on futures using the BSM model is expressed as follows:

c = F0erTN(d1) KerTN(d2)

where:

F0 = current futures price = EUR 63

K = strike price of the option on futures = EUR 68

T = time to expiration of option = 0.5

r = risk-free interest rate = 3%

N(d1) = 0.4678

N(d2) = 0.3449

Therefore,

c=63 * e0.03 * 0.5 * (0.4678) 68 * e0.03 * 0.5 * (0.3449)=EUR 5.9286

A is incorrect. This values the option using the time to maturity of the futures contract rather than the time to expiration of the option.

C is incorrect. This omits the “erT” from the futures price term in the equation.

D is incorrect. This multiplies the futures price by eqT instead of e-qT in the equation.

如题

1 个答案

李坏_品职助教 · 2025年03月23日

嗨,爱思考的PZer你好:


这道题分析的是期权的价格,所以BSM定价公式里面的T指的是期权的期限,那也就是· Time to expiration of the option: 6 months。


等到了6个月之后,期权就到期了,至于期权的标的资产(标的资产就是期货)是什么时候到期,与本题无关了。

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NO.PZ2023091802000210 问题如下 A rivatives aler actively tras options on various unrlying assets with its clients. The firm wants to apply the Black-Scholes-Merton (BSM) mol to pria call option on a futures contract. Relevant ta is provibelow:· Current futures price: EUR 63· Strike priof the option: EUR 68· Time to expiration of the option: 6 months· Time to maturity of the unrlying futures contract: 18 months· Continuously compounannurisk-free interest rate: 3%· N(): 0.4678· N(): 0.3449Whiof the following is closest to the value of this option estimateusing the BSM mol? A.EUR 5.75 B.EUR 5.93 C.EUR 6.36 EUR 6.81 B is correct:The option on futures using the BSM mol is expressefollows:c = F0e−rTN() − Ke−rTN()where:F0 = current futures pri= EUR 63K = strike priof the option on futures = EUR 68T = time to expiration of option = 0.5r = risk-free interest rate = 3%N() = 0.4678N() = 0.3449Therefore,c=63 * e−0.03 * 0.5 * (0.4678) − 68 * e−0.03 * 0.5 * (0.3449)=EUR 5.9286A is incorrect. This values the option using the time to maturity of the futures contrarather ththe time to expiration of the option.C is incorrect. This omits the “e−rT” from the futures priterm in the equation.is incorrect. This multiplies the futures prieqT insteof e-qT in the equation. A rivatives aler actively tras options on various unrlying assets with its clients. The firm wants to apply the Black-Scholes-Merton (BSM) mol to pria call option on a futures contract. Relevant ta is provibelow:· Current futures price: EUR 63· Strike priof the option: EUR 68· Time to expiration of the option: 6 months· Time to maturity of the unrlying futures contract: 18 months· Continuously compounannurisk-free interest rate: 3%· N(): 0.4678· N(): 0.3449Whiof the following is closest to the value of this option estimateusing the BSM mol?

2024-07-29 16:32 1 · 回答