Delta

From WilmottWiki

The delta, , of an option or a portfolio of options is the sensitivity of the option or portfolio to the underlying asset. It is the rate of change of value with respect to the asset:

.

Speculators take a view on the direction of some quantity such as the asset price and implement a strategy to take advantage of their view. If they own options then their exposure to the underlying is, to a first approximation, the same as if they own delta of the underlying.

Those who are not speculating on direction of the underlying will hedge by buying or selling the underlying, or another option, so that the portfolio delta is zero. By doing this they eliminate market risk.

Typically the delta changes as stock price and time change, so to maintain a delta-neutral position the number of assets held requires continual readjustment by purchase or sale of the stock. This is called rehedging or rebalancing the portfolio, and is an example of dynamic hedging.

Sometimes going short the stock for hedging purposes requires the borrowing of the stock in the first place. (You then sell what you have borrowed, buying it back later.) This can be costly, you may have to pay a repo rate, the equivalent of an interest rate, on the amount borrowed.

Formulae

• Call option
• Put option
• Binary call option
• Binary put option

References

• Taleb, NN 1997 Dynamic Hedging. John Wiley & Sons
• Wilmott, P 2001 Paul Wilmott Introduces Quantitative Finance. John Wiley & Sons
• Wilmott, P 2006 Frequently Asked Questions in Quantitative Finance. John Wiley & Sons