The Greek Letters Hull Chapter 15

[Genki]

So, I was doing problem #14 in the Hull book end of chapter 15 questions. Most of the necessary equations are not in the FET Formulae sheet provided by the SOA. These are pretty long formulas. Do any of you think it is actually worthwhile to memorize them? Or do you think the SOA left them off because we don't need to know them?

I'm specifically referring to the formulas for Gamma, Theta, Vega, and Rho. The only formula in the formulae sheet is the one for Delta.

:oops:

[campbell]

I would not memorize the formulas for the Greeks. I would memorize what each of them means.

There was a question on Fall 2006 8V on graphing the Greeks for a certain situation, as they vary in time (I think) -- it involved qualitatively reasoning through how they behave, and did not require knowing analytic formulas for the Greeks in question.

[yanz]

I think C6 had a Q on the greeks last year - I skipped it so I can't remember whether it asked for formulas or not, but I think it might have...

I realize that the syllabus for C6 was different, but the reading about the greeks on C6 was much less intense than the Hull chapter, so it wouldn't surprise me...

[_BullDog_]

I've decided not to memorize these formulas. My thinking is they gave us a formula sheet and left of some formulas. Most of them are easy so I would think it wouldn't take much time to learn and could be asked. These however I feel should be on the formula sheet if they wanted us to use them. After all the reason for the formula sheet is to keep us from spending time memorizing formulas.

[yanz]

I've decided not to memorize these formulas. My thinking is they gave us a formula sheet and left of some formulas. Most of them are easy so I would think it wouldn't take much time to learn and could be asked. These however I feel should be on the formula sheet if they wanted us to use them. After all the reason for the formula sheet is to keep us from spending time memorizing formulas we obviously won't need.
IFYP
My bet is that the formulas not on the sheet are the ones that will be "tested" but what do I know...

[Kippy]

gamma and vega can be derived from b-s pretty quickly. as for the others, im on the fence as to whether to memorize or leave to fate

[TiderInsider]

Gamma I just memorize
Vega has all the same terms as Gamma (except sigma...obviously) so that ones easy too
Rho (for a call) take the derivative of BS with respect to r...what do you get? KT^-rT*N(d2). I know that's technically not how to derive it, but that works for me
I get theta by using the same method as for Rho, but I remember that first term.

[carzymathematician]

Gamma I just memorize
Vega has all the same terms as Gamma (except sigma...obviously) so that ones easy too
Rho (for a call) take the derivative of BS with respect to r...what do you get? KT^-rT*N(d2). I know that's technically not how to derive it, but that works for me
I get theta by using the same method as for Rho, but I remember that first term.

Theta is way too long for me so I've skipped that but I have memorized all the others. Still not sure how to derive the graphs though. Oh well..:roll:

[TiderInsider]

Theta is way too long for me so I've skipped that but I have memorized all the others. Still not sure how to derive the graphs though. Oh well..:roll:Remembering Theta only involves remembering the first term...the rest can be gotten by taking the "derivative" with respect to T.

[Eroboy]

So, I was doing problem #14 in the Hull book end of chapter 15 questions. Most of the necessary equations are not in the FET Formulae sheet provided by the SOA. These are pretty long formulas. Do any of you think it is actually worthwhile to memorize them? Or do you think the SOA left them off because we don't need to know them?

I'm specifically referring to the formulas for Gamma, Theta, Vega, and Rho. The only formula in the formulae sheet is the one for Delta.

:oops:


You can get Gamma by differentiate Delta, which is just N(d1')*(d(d1)/d(s)), the formula sheets has the N(d1') and (d(d1)/(d(s)) is straight forward, so you can easily derive the gamma.

The formula sheet also provides the relationship between gamma, theta, delta and the portfolio value, the BS PDE form. With gamma and delta, and call or put formula, you can derive theta.

For the rho, if you know S*N(d1')=Kexp((-r)*T)*N(d2'), you can derive the rho by differentiate call option and get the rho.

For Vega, you probably have to remember it, since the deriviation is time consuming.

[carzymathematician]

The formula sheet also provides the relationship between gamma, theta, delta and the portfolio value, the BS PDE form. With gamma and delta, and call or put formula, you can derive theta.

This is certainly good to know since the only one that I refuse to memorize is theta!

[TiderInsider]

This is certainly good to know since the only one that I refuse to memorize is theta!If it comes up on the exam I'm going to answer

Theta = Your mom never loved you*

*yes, grader, I'm talking to you!

[rekrap]

I would not memorize the formulas for the Greeks. I would memorize what each of them means.

There was a question on Fall 2006 8V on graphing the Greeks for a certain situation, as they vary in time (I think) -- it involved qualitatively reasoning through how they behave, and did not require knowing analytic formulas for the Greeks in question.

