Options

Adjust parameters, watch Greeks change in real time. Based on the Black-Scholes model, this calculator covers first-order Greeks (Delta, Gamma, Theta, Vega, Rho) and second-order Greeks (Vanna, Charm, Volga). Drag any slider and both the numbers and the curve update instantly. For formula derivations, see the Option Greeks Guide. For second-order Greeks, see Vanna, Charm, Volga Explained. For trading applications, see Greeks in Practice. ...

Options trading has two profit engines: directional bets and volatility bets. Most retail traders only use the first one, buying calls to bet up and puts to bet down. But the other half of an option’s value comes from volatility trading: you do not need to know which way the underlying moves, only whether the magnitude of the move will exceed or fall short of market expectations. This article covers six core volatility trading strategies, split into long vol and short vol groups. Each strategy comes with a payoff diagram, use cases, and concrete numbers, building toward a practical decision framework: check IV Rank, pick a strategy. ...

The first two articles covered first-order Greeks and second-order Greeks, building up the math, the intuition, and the code. This article does one thing: use those numbers to make trading decisions. What Greeks profile does each strategy carry? How does Delta hedging actually work in discrete time? When does Gamma Scalping have positive expected value? How do market makers use Greeks for risk management? Numbers and code throughout. This is the final article in the Option Greeks series. ...

The previous article covered the five first-order Greeks: Delta, Gamma, Theta, Vega, and Rho. They handle hedging and risk management well, with one assumption: the first-order Greeks themselves are stable. They are not. The underlying moves, and Delta changes (that is Gamma). Volatility shifts, and Delta changes again, but first-order Greeks have no name for this effect. Second-order Greeks fill that gap: they quantify the instability of first-order Greeks themselves. This is part two of the Option Greeks series. It covers the three most important second-order Greeks (Vanna, Charm, Volga), plus their role in volatility surface modeling. Part three covers trading applications. ...

Options pricing is not about predicting direction. It is about quantifying multi-dimensional risk. The underlying price moves, time passes, volatility shifts, interest rates change, all simultaneously affecting an option’s value. Option Greeks extract the sensitivity of the option price to each of these variables, turning abstract risk into numbers you can hedge against. This is part one of a three-part series on option Greeks, covering the five first-order Greeks (Delta, Gamma, Theta, Vega, Rho) with their mathematical formulas, intuitive explanations, and Python implementations. Parts two and three will cover second-order Greeks and trading applications, respectively. ...