Sunday, July 4, 2010

why delta overshadows other greeks

If your own money is at stake, which risk factor do you worry most? Which variable do you watch most? I bet #2 is theta, not vega, but #1 is delta/gamma i.e. how underlier moves.

One reason is, underlier changes much faster.
- Implied vol doesn't change by the minute. I think people re-calibrate vol surfaces as frequently as every few minutes. However, imp vol is a guesstimate "soft" market data, with a lot of guessing.
- realized vol changes usually by the day.
- TTL doesn't change by the hour. We typically treat it as changing by the day.

In contrast, Underlier spot price changes by the second, and is Directly observable. Therefore, among all of the input variables to option valuation models, spot price changes fastest.

Note spot isn't always the most significant input in every pricing formula. Volatility and TTL (when expiring) are sometimes more significant.

Another reason -- hedging. An option/swap often exists along with a position in underlier. In that case it's paramount to analize the nett impact of an underlier move. No such thing with the other greeks.

pace of change -- for TTL pace is constant, whereas pace of change in S can be very fast in a crash. Sigma can change fast, but not as fast as S.

I feel theta matters mostly in the last few months. "Decay" is a slow process until the dying days.

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