Dynamic hedge

A dynamic hedge is one that needs to be adjusted as the price (and sometimes other characteristics) of the portfolio or security it is hedging changes.

Some securities cannot be hedged with a static position. For example, the change in the price of an option is not linear with (in a constant proportion to) the change in the value of the underlying asset. This means that options can only be hedged using the underlying (or other simple securities) dynamically — options can be statically hedged using other options (e.g. an exotic option with a portfolio of vanilla options).

The description above implicitly tells us what is problematic about dynamic hedging. The root problem is that it requires constant re-balancing. Consider a simple delta hedge where the value of an option is hedged with a holding of the underlying asset. What happens when the value of the underlying asset changes? The amount of the underlying asset needed to hedge the option changes, and so the position has to be re-balanced?

What happens when change in price is a substantial jump? Not only is the position no longer be fully hedged, but it could even show a sudden loss. In the type of highly geared arbitrage like strategies where dynamic hedging is typically employed, this could be disastrous.

The answer would be to hedge against changes in the delta by gamma hedging. Of course this still does not cover really big jumps, because gamma also changes with price. In addition other factors may change such as changes in option value because (the markets perception of) the volatility of the underlying.

We can cover some possibilities by hedging using rho (to hedge changes in interest rates), and vega (to hedge changes in volatility). In addition hedging theta offsets the decline in option value as time passes.

Even after all this, a dynamic hedge would still not be perfect. A sudden jump in price often implies a sudden jump in volatility.

All this is, of course, why strategies that depend on dynamic hedging, even if they are basically arbitrage strategies, are risky.

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