Taylor Series Approximation

[nikogeorgiev]

Hi David

Last one from me until the next weekend.

With regard to the Taylor series of approximation, are we supposed to be able to calculate that on the exam? I am conscious that it involves cumbersome calculations, etc...

Kind regards
N

 

[David Harper CFA FRM]

Hi @nikogeorgiev

You should be able to apply Taylor; the probability of the application of Taylor on the exam is high. This does not require a deep understanding of its derivation so much as a conceptual understanding of why it works. And we don't use the whole thing, as the readings/Jorion show. We typically only use the first partial derivatives (e.g., delta, vega, dollar duration) and among the second partial derivatives we tend to use only convexity (bonds) or gamma (options), so that realistically we care about these truncated Taylors:

• Bonds: dP/P = -D*Δy + 0.5*convexity*Δy^2 <-- risk factor is yield change
  
• Options [ delta gamma only] : df = delta*ΔS + 0.5*gamma*ΔS^2 <-- risk factor is change in underlying stock price; or maybe also vega:
• Options [ delta gamma vega]: df = ∂f/∂S*dS + 0.5*∂^2f/∂S^2*dS^2 + ∂f/∂σ*dσ
  
• And in Part 2 per Topic 8 (but not Part 1), the portfolio VaR Taylors; e.g., marginal VaR, component VaR

I hope that helps, thanks!

 

[nikogeorgiev]

This is brilliant, David. Many thanks.