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    Use the Black-Scholes Model to find the price for a call option with the following inputs: (1) current stock price is $30, (2)excise price is $35, (3) time to expiration is 4 months, (4)annualized risk-free rate 5%, AND (5) variance of stock return is 0.25.

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    1. Use the Black-Scholes Model to find the price for a call option with the following inputs: (1) current stock price is $30, (2)excise price is $35, (3) time to expiration is 4 months, (4)annualized risk-free rate 5%, AND (5) variance of stock return is 0.25.

    2. The current price of a stock is $15. In 6 months, the price will be either $18 or $13. The annual risk-free rate is 6 percent. Find the price of a call option on the stock that has an excercise price of $14 and that expires in 6 months. Hint, use the daily compounding.

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    Solution Preview

    Question 1
    The B-S formula for call options is the following:

    c = S*N(d1) - X*exp(-r(T-t))*N(d2)

    where

    S is the price of the underlier (price of the stock) = $30
    r is the risk free interest rate = 0.05
    T - t is the time left to expiry = 1/3 (four months, or one third of a year)
    X is the strike price = $35
    N( ) is the the cumulative distribution function for a standard normal random variable.

    and

    d1 = ( ln(S/X) + (r +0.5*s^2)*(T - t ) ) / (s*sqrt(T-t))
    d2 = d1 - s*sqrt(T-t)

    where s^2 is the variance of the stock = 0.25 (so s = 0.5)

    After plugging all the appropiate values, we get:

    d1 = -0.3319...
    d2 = -0.6206...

    c = 1.8938...

    So ...

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