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MMLU-Pro / 212 / Assume the Black-Scholes framework. For t≥0, let S(t) be the time-t…

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question

Assume the Black-Scholes framework. For t≥0t \ge 0, let S(t)S(t) be the time-tt price of a nondividend-paying stock. You are given: (i) S(0)=0.5(ii)ThestockpriceprocessisS(0)=0.5 (ii) The stock price process is \frac{dS(t)}{S(t)} = 0.05dt+0.2dZ(t)where where Z(t)isastandartBrownianmotion.(iii) is a standart Brownian motion. (iii) E[S(1)^\alpha]=1.4,where, where \alphaisanegativeconstant.(iv)Thecontinuouslycompoundedrisk−freeinterestrateis is a negative constant. (iv) The continuously compounded risk-free interest rate is 3%.Consideracontingentclaimthatpays. Consider a contingent claim that pays S(1)^\alpha$ at time 1. What is the time-0 price of the contigent claim?
Plain-text mathematical notation (without MathML)
Assume the Black-Scholes framework. For t≥0, let S(t) be the time-t price of a nondividend-paying stock. You are given:
(i) S(0)=0.5(ii)Thestockpriceprocessis\frac{dS(t)}{S(t)} = 0.05dt+0.2dZ(t)whereZ(t)isastandartBrownianmotion.(iii)E[S(1)^\alpha]=1.4,where\alphaisanegativeconstant.(iv)Thecontinuouslycompoundedrisk−freeinterestrateis3%.ConsideracontingentclaimthatpaysS(1)^\alpha$ at time 1. What is the time-0 price of the contigent claim?
Original LaTeX notation
Assume the Black-Scholes framework. For $t \ge 0$, let $S(t)$ be the time-$t$ price of a nondividend-paying stock. You are given:
(i) $S(0)=0.5
(ii) The stock price process is $\frac{dS(t)}{S(t)} = 0.05dt+0.2dZ(t)$ where $Z(t)$ is a standart Brownian motion.
(iii) $E[S(1)^\alpha]=1.4$, where $\alpha$ is a negative constant.
(iv) The continuously compounded risk-free interest rate is $3%$.
Consider a contingent claim that pays $S(1)^\alpha$ at time 1. What is the time-0 price of the contigent claim?

category

business

options

  1. 1.450
  2. 1.475
  3. 1.415
  4. 1.250
  5. 1.360
  6. 1.390
  7. 1.325
  8. 1.500
  9. 1.287
  10. 1.372

src

theoremQA-Finance

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Source and history

upstream_id / Original problem ID
212
task_id
a258472b-670e-5a1c-b318-35f0102a180f
task_key
default--test--212
task_revision_id
3
config / split
default / test

Official source

initial import