Friday, October 1, 2010

vol skew and thick tail -- bit of insight

(a beginner's understanding.)

As observed on any equity vol surface, implied volatilities almost always increase with Decreasing strike – that is, OTM puts (dominating low strikes) trade at higher implied volatilities than OTM calls (dominating high strikes).

In theory, The naive constant-vol model [1] predicts the vol smile curve flattens to a flat line. Lognormal distribution assumes a stock is equally likely to gain 25% or drop 20% (see separate blog), but for a real stock, -20% is more likely. Real world stocks are more "panicky".

[1] exact def? not sure. It could possibly mean "const local vol". But i guess it means "at any moment in time, fair valuations (and bid/ask) of a chain of options should reflect the same implied volatility" -- BS assumption.  When market players perceive a vol hike, it has to be a parallel shift across strikes, and all options on the chain should rise exactly those amounts to reflect the same but /heightened/ vol.

Skew steepens when markets decline -- observation over the past decades (probably since 1987 crash). When markets crash, stocks can drop more than constant-vol suggests. Downside risk is higher than predicted. Option writers are insurers. Insurers know "downside" is bigger so they charge higher premiums. Buyers are actually willing to pay higher because they too know downside is more likely.

Therefore implied vol for low strike Puts are higher than ATM puts. Note bid/ask premium is obviously lower than near-the-money Puts -- due to arbitrage.

If you plot log(daily close price relative) in a _histogram_, constant-vol predicts a bell histogram, but I believe a real histogram actually shows a thick tail.

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