The Greek Letters

The Greek Letters

Each Greek letter measures a different dimension to the risk in a portfolio and the aim of a trader is to manage the Greeks so that all risks are acceptable.

Delta

The delta of a portfolio is defined as the rate of change of the portfolio price with respect to the price of the underlying asset.

The delta of a portfolio can be calculated from the deltas of the individual derivatives in the portfolio.

TODO: delta hedging.

Theta

The theta of a portfolio is the rate of change of the value of the portfolio with respect to the passage of time with all else remaining the same. Theta is sometimes referred to as the time decay of the portfolio.

Note that theta is not the same type of hedge parameter as delta. There is uncertainty about the future price of the underlying asset, but there is no certainty about the passage of time. It makes sense to hedge against changes in the price of the underlying asset, but it does not make any sense to hedge against the effect of the passage of time on a portfolio. In spite of this, many traders regard theta as a useful descriptive statistic for a portfolio. This is because in a delta-neutral portfolio, theta is a proxy of gamma.

Gamma

The gamma of a portfolio is the rate of change of the portfolio's delta with respect to the price of the underlying asset. It is the second partial derivative of the portfolio with respect to asset price.

If gamma is small, delta changes slowly, and adjustments to keep a portfolio delta-neutral need to be made only relatively infrequently. However, if gamma is large in absolute terms, delta is highly sensitive to the price of the underlying asset. It is then quite risky to leave a delta-neutral portfolio unchanged for any length of time.

TODO: gamma hedging.

Relationship Between Delta, Theta and Gamma

TODO: Who can tell me how to write mathematical formula in HTML?

Vega

The vega of a portfolio is the rate of change of the value of the portfolio with respect to the volatility of the underlying asset.

If vega is high in absolute terms, the portfolio's value is very sensitive to small changes in volatility. If vega is low in absolute terms, volatility changes have relatively little impact on the value of the portfolio.

Rho

The rho of a portfolio is the rate of change of the value of the portfolio with respect to the interest rate.