Mixture-Preserving, Arbitrage-Free Interpolation for Volatility-Surface Models

Battle Count: 73

Highly relevant for options desks and quantitative finance practitioners. The paper provides a practical, constructive method for interpolating volatility surfaces between quoted expiries while guaranteeing no calendar-spread arbitrage. Directly applicable to Brigo-Mercurio and SANOS model implementations used in production. The additive-cost chaining across expiries makes it computationally feasible for real-time pricing and hedging. However, it is a modeling/calibration tool rather than a trading strategy per se.

The core algorithm is straightforward: concatenate components, set up weight vectors, interpolate linearly, compute density and local volatility. The main complexity lies in: (1) ensuring the peacock check on the strike grid, (2) handling the 2N-component bookkeeping, (3) computing Dupire local volatility numerically (requires ∂tC and pt(K)), and (4) managing the conditioning issues in bimodal regimes. The mathematical prerequisites (convex order, Fokker-Planck, Lowther theorem) are non-trivial but the implementation itself is algorithmic.

The algorithm is clearly specified in Figure 1 with 6 well-defined steps. The mathematical framework (peacock property, Dupire formula, Lowther theorem) is fully stated. However, no code or numerical examples with specific parameters are provided beyond illustrative figures. The construction is deterministic given inputs, making it straightforward to implement.