Multivariate Hawkes-based Models in LOB: European, Spread and Basket Option Pricing

TL;DR

This paper develops multivariate Hawkes process models for limit order book dynamics to improve European, spread, and basket option pricing, incorporating limit theorems, Greeks, and numerical examples.

Contribution

It introduces multivariate Hawkes-based models for option pricing in LOB, including new limit theorems, Greeks, and numerical methods, advancing beyond classical models.

Findings

Hawkes-based models outperform Black-Scholes in capturing market dynamics.

Explicit formulas for Greeks in Hawkes models are derived.

Numerical examples demonstrate the effectiveness of the proposed models.

Abstract

In this paper, we consider pricing of European options and spread options for Hawkes-based model for the limit order book. We introduce multivariate Hawkes process and the multivariable general compound Hawkes process. Exponential multivariate general compound Hawkes processes and limit theorems for them, namely, LLN and FCLT, are considered then. We also consider a special case of one-dimensional EMGCHP and its limit theorems. Option pricing with $1D$ EGCHP in LOB, hedging strategies, and numerical example are presented. We also introduce greeks calculations for those models. Margrabe's spread options valuations with Hawkes-based models for two assets and numerical example are presented. Also, Margrabe's spread option pricing with two $2D$ EMGCHP and numerical example are included. Basket options valuations with numerical example are included. We finally discuss the implied volatility and implied order flow. It reveals the relationship between stock volatility and the order flow in the limit order book system. In this way, the Hawkes-based model can provide more market forecast information than the classical Black-Scholes model.