Revisiting Stochastic Collocation with Exponential Splines for an Arbitrage-Free Interpolation of Option Prices

TL;DR

This paper examines the effectiveness of stochastic collocation with exponential quadratic splines for arbitrage-free option price interpolation, comparing two different parameter optimization strategies.

Contribution

It provides a detailed analysis of fixing versus optimizing spline parameters, offering insights into more effective arbitrage-free interpolation methods.

Findings

Optimal parameter fixing improves interpolation stability

Exponential splines effectively prevent arbitrage opportunities

Method comparison guides better spline-based option pricing

Abstract

We revisit the stochastic collocation method using the exponential of a quadratic spline. In particular, we look in details whether it is more appropriate to fix the ordinates and optimize the abscissae of an interpolating spline or to fix the abscissae and optimize the parameters of a B-spline representation.