You have the following data: S= 50; X= 45; R f = 6%, ^2= 20%; and T=

You have the following data: 

S= 50; X= 45; R_f = 6%, σ^2= 20%; and T= 3 months.

1. Find the value of the call using an excel spread sheet. It should equal $7.62.

2. Using the data above, find the value of the call for a range of stock prices, say from $5 to $300 in increments of $5. Plot these values in excel. Comment on how the value approaches certain limits, i.e. when the option is deep in the money, what is the limit on the value of the option. What happens to the time value of the option? 

3.  Find the value of the call for a range of volatilities.  Plot these values in excel.  I would suggest going from 5% to 300%. 

4.  Find the value of the call for a range of exercise prices say from $5 to $100 in increments of $5.  Plot these values in excel. 

5. Find the value of the call for a range of maturities say from 1 month to 12 months.  Plot these values in excel. the stock price was set at $50, the exercise price at $45, the risk-free rate at 0.06, the variance at 0.2, and the time in years at 0.25. By plugging these values into the formula, the base value of the call was calculated at $7.62:

            Stock Price (S)            50

            Exercise Price (X)       45

            Risk-Free Rate (RD    0.06

            Variance (o)                 0.2

            Time in Years (T)        0.25