Probability-Option crossover question

CFA Level I Derivatives
#1

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)

  1. Which of the following are true for the “Expected Profit” on a stock option trade? (terminal stock price = stock price at the expiration of the option) A. For a call The greater of (the terminal stock price minus the strike or zero) minus the premium is the “Expected Profit” For a put The greater of (the strike minus the terminal stock price or zero) minus the premium is the “Expected Profit” B. For a call The greater of (the terminal stock price that has the greatest probability minus the strike or zero) minus the premium is the “Expected Profit” For a put The greater of (the strike minus the terminal stock price that has the greatest probability or zero) minus the premium is the “Expected Profit” C. For a call (the sum of the greater of (the stock price minus the strike or zero) at each potential stock price multiplied by the probability of that stock price being the terminal stock price) minus the premium is the “Expected Profit” For a put (the sum of the greater of (the strike minus the stock price or zero) at each potential stock price multiplied by the probability of that stock price being the terminal stock price) minus the premium is the “Expected Profit” D. For a call (the sum of the greater of (the stock price minus the strike or zero) at each potential stock price multiplied by the probability that the terminal stock price will exceed that stock price) minus the premium is the “Expected Profit” For a put (the sum of the greater of (the strike minus the stock price or zero) at each potential stock price multiplied by the probability that the terminal stock price will be below that stock price) minus the premium is the “Expected Profit” E. The sum of the “Expected Profit” on one thousand independent option trades will be very close to the sum of the actual profit on those same trades. (Please give True / False for A through E)

Thanks!

#2
  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.