Binomial pricing: Consider two call options written on different shares. 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 share 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, Ltd., whose current share price is also $16. One year from now shares of HighVol Ltd. will either rise to $22, or fall to $0. The risk-free interest rate is 0 per cent. Which call option is worth more?

Question

Quizplus · Accepted Answer

To calculate the value of each call option using binomial pricing, we need to first calculate the probabilities of the share price rising or falling for each company.

For LowVol Co., the probability of the share price rising is 0.5 and the probability of the share price falling is also 0.5. Using the binomial pricing formula, the value of the call option on LowVol Co. is:

(Value if share price rises x Probability of rise) + (Value if share price falls x Probability of fall)
= ($3 x 0.5) + ($0 x 0.5)
= $1.50

For HighVol, Ltd., the probability of the share price rising is 0.5 and the probability of the share price falling is also 0.5. Using the binomial pricing formula, the value of the call option on HighVol, Ltd. is:

(Value if share price rises x Probability of rise) + (Value if share price falls x Probability of fall)
= ($7 x 0.5) + ($0 x 0.5)
= $3.50

Therefore, the call option on HighVol, Ltd. is worth more than the call option on LowVol Co.

Binomial Pricing: Consider Two Call Options Written on Different Shares