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There is a 49 U call option with 199 days to maturity on a stock that is selling at present at 50 U. The annualized continuously compounding risk-free interest rate is 7%. The variance of the stock is estimated at 0.09 per year. Using the Black-Scholes model, the value of the option would be
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which is about 5.85 U.
Let us examine how this result changes by changing the parameters. Increasing the stock price
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the option value increases.
Increasing exercise price
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the option value decreases.
Increasing the risk-free interest rate
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the option value increases.
Increasing the time to expiration
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the option value increases.
Increasing the stock volatility
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the option value increases. Plot the value of the call with respect to the share price.
The upper bound: option is never worth more than the share. The lower bound: option is never worth less than what one would get for immediate exercise of the call.
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