Delta-gamma value at risk (VaR) with the Taylor Series Approximation (FRM T4-4)

[here is my xls trtl.bz/2rlVj7H] The Taylor Series lets us approximate a smooth function with a polynomial. Here we apply it to both an option position (where the second term captures gamma) and a bond position (where the second term captures convexity).
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[@Dalal_For_A_Reason]

Undoubtedly one of the best sources for learning market risk. Thanks a ton for these videos.

[@millamulisha]

So VaR is just gradient of the instrument w.r.t. its variables evaluated at forecasted or expected values? In other words, just ‘sensitivity analysis’ in multi variable calculus... What are most nonlinear terms in either bonds or options?

[@bionicturtle]

Yes, exactly correct (at least, that is correct by definition under the so-called "analytical VaR" approach; aka, parametric VaR). For bonds, convexity is the second-derivative term (under a single-factor model where the single factor is yield to maturity,YTM); for options, gamma is the second-derivative; i.e., rate of change of delta. The other option risk factors have linear terms: theta, rho and vega; each of these, in turn, have associated non-linear (2nd derivative) terms, although I do not think used too often.

[@WondererSeeker]

Hi David. I always watch your videos which I consider very engaging and clear. Thanks for sharing them. I wanted to ask you if you know some material (academic paper, book or xls spreadsheet) in which the third order term calculation is detailed for fixed income approximations. As you mention, normally with modified duration and convexity the approximation is satisfactory. However, in emerging markets (for example Argentina) shocks in interest rates can and do reach more than 500 bps regularly. In this context an MD+Convex approximation is very inaccurate. I wanted see if a third order term can be added to get a proxy before doing an exact yield-price calculus function. Thank you very much. Greetings from Argentina.

[@B7S1]

Very interesting. Could this be applied to a analyze a complex position, a butterfly for example? Or even more to analyze what strikes, expirations, etc. to chose in order to maximize your profit chances? First and second derivatives are useful to construct the graph of a function. For an option these are delta and gamma. Could they be used? And maybe vega as a parameter?

[@liangyumin9405]

Support!

[@bionicturtle]

Thank you!

[@anuragbardia]

The excel is not there at the location.

[@samrathore9396]

Excellent

[@bionicturtle]

Thank you, much appreciated! (I put some extra prep work into this one ... )

[@zhensu5439]

where can I download the excel