# Probability-Option crossover question

HI can anyone help with these two example questions? I’m stuck. Thanks

1. If chances are 22% that a \$30 put will expire in the money and 25% that the \$40 call will expire in the money and you buy a 30 call and sell a 40 call then what is the probability… A) that the combination is worth less than \$10 on expiration? B) that the combination is worth more than \$10 on expiration? C) that the combination is worth zero on expiration?

(Not multiple choice, need 3 answers)

Thanks!

1. Buy 30 call / sell 40 call is a bull call spread with max payoff \$10 as follows:
• if stock

• if \$30<=stock price<=\$40, payoff increases linearly from 0 (if stock price =\$30) to \$10 (if stock price=\$40)

• if stock price>\$40, payoff = \$10

A) that the combination is worth less than \$10 on expiration?

this is the probability that stock price\$40 (i.e. 1 minus prob. \$40 call will end up in the money) = 1-0.25=75%

B) that the combination is worth more than \$10 on expiration? 0

the payoff for a bull call spread cannot exceed the difference in strikes

C) that the combination is worth zero on expiration?

this happens when stock price <=\$30, the probability of which is the same as prob. of \$30 put in the money = 22%

1. A is true,

B is false because the statement makes reference to “terminal stock price that has the greatest probability” i.e. a point probability, which is zero

C is true

D is false

E is false. I’d think that the 1000 independent trades would have a total expected profit with some statistical distribution. Hence the actual profit might vary per the distribution and could differ from the “expected” value.