$8$ Excel Activity: Black$-$Scholes Model

Start with the partial model in the file Ch$05$ P$09$ Build a Model.xlsx$.$ You have been given the following information for a call option on the stock of Puckett Industries: P $=$ $$53\mathrm{.}00,$ X $=$ $$56\mathrm{.}00,$ t $=0\mathrm{.}50,$ rRF $=6\mathrm{.}00\%,$ and $\backslash$sigma $=0\mathrm{.}45.$

The data has been collected in the Microsoft Excel file below. Download the spreadsheet and perform the required analysis to answer the questions below. Do not round intermediate calculations. Round your answers to the nearest cent.

Download spreadsheet Ch$05$ P$09$ Build a Model$-49$efb$8.$xlsx

Use the Black$-$Scholes option pricing model to determine the value of the call option.

$ fill in the blank $2$

Suppose there is a put option on Puckett's stock with exactly the same inputs as the call option. What is the value of the put?

$ fill in the blank $3$Black$-$Scholes Model

$\backslash$table$[[$Current price of the underlying stock, P$,$$$53,00],[$Strike price of the option, x$,$$$56,00],[$Time until the option expires, t$,0,50],[$Risk$-$free interest rate, r$\_($RF$),6,00\%],[$Standard deviation of the rate of return on the stock, $\backslash$sigma $,0,45]]$

a$.$ Using the Black$-$Scholes option pricing model to determine the value of the call option

$d_1$

Formulas

$d_2$

$N(d_1)$

$N(d_2)$

Value of the call option, $V_C$

#N$/$A

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b$.$ Using the Black$-$Scholes option pricing model to determine the value of the put option

Value of the put option, $V_P$

#N$/$A