hull 21.11

[Pflik]

I'm working out this question with regards to volatility estimation and i'm looking at the sheet. It uses a simple return estimate with the formula (Si/Si-1) - 1. I'm guessing this is something specific to chapter 21 of hull? as chapter 22 is using either ln(Si/Si-1) or Si-Si-1/Si-1.

Second question is with regards to the last two formula's. I've been faithfully using the lognormal formula (the first one). However I'm not sure when and where i can use the second one (or if i just need to ignore that one?)

thanks.

 

[David Harper CFA FRM]

Hi Pflik,

Right, in the overall, Hull is typical among authors (e.g., Jorion) in ultimately allowing for either continuous, u = LN[S(i)/S(i-1)], or discrete, u = S(i)/S(i-1) - 1, as the return input into volatility (I realize he settles on discrete in Chapter 22, due to consistency with Chapter 21, but notice that it's actually due to an approximation of the continuous where his technical definition assumes continuous; bottom line: either is okay in Hull). His usage of discrete is also typical: it is because the discrete version supports returns in a linear portfolio, specifically ...

The basic trade-off is that log returns are time additive but discrete returns are "cross-sectionally" additive across portfolio components. Here is an old video I recorded which illustrates: