CAS 2005 Exam: Q#19 Help?

[UCSDKID]

Can someone help me with question #19. I know the answer is probably very easy but I am just not getting it right.
Current Stock Price =15
Exercise Price = 17
Risk Free Rate = 4%
In 1 year the stock will either increase 25% or decrease 10%
What is the price of the european call option? CAS solution = 0.67

My solution:
Scenario A) The stock increases 25%: 15*1.25 = 18.75
Scenario B) The stock decreases 10%: 15*0.9 = 13.5

Profit under scenario A is 18.75 - 17 = 1.75
Profit under scenario B is 0 (don't exercise option)

Expected profit in 1 year = 0.5*1.75+0.5*0 = 0.875

Present value of the call option = 0.875/1.04 = 0.84

What am I doing incorrectly?

[ctperng]

Can someone help me with question #19. I know the answer is probably very easy but I am just not getting it right.
Current Stock Price =15
Exercise Price = 17
Risk Free Rate = 4%
In 1 year the stock will either increase 25% or decrease 10%
What is the price of the european call option? CAS solution = 0.67

My solution:
Scenario A) The stock increases 25%: 15*1.25 = 18.75
Scenario B) The stock decreases 10%: 15*0.9 = 13.5

Profit under scenario A is 18.75 - 17 = 1.75
Profit under scenario B is 0 (don't exercise option)

Expected profit in 1 year = 0.5*1.75+0.5*0 = 0.875
Present value of the call option = 0.875/1.04 = 0.84

What am I doing incorrectly?

The question says that the stock would either go up or down by certain percentages, but it doesn't provide the probability of going up or down. To solve this, you use the relation r_f = E(r), where r_f is the risk-free rate and r is the return on the stock. Once you get the probability, plug in back to your formula to get the final result.

ctperng

[UCSDKID]

The question says that the stock would either go up or down by certain percentages, but it doesn't provide the probability of going up or down. To solve this, you use the relation r_f = E(r), where r_f is the risk-free rate and r is the return on the stock. Once you get the probability, plug in back to your formula to get the final result.

ctperng

Thank you! That makes perfect sense. I am able to get the answer now.

I knew it was easy and I was just missing something.

[Aardvark]

Just like what CTPERNG said. I think the solution be the following. Even though I may be wrong.

(A)
[18.75*P+ (1-P)13.5]/15=1.04 P=0.4

[0.4*(18.75-17)]/1.04=0.6731

or

(B)

[18.75*((18.75-17)/(18.75-13.5))] -Debt Repayment= 1.75

Debt Repayment=4.5

15 *((18.75-17)/(18.75-13.5))-4.5/1.04=0.6731

Good Luck!! everybody!!! :guitarwo: :guitarwo: