What is the role of derivatives of Serial Autocorrelation

Question

What is the role of the derivatives of Serial Autocorrelation?

Answer 1

So far as pricing and hedging of derivatives is relates there are three certain points of interest.

1. The definition of ‘volatility’ is subtly different while there is SAC. The sequence +1, −1, +1, −1, +1, has ideal negative SAC and a volatility of zero! There difference among volatility with and without SAC is a factor of √(1 − ρ²),here ρ is the SAC coefficient.

2. When we can hedge continuously then we don’t care regarding the probability of the stock rising or falling and therefore we don’t really care regarding SAC. A fun consequence of which is that options paying off SAC always has zero value theoretically.

3. However, in practice, hedging must be done discretely. And it is where non-zero SAC becomes significant. If you expect that a stock will oscillate up and down madly from one day to the next, as the above +1, −1, +1, −1, illustration, then what you must do depends on whether you are long or short gamma. When gamma is positive then you trade to capture the extremes while you can. Whereas when you are short gamma then you can wait, since the stock will return to its current level and you will have gained time value. Obviously this is very simplistic, and only for short gamma positions needs nerves of steel!