论文标题
LOB中的多元鹰队模型：欧洲，传播和篮子选项定价
Multivariate Hawkes-based Models in LOB: European, Spread and Basket Option Pricing
论文作者
论文摘要
在本文中，我们考虑定价欧洲选择权，并为限制订单簿的基于霍克斯的模型提供分配选择。我们介绍了多元霍克斯流程和多变量的一般复合霍克斯过程。当时考虑了指数的多元一般化合物鹰队过程，并限制了它们的定理，即LLN和FCLT。我们还考虑了一维EMGCHP及其极限定理的特殊情况。提出了带有$ 1D $ EGCHP的$ 1D $ LOB，对冲策略和数值示例的选项定价。我们还为这些模型介绍了希腊人的计算。介绍了Margrabe的两种资产和数值示例的Margrabe的差价估值。此外，包括两个$ 2D $ EMGCHP的Margrabe的差价选项定价和数值示例。包括具有数值示例的篮子选项估值。我们最终讨论了隐含的波动性和隐含的顺序流。它揭示了股票波动与限制顺序簿系统中的顺序流之间的关系。通过这种方式，基于霍克斯的模型可以提供比古典黑色choles模型更多的市场预测信息。
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.
