A simple time-consistent model for the forward density process

TL;DR

This paper introduces a simple, time-consistent model for the forward density of asset prices that can be calibrated easily to option data and aligns well with empirical observations, reducing the need for frequent recalibration.

Contribution

The paper proposes a novel, straightforward model for forward density evolution that is both easy to calibrate and empirically consistent, using particle filtering for Brownian motion inference.

Findings

Model fits option price data well

Particle filtering effectively estimates Brownian motion

Reduces calibration frequency needed in practice

Abstract

In this paper a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with empirical findings from option price data. The model is constructed with the aim of being both simple and realistic, and avoid the need for frequent re-calibration. The model prices of $n$ options and a forward contract are expressed as time-varying functions of an $(n+1)$-dimensional Brownian motion and it is investigated how the Brownian trajectory can be determined from the trajectories of the price processes. An approach based on particle filtering is presented for determining the location of the driving Brownian motion from option prices observed in discrete time. A simulation study and an empirical study of call options on the S&P 500 index illustrates that the model provides a good fit to option price data.