CAS 3 S07

[Howard Mahler]

The CAS Exam 3 for Spring 07 has been posted.

http://www.casact.org/admissions/studytools/exam3/

Those taking MFE might want to look at the questions on Financial Economics,
since they are our first example of actual exam questions on this subject.

Skip question 36.

I would skip poorly worded statement III of Q. 33.

Q.35 should read S(t) = S(0) exp[(alpha - delta - sigma^2/2)t + sigma Z(t)].
Where the sigma Z(t) is inside the exponential.

Financial Economics: 3, 4, 12-17, 20-21, 32-37.

Life Con.: 5-9, 24-27, 38-39.

Stochastic Models: 1, 2, 28, 40.

Statistics (CAS only): 10, 11, 18, 19, 22, 23, 29-31.

Howard Mahler

[mmamin]

would somebody be kind enough to give the complete solutions to the CAS 3 exam administered, it would certainly help all of those taking the exam on May 17th. If not for the whole exam, atleast the MFe part/questions that Mahler mentioned above

[nittanylions]

I found most of them to be pretty straight-forward. I don't particularly feel like posting every solution, but if you have any questions on a specific problem, I'll try my best to post a clear solution.

[nkt]

I get that sigma = .2 and K = 40 but I don't get the final answer. In fact, do we use the profit formula:
Profit=-[C(S1)-C(S0)] + delta*(S1-S0) - (exp(r/365)-1)*(delta*S0-C(S0))?
If so, then the first term, the difference in the call prices is given to us to be $56.08 and i calculated delta=.54014 and C(S0)=3.32681. If I substitute in the above equation, I don't get the answer.

Could anyone help me with what I am doing wrong; thanks a lot.

[nittanylions]

My understanding of the problem is that the stock increased by $1 immediately, so the price of one call option increased by $56.08. Since the market-maker sold 100 call options, the first component of his profit is a loss of $56.08 * 100 = $5608.

Next, I figured out that delta = e^-divrate*T*N(d1) = e^-.07*.5793 = .5401
Therefore, in order to delta-hedge, he purchases .5401 * 100 (shares per option) = 54.01 shares of stock PER OPTION he sold. Since he sold 100 options, he purchases 54.01 * 100 = 5401 shares of the stock. The $1 increase in stock price therefore increased the market makers profit by $5401 (the numbers of shares owned * the increase).

Since the stock price increase was immediate, no interest is paid on the borrowed amount.

Profit = -5608 + 5401 - 0 = -$207

This coincides with answer choice C (between -800 and 0 dollars).

[nkt]

Thanks nittanylions! Your solution makes sense. There is a bit of too much information in this problem though, which ends up unused. I guess that confused me.

[KingWithoutACrown]

Now if the SOA exam looks similiar to this, then I'll be a happy camper.

[GeekGoddess]

Thanks nittanylions! Your solution makes sense. There is a bit of too much information in this problem though, which ends up unused. I guess that confused me.

I have a feeling that is how most of the questions will be. At least that is what I have noticed in doing the Derivatives markets problems.

[CaptainAwesome]

Now if the SOA exam looks similiar to this, then I'll be a happy camper.

Agreed. There's no way MFE can be that easy...is there? I thought that CAS exams, as a rule, are harder.

[jenn3539]

Agreed. There's no way MFE can be that easy...is there? I thought that CAS exams, as a rule, are harder.

Well, there were three other topics on the exam, too.

[Howard Mahler]

Professor Broverman has posted his solutions to the CAS 3 Exam.

http://www.sambroverman.com/07s-cas3sol.pdf