Multivariate Hawkes-based Models in LOB: European, Spread and Basket Option Pricing
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Pricing multivariate european equity option using gaussian mixture distributions and evt-based copulas
In this article, we present an approach which allows to take into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associeted options. Specifically, the marginal …
Sum of all Black-Scholes-Merton models: An efficient pricing method for spread, basket, and Asian options
Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) mo…
AllBounds on Multi-asset Derivatives via Neural Networks
Using neural networks, we compute bounds on the prices of multi-asset derivatives given information on prices of related payoffs. As a main example, we focus on European basket options and include information on the pric…
MathPricing VIX options under the Heston-Hawkes stochastic volatility model
We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clusteri…
High-order compact schemes for Black-Scholes basket options
We present a new high-order compact scheme for the multi-dimensional Black-Scholes model with application to European Put options on a basket of two underlying assets. The scheme is second-order accurate in time and four…
Vocal Bursts Intensity Prediction