Using Black-Scholes Delta and Gamma to Monitor Option Exposure
Summary
The document explains Delta as an option’s sensitivity to the underlying price and Gamma as the rate at which Delta changes. It contrasts long options, which have positive Gamma, with short options, which have negative Gamma, and describes why Gamma is greatest near the strike and diminishes farther away. These relationships help explain why long Gamma positions can benefit from large price moves while short Gamma positions are exposed when prices move sharply.
An MQL5 example calculates call Delta and option Gamma using Black-Scholes inputs, including price, strike, volatility, time, rates, and dividend yield. The article also describes collecting historical prices and exporting results for plots of Delta, Gamma, and Gamma exposure. It gives a conceptual account of the calculations and their use in exposure analysis, but the supplied results are limited and do not establish a trading strategy’s performance. Black-Scholes estimates also depend on model inputs and assumptions, so the outputs are not guarantees of realized risk or profit.
Key ideas
- Delta measures an option’s price sensitivity to the underlying, while Gamma measures how that sensitivity changes.
- Long options have positive Gamma, whereas short options have negative Gamma.
- Gamma is described as highest near the strike and smaller when the underlying is far from it.
- The example computes Black-Scholes call Delta and option Gamma from market and contract inputs.
- Plots of the Greeks can help visualize exposure, but the article provides no performance validation.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.