Binomial pricing: Consider two call options written on different stocks. Both call options have a strike price of $15 and expire one year from today. The first option is written on LowVol Co., whose current stock price is $16. One year from now, shares of LowVol Co. will either rise to $18 or fall to $14. The second option is written on HighVol, Inc., whose current stock price is also $16. One year from now shares of HighVol Inc. will either rise to $22, or fall to $0. The risk-free interest rate is 0 percent. Which call option is worth more?

Question

Quizplus · Accepted Answer

Using the binomial pricing model, we can calculate the value of each call option. For the call option on LowVol Co., there are two possible outcomes: the stock price will either rise to $18 or fall to $14. The probability of the stock price rising is 0.5, and the probability of the stock price falling is 0.5. Using the binomial pricing model, we get:

Value if stock price rises to $18: $3
Value if stock price falls to $14: $0

Expected value of call option on LowVol Co.: $1.50

For the call option on HighVol Inc., there are also two possible outcomes: the stock price will either rise to $22 or fall to $0. The probability of the stock price rising is 0.5, and the probability of the stock price falling is 0.5. Using the binomial pricing model, we get:

Value if stock price rises to $22: $7
Value if stock price falls to $0: $0

Expected value of call option on HighVol Inc.: $3.50

Therefore, the call option on HighVol Inc. is worth more.

Binomial Pricing: Consider Two Call Options Written on Different Stocks