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    Binomial Model

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    How can I use binomial model to answer to the following questions?

    Consider the stock with the current price of $20. It pays no dividends.

    1) Maturity: in 4 months
    Strike price:$20
    Volatility = 30% per annum
    Risk-free rate: 10%
    What's the value of European call option?

    2) What would be the value of option in 1), if you expect volatility over the next 4 month to be 20%?

    3) Given the information in 1) and the expectation declared in 2), what option priced position should we take on?

    4) Given that volatility = 30% per annum, what would be the replicating portfolio for the option?

    5) What's the price of European put using put-call parity and volatility = 30% per annum?
    What's the price of American put using put-call parity and volatility = 30% per annum?

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    https://brainmass.com/business/options/binomial-model-18234

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    1) To be able to solve this problem, and the subsequent ones, we must first set up the problem with the data we are given. We have the following situation:

    The binomial tree shown above can be used to calculate the price of the option today. We will use the following terminology:

    C = Value of the call option today
    X = Exercise price = $20
    T = Time period for which the option is active = 4 months = 4/12 years
    R = Risk-free interest rate = 10%
    S = Price of the stock today = $20
    Su = Price of the stock after one year in the up state
    Sd = Price of the stock after one year in the down state
    Cu = Value of the option after one year in the up state
    Cd = Value of the option after one year in the down state
    u = Stock return in the up state
    d = Stock return in the down state
    Pr = Risk-neutral probability of a stock movement in the up state
    (1 - Pr) = Risk-neutral probability of a stock movement in the down state

    We will use the following formulas using binomial risk-neutral option pricing:

    (1)
    (2)

    First we calculate the stock returns in both states:

    Su = S*1.30 = ...

    Solution Summary

    The expert examines binomial models for current price.

    $2.19

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