Saturday, January 7, 2012

delta 1, non-linear, optionality

Delta 1 derivatives are intuitive -- you can "feel" that a 1-cent drop in underlier causes an (almost exactly[3]) 1-cent drop in the derivative. A common synonym for Delta 1 is ..... Linearity. I think Linear basically means the graph of MV/underlier is straight.

Why is delta one important? Price sensitivity (including greeks, duration, dv01) are the focus on market risk, and delta is the #1 most important sensitivity.

Optionality is the defining feature of non-delta1.

A big bank often puts FX options in a different trading desk than FX forwards/futures and spot -- delta 1

A big bank often organizes equity trading along delta 1 (NOT along OTC/listed). As a result,
* all equity options (including index or OTC structured options) and variance swaps are grouped into "volatility" desk. I think convertible bonds too.
* equity futures and basket trading (including ETF) are grouped into equity cash desk. I think equity swaps too.

How about IRS or bonds? I believe they are not delta 1. For interest rate sensitivity in general, DV01 and duration are more useful (probably more comprehensive) than delta. There's not a single underlier variable like a ETF or currency price, but a term structure of Spot yields. Notice I don't mean forecast values of yield but rather spot yield. Let me try to explain a bit.

Outside the fixed income space, a derivative contract uses a Reference variable. The variable has a spot value. On any valuation-date now or in the future, there's just one spot value. In the IR space, the reference entity exists on a yield curve. On any valuation-date, there's an entire spot yield curve (so-called term structure) [2]. A particular position is often sensitive to changes in the reference yield curve [1]. Therefore, an analysis of market-value change due to a change in one interest-rate is inadequate.

[2] actually I feel volatility smile is a "spot" term structure of vol. We construct a smile curve using today's implied vol and get a spot smile. If we use 1/1/2009 implied vol, then we get a spot smile curve as of that date. Using today's information, can we forecast next year's vol smile curve? I don't think we can, but people try anyways.

[1] example - a vanilla bond paying 600bps/year. It's trading t 98.1. What if a there's a parallel yield shift? All upcoming payouts will devalue.  What if there's a yield drop in the far end? Now you see IR sensitivity is not about a single reference variable, but a change to a yield curve.

[3] if delta is almost 1.0, then it's delta 1.

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