20. (6 points)
(a) (1 point) Define the following Greeks:
(i) Delta
(ii) Gamma
(iii) Rho
(iv) Vega
(b) (2 points) Sketch the curve of each of the above Greeks as a function of time to maturity for an at-the-money put option on a non-dividend paying stock.
(c) (3 points) Explain the reasons for the shapes of the curves in (b).

Course 8V 1106 (http://www.soa.org/files/pdf/Course%208V_1106.pdf) [pdf]

[rekrap]

I think C6 had a Q on the greeks last year - I skipped it so I can't remember whether it asked for formulas or not, but I think it might have...

I realize that the syllabus for C6 was different, but the reading about the greeks on C6 was much less intense than the Hull chapter, so it wouldn't surprise me...

Course 6: Spring 2006
Afternoon Session
13. (5 points)
(a) Describe delta, gamma and theta as they apply to derivatives.
(b) You are given the following for a one-year European call option that can be
valued using a binomial model:
• Number of time intervals: 25
• Value of call option: 0.1
Node (i, j) (1, 0) (1, 1) (2, 0) (2, 1) (2, 2)
S (i, j) 1.25 1.50 1.40 1.65 1.60
V (i, j) 0.25 0.30 0.15 0.20 0.10Calculate delta, gamma and theta at node (0, 0).
Show all work.
Course 6Spring 06 (http://www.soa.org/files/pdf/06-SOA-Course6Spring.pdf) [pdf]

[Car'a'carn]

Course 6Spring 06 (http://www.soa.org/files/pdf/06-SOA-Course6Spring.pdf) [pdf]

This one may not count since we have the continuos case only on the syllabus.

[rekrap]

This one may not count since we have the continuos case only on the syllabus.

Part (a) is generic enough to still apply, I'm sure.
I was just substituting memories with tests... :tup:

[rekrap]

If it comes up on the exam I'm going to answer

Theta = Your mom never loved you*

*yes, grader, I'm talking to you!

Send that to the test writer. You want the grader on your good side. I wouldn't even ask the grader to pass that along to the writer, as he/she might be offended by the request. I would try a joke instead, such as,
Q. Why did theta sit out in the sun?
A. Because it wanted a tan!

[TiderInsider]

Send that to the test writer. You want the grader on your good side. I wouldn't even ask the grader to pass that along to the writer, as he/she might be offended by the request. I would try a joke instead, such as,Of course I was kidding, but I thought the writer/grader were one in the same...they don't have that many folks working on this exam do they?

[rekrap]

Of course I was kidding, but I thought the writer/grader were one in the same...they don't have that many folks working on this exam do they?

Check out page 65-67 of last year's yearbook (http://www.soa.org/files/pdf/about-2006-yearbook.pdf) [pdf] for the 8F and 8V writers and graders.

[TiderInsider]

Check out page 65-67 of last year's yearbook (http://www.soa.org/files/pdf/about-2006-yearbook.pdf) [pdf] for the 8F and 8V writers and graders.:notworth:

[zjmgyx]

I think theta can be memorized via ITO Lemma?
r*option=theta+delta*r*stock price+1/2*gamma*(sigma*stock price)squared?

[yanz]

I just tried this for a call and I only got 2 of the 3 terms for theta because delta*r*S cancelled with the first term of r*option. This left me with only the gamma term and the second term of r*option --ie, only 2 terms. I'm missing the term that starts with q.
Did I mess up the algebra or am I missing something? Or does this method not work?

[yanz]

I just tried this for a call and I only got 2 of the 3 terms for theta because delta*r*S cancelled with the first term of r*option. This left me with only the gamma term and the second term of r*option --ie, only 2 terms. I'm missing the term that starts with q.
Did I mess up the algebra or am I missing something? Or does this method not work?

ETA: ok, I just tried the put and came out with the same issue. I have no idea where the q term comes from, since I don't see anything with a q in it.

help!

[TiderInsider]

I think the BS PDE assumes that no dividend are paid.

If you really want to remember it...just get that first term, the rest can be done from an oversimplified chainrule approach.

[yanz]

I think the BS PDE assumes that no dividend are paid.

ah! that would explain why I had no q's. thanks.

[zjmgyx]

ah! That make sense!

[zjmgyx]

Try this:

modify the GBM process to adjust q for stock price.

dS=(r-q)*mu*Sdt+sigma*Sdz

the BSPDE will be:
r*option=theta+delta*(r-q)*stock price+1/2*gamma*(sigma*stock price)
squared

The theta is easy to get.

[yanz]

thanks - I'll try that :tup: