SANOS Smooth strictly Arbitrage-free Non-parametric Option Surfaces

TL;DR

This paper introduces a simple, efficient non-parametric method for constructing smooth, arbitrage-free option price surfaces that can be calibrated quickly to market data, with a novel local volatility parameterization.

Contribution

It presents a new flexible approach for arbitrage-free option surface modeling that is computationally efficient and incorporates bid-ask spreads directly, along with a novel local volatility parameterization.

Findings

Method achieves smooth, arbitrage-free surfaces with low computational cost.

Calibration via linear programming allows direct incorporation of bid-ask spreads.

First construction of arbitrage-free surfaces using positive local volatility variables.

Abstract

We present a simple, numerically efficient but highly flexible non-parametric method to construct representations of option price surfaces which are both smooth and strictly arbitrage-free across time and strike. The method can be viewed as a smooth generalization of the widely-known linear interpolation scheme, and retains the simplicity and transparency of that baseline. Calibration of the model to observed market quotes is formulated as a linear program, allowing bid-ask spreads to be incorporated directly via linear penalties or inequalities, and delivering materially lower computational cost than most of the currently available implied-volatility surface fitting routines. As a further contribution, we derive an equivalent parameterization of the proposed surface in terms of strictly positive "discrete local volatility" variables. This yields, to our knowledge, the first construction of smooth, strictly arbitrage-free option price surfaces while requiring only trivial parameter constraints (positivity). We illustrate the approach using S&P 500 index options