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Asian Put Options & European Hedging Options

Posted by:Prof. Lexx Posted on:May 6,2016
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Problem 1) Pricing Asian Put Option

Stock current price S0: 100

Driftm: 0.08 (annual)

Volatility s: 0.12 (annual)

Exercise price K: 97

Period length Dt: 1/52 yr (week)

Expiration time T: 1 yr

Risk-free rate r: 0.059

Sample size: 1000 (runs/replications/years)

Q0: Plot the sample paths {St} for the first 3 runs (each is 1yr starting with S0). Are there any patterns?

Q1: What is the distribution (histogram) of R0?

Q2: How should it the put option be priced, i.e., E[R0]=?

Q3: What is the probability Pr[R0>1.1]?

Q4: Answer Q1, Q2, Q3 for Asian call option

Problem 2) Financial Hedging

Stock current price S0: 100

Drift m: 0.08 (annual)

Volatility s: 0.12 (annual)

Time delay (maturity) t: 0.5 (year)

Risk-free rate r: 0.059

Put option price c: 0.57

Exercise price K: 97

Sample size N: 2000

Q1: What is the distribution of the stock price St? mean and its 95% CI? Downside risk P(St –S0

Q2: What is the distribution of R0 (the present value of the payoff of the put option)? How should it the put option be priced, i.e., E[R0]=? What is its 95% CI? Is .57 in the CI?

Q3: Compare the return of the next two investment strategies. Which one is riskier? Why? Draw your conclusion by the comparison of the distribution; mean; variance; downside risk of each strategy.

Stock only (no hedging)

Stock plus put option (hedging)

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Prof. Lexx

Overview I have a Bachelor of Arts, majoring in English and minoring in History. I have worked in various fields ranging from academic research to freelance translating to editing to customer support and data entry. These include editing my old university's newspaper as well as co-leading their creative writing team; serving as a junior member in the history department's research network; publishing music and film reviews for several different magazines and webzines; and translating papers and books for numerous researchers in various languages, including Russian, Spanish, and Romanian. I am also a skilled typist, with a rate of at least 70 words per minute, and have myself digitized dozens of books and essays for both private and commercial use. I have a very strong work ethic, and make sure to prioritize the task I am given so that it is completed as quickly as possible. I am organized and disciplined, ensuring a job done professionally and efficiently.

    I have a background of 8 years in writing profession and currently pursuing also as an editor and proofreader. I have a knack for writing and thus, it was obvious to enhance my skills and serve others. Currently joined ‘Member of Association of Professional Writers and Editors’ a

    Pro Alex
    USA