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# Price, Delta of a Call Option

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Determine the price of a call option assuming that the exercise price is \$45, the value of the stock is \$43, risk -free rate is 3%, standard deviation of 35%, and 6 months to maturity. What is the price sensitivity of the option to changes to the price of the stock? Would the sensitivity be different if the exercise price was \$60?

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** Please see attached file **

Determine the price of a call option assuming that the exercise price is \$45, the value of the stock is \$43, risk -free rate is 3%, standard deviation of 35%, and 6 months to maturity.

We will use Black Scholes model to calculate the price of a call option.
The price sensitivity of the option to changes to the price of the stock is measured by delta
delta = incremental change in price of the option / incremental change in the price of the stock

Value of call= S N(d1) - X * e -r(T-t) * N(d2)
We therefore need to calculate the values of d1 and d2
d1= {ln (S/X) + ( r + ½ s2 ) x (T-t)}/ (s x square root of (T-t))
d2= {ln (S/X) + ( r - ½ s2 ) x (T-t)}/ (s x square root of (T-t)) =d1-s x square root of (T-t)

Inputs

Stock Price= S= \$43.00
Exercise price = X= ...

#### Solution Summary

Determines the price of a call option using Black Scholes option valuation model, and the price sensitivity of the option to changes to the price of the stock.

\$2.19