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Delta Gamma Approximation using Taylor formula

jyothi1965

New Member
Hi David


This is pretty obvious one, but then I thought it would be useful to check your views on this:

As you would have seen, the second part of the formula for D-G approx (.5)*Gamma*(Stockprice^2 is approximated to (delta + gamma) by Meissner in Chap 6 (assigned reading). He calls this as "trading practice"

In a typical FRM question I am sure there will be two choices with both these methods!!! Which one will be the right answer?

Further what I find weird is that he has extended the concept of delta and gamma to credit assets (what does this mean) and comes up with credit delta and credit gamma!! ...weird I thought that deltas and gammas apply to options, so is he talking of bond options. (same chapter as the above)

Or he is talking of (duration + convexity) and calling it a sophisticated new fangled term!!!!

Jyothi
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi Jyothi,

Yes, I only worry that you know too much for the exam :). This is important, the test will only use the Meissner approximation, as evidenced by the example workouts:

http://www.bionicturtle.com/images/forum/betaStar.jpg

The Taylor series is an approximation. The (delta + gamma) is an approximation on same: an approximation of an approximation. It would NOT be incorrect to use, instead, (0.5)(Gamma) but the test here will ONLY use the above approximation.

On language, delta is really a mathematical thing, a first derivative. Gamma, a second derivative. So, they can find application on any x-y relationship. Duration is the bond manifestation; Option delta is the option manifestation; Marginal VaR is the portfolio VaR manifestation of delta (i.e., change in VaR for a given position/component change)...so, delta doesn't subscribe to a particular asset class...i would think of it as showing up whenever the price-variable relationship is nonlinear. (in a linear relationship, delta is constant and gamma = 0)

David
 
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