Question

In any given one-year period, a stock will either go up by 30% or down by 15%. r=10%. The stock is worth $40 today.

It pays a 4% dividend.
a. Using a two-period binomial model, find the value of a two-year put with strike=$35.
b. Assume that you buy the option in part a. Also assume that the stock goes down over the first year. At this
point (at t=1), how sensitive is the option’s price to stock price movements... more specifically, if the stock would go up
by one dollar (instantaneously at t=1), what do you think would happen to the value of your option?
c. Assume that you own the option in part a. Also assume that the underlying stock has an expected return of
15%. At t=0, what is the expected return of the option? (do something similar to what we did in class on Tuesday... the
expected return of a portfolio is the weighted average of the expected returns of the things in the portfolio)

Answer 1

Finance questions involve using a two-period binomial model for option valuation, assessing option sensitivity to stock price movements, and calculating expected returns considering dividends and capital gains. The probability calculations for a stock's value are based on a uniform distribution.

Step-by-step explanation:

The questions posed revolve around stock price movements and option valuation within a binomial model framework, considering dividends, capital gains, and option sensitivity to price movements. In the context of finance and investments, a two-period binomial model is used to estimate the potential future value of a stock and derivative securities, such as options, over a discrete number of time periods. A put option provides the option buyer with the right to sell a stock at a predetermined price (strike price), and its value is influenced by stock price movements, volatility, time to expiration, and interest rates. Option sensitivity to stock price movements is often assessed by the 'delta', which represents how much an option's price moves for a one-dollar change in the underlying stock price. Expected returns are calculated based on the probability-weighted outcomes of the possible rates of return, considering the direct payments made to shareholders via dividends and the increase in the value of the asset, known as capital gains.

For question 83, the uniform distribution of stock values is used to calculate probabilities of the stock being within or above a certain price range. Subject to this distribution, specific probabilities and quartile values are determined, demonstrating the application of basic statistical concepts in finance.