Thursday, June 2, 2011

OTM put -- on left or right of a graph against underlier

It's well known that the implied volatility smile curve is skewed for stock options. The implied vol is Higher on the far Left than far right on a smile curve. The Left derive from OTM Put quotes from the market, whereas the Right is derived from OTM Calls.

In other words, on Low strikes implied sigmas are much higher, and derive from OTM Puts.

On a PnL graph however, you may see a different pattern. For example Look at a simple put PnL graph. OTM is on the Right -- At sky high prices, our put is worthless and deep OTM.

So OTM put is on left or right?

Well, what's the horizontal axis?
- it's underlier prices on the PnL graph, where strike is a fixed part of the put contract we are analyzing.
- it's strikes on the smile curve, where current spot level is (roughly) the lowest point on the smile. The current spot doesn't move on this smile curve. The smile curve is a snapshot of the option quotes and implied sigmas.

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