Delta

The delta (the Greek letter Δ) of a derivative is the rate of change in the price of a derivative with the price of the underlying. A delta may also be the rate of change in the price of a portfolio with the price of the security.

This is roughly the same as the change in the price of derivative (or portfolio) that would result from a one unit change in the price of the underlying security.

A more accurate (if more mathematical) definition is that the delta is the derivative of the price of the derivative against the price of the underlying, i.e.:

Δ= (∂P)/(∂S)

where P is the price of the derivative or the value of the portfolio
and S is the price of the underlying.

The delta, along with a group of other similar numbers known as the greeks, is of great importance in options valuation and trading. The delta is best known in the context of delta hedging, but other strategies for dynamic hedging.

The delta is not a fixed value, it depends on the price of the underlying security. The relationship between the two depends on the characteristics of both the derivative and the underlying. This means that hedges using delta have to be constantly re-balanced.

The delta of a call option must be between zero and one. A deeply in the money call has an intrinsic value that varies exactly in line with the price, and an option value that falls, approaching zero as the price increases. Therefore, the delta must be less than one. However much the price of the underlying falls, the option value must remain positive (except in the pathological case of the underlying being worth zero).

Similarly the delta of a put option must be between minus one and zero.

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