How institutional lenders price option hedges: SVI, SABR, Vanna-Volga, PCHIP
How institutional lenders price option hedges: SVI, SABR, Vanna-Volga, PCHIP
To hedge with options, you first have to price them, and pricing them means knowing the implied volatility at every strike and expiry, not just the handful where the market quotes prices directly. Filling in that full volatility surface, smoothly and without introducing arbitrage, is a specialized modeling problem, and a few named methods do most of the work.
How it works
The market only quotes a limited number of option strikes and expiries directly. But to price an arbitrary hedge, at a strike between the quoted ones, or for a custom structure, you need a continuous volatility surface: implied volatility as a smooth function across all strikes and maturities. Constructing that surface from sparse market data is what these methods do, each making different trade-offs between flexibility, stability, and guarantees against arbitrage.
SVI (Stochastic Volatility Inspired) is a parametric model for the volatility smile at a given expiry. It fits the observed smile with a small number of parameters that have intuitive meanings (level, slope, curvature) and, when constrained properly, guarantees the fitted smile is free of static arbitrage. SVI is popular precisely because it's both parsimonious and well-behaved: a handful of parameters produce a clean, arbitrage-free smile.
SABR (Stochastic Alpha Beta Rho) models how volatility itself evolves, and is especially common where the dynamics of the smile matter, not just its shape at one moment. It's widely used in rates and derivatives markets because it captures how the smile shifts as the underlying moves, which matters for hedging positions whose risk changes with the market.
Vanna-Volga is a more practical, market-maker-oriented method that prices exotic or off-market options by adjusting the base price for the cost of hedging the specific higher-order risks (vanna and volga, sensitivities to how volatility and spot interact). It's less a full surface model and more a fast, practitioner's adjustment anchored to a few liquid reference options.
PCHIP (Piecewise Cubic Hermite Interpolating Polynomial) is an interpolation method, not a volatility model per se. It's used to interpolate smoothly between known points on the surface while preserving shape and avoiding the spurious oscillations that naive polynomial interpolation can introduce. It's the tool for filling gaps between reliable data points cleanly.
Why it matters
The choice of method directly affects hedge pricing accuracy, and mispricing a hedge is expensive in both directions: overpay and you erode returns, underestimate and you buy less protection than you thought. A robust surface-construction method is what lets a hedging desk price protection consistently across strikes and expiries rather than being limited to the few points the market happens to quote.
Arbitrage-freedom is the non-negotiable property underneath all of this. A volatility surface that permits static arbitrage isn't just theoretically ugly, it produces prices that are internally inconsistent, which means hedges built on it can have hidden, unintended exposures. Methods like SVI are valued specifically because they guarantee the surface holds together as a coherent whole.
Where this shows up in Rekord
Rekord's hedging program relies on robust, arbitrage-free volatility surface construction to price option hedges consistently across strikes and expiries. For the underlying concept these methods model, see Implied volatility, volatility smiles, and option pricing.