Volatility Swap (Settlement)
Computes the settlement of a volatility swap: the volatility notional multiplied by the difference between the realized volatility and the strike, in volatility points. It's a cousin of the variance swap, but pays linearly in volatility, not its square, which makes it more intuitive yet harder to replicate. The difference between the two fair strikes is the convexity adjustment. Enter the realized volatility, the strike volatility and the volatility notional.
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Volatility Swap (Settlement)
Computes the settlement of a volatility swap: the volatility notional multiplied by the difference between the realized volatility and the strike, in volatility points. It's a cousin of the variance swap, but pays linearly in volatility, not its square, which makes it more intuitive yet harder to replicate. The difference between the two fair strikes is the convexity adjustment. Enter the realized volatility, the strike volatility and the volatility notional.
Volatility without the square
The volatility swap is the more intuitive sibling of the variance swap. Instead of settling on variance, it settles on volatility itself: the difference, in volatility points, between the volatility that materialized and the contracted strike. For many, thinking in vol points is more natural than in variance points.
That intuition has a technical cost. Being linear in volatility, not its square, the volatility swap can't be replicated exactly with options, unlike the variance swap. The difference between the fair strike of one and the other is the so-called convexity adjustment, which depends on the volatility of volatility itself.
Enter the realized volatility, the strike volatility and the volatility notional. The tool returns the settlement in currency. Since the payoff is linear, the exposure is simpler to understand than the variance swap's, but the fair strike price embeds that convexity adjustment that separates the two.
Related Tools
Variance Swap (Settlement)
Computes the settlement of a variance swap: the variance notional multiplied by the difference between the realized variance and the variance strike (the square of volatility). It's the pure volatility derivative — unlike an option, it has no directional exposure to the asset, only to the variance that actually occurred. The buyer profits if the market swings more than expected. Enter the realized volatility, the strike volatility and the variance notional.
Forward Volatility
Computes the implied forward volatility between two maturities from the corresponding spot volatilities. Just as there's a forward interest rate embedded in two spot rates, there's a forward volatility embedded in two volatilities of different terms, given by √((σ2²·T2 − σ1²·T1)/(T2 − T1)). It's what the market prices for the volatility of the period between the two dates. Enter the two spot volatilities and their terms.
Implied Volatility (Black-Scholes)
Computes the implied volatility of a European call option by inverting the Black-Scholes formula via bisection: given the market price, it finds the volatility the model would need to reach it. It's the volatility the market is actually pricing in, the number behind the volatility smile and the VIX. Unlike the other Greeks, it has no closed form and requires a numerical solution. Enter the spot price, the strike, the interest rate, the term and the market price of the call.
Volatility Drag (Variance Drag)
Computes volatility drag: the loss of the compound (geometric) return relative to the average (arithmetic) return, approximately volatility squared divided by two. It's the reason a portfolio that does +50% and then −50% doesn't return to the start: volatility erodes compound growth. The more volatile the asset, the larger the drag, even with the same average return. Enter the arithmetic mean return and the volatility.
Par Swap Rate
Computes the par swap rate from discount factors: the fixed rate that makes the interest rate swap's value zero at inception, equating the fixed and floating legs. The formula is (1 − last discount factor) divided by the sum of discount factors weighted by the period. It's a swap's market quote and the basis for marking existing positions to market. Enter the list of discount factors by payment date and the year-fraction of each period.
Option Price (Heston Model)
Prices a European call under the Heston (1993) model, where the asset volatility is itself stochastic and mean-reverting — reproducing the volatility smile and skew that constant-vol Black-Scholes misses. The price comes out in semi-closed form by numerically integrating the characteristic function (Little Heston Trap formulation, Gauss-Legendre quadrature). Enter spot, strike, maturity, rate, dividend and the five model parameters: initial variance, kappa, theta, vol of vol and correlation.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.