Option pricing - Multiperiod binomial approach The value of an option can be calculated by using a step-by-step approach in the case of single periods or by using sophisticated formulas that can be easily created through a spreadsheet. In the real world, two possible outcomes for a stock price in six months is an assumption. The stock markets are volatile, and stocks move up and down based on market- and firm-specific factors.
Use the following formula to calculate the value of any call option within the same time period.
VcVc=Cu[erRF(t/n)−du — d]+Cd[u−erRF(t/n)u — d]erRF(t/n)Cu[erRF(t/n)−du — d]+Cd[u−erRF(t/n)u — d]erRF(t/n)
Based on your understanding of the binomial option pricing model, is the following statement true or false?
∏u∏u is the price of an option that will return $1 if the price of the underlying stock goes up and $0 if the price of underlying stock goes down.
a. False
b. True
You have the following information about LearnMore Inc.’s stock and a two-month call option with a strike price of $140.00. LearnMore Inc.’s current stock price is $100.00. You are using the multiperiod binomial option pricing model to find the value of the two-month option with two periods. ∏u∏u and ∏d∏d values given here apply to any period. Data Collected for LearnMore Inc.
u 1.5032
d 0.5922
∏u∏u 0.2357
∏d∏d 0.3555
You work with a junior analyst to calculate the value of the option, and she submits her inferences to you. Which of the following points are true in the case of LearnMore Inc.’s stock options?
a. LearnMore Inc.’s stock price after two months likely will be $150.32 if the stock goes up by a factor of 1.5032.
b. The value of the call option will always remain $2.43, irrespective of the time until expiration.
c. The option payoff if the stock goes up in two months will be $10.32.
d. The value of the two-month call option with a strike price of $140.00 at the end of two months will be $2.43.