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# Black-Scholes Option Pricing Model: Call option

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Can I find the probabilities using Excel?
A firm wants one to show what they know about the Black-Scholes option pricing model through finding the call price of an U.S call option with the following characteristics:

stock price = \$60
exercise price = \$60
risk-free rate is 12%
volatility (variance of stock returns) = 9% per year
time to maturity = 6 months

#### Solution Preview

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The Black-Scholes model is used to build a riskless hedge, where the investor will earn the risk-free rate.

Step 1. Using the Black-Scholes Option Pricing Model, calculate the current value of a call option = V= P[N(d_1 )]-Xe^(-rrf)(t) [N(d_2 )]
d_1=(ln(P/X)+[rrf+(sigma2/2)]t)/(sqrt sigma*t) and d_2=d_1-Vsigmat

Where P = current price of the underlying stock, X = ...

#### Solution Summary

This solution explains in-detail how to solve the price of a call option using the Black-Scholes Option Pricing Model. The solution outlines each step of the pricing model and explains how the probabilities can be found using Excel.

\$2.19