TUTORIAL $3$

GOOGL is currently priced at R$60.$ You want to determine the price of the stock in $1$

year.

You believe there is a $20\%$ chance that the stock will increase by a factor $1\mathrm{.}8$ or decrease

by a factor $0\mathrm{.}7.$

A call option on GOOGL with an exercise price of R$50$ that expires in one year.

Calculate:

a$)$ the price of the stock in the event of an increase

b$)$ the price of the stock in the event of a decrease

c$)$ the value of the call option in the up state

d$)$ the value of the call option in the down state

An American$-$style call option with nine months to maturity has a strike price of R$50.$ The

underlying stock now sells for R$62.$ The call premium is R$15.$

a$.$ What is the intrinsic value?

b$.$ What is the time value?

Discuss the relationship between option prices and time to expiration, volatility of the

underlying stocks, and the exercise price.