Hawkes Process
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Author(s):  
Lu-ning Zhang ◽  
Jian-wei Liu ◽  
Zhi-yan Song ◽  
Xin Zuo

Author(s):  
Tumellano Sebehela

The stock jumps of the underlying assets underpinning the Margrabe options have been studied by Cheang and Chiarella [Cheang, GH and Chiarella C (2011). Exchange options under jump-diffusion dynamics. Applied Mathematical Finance, 18(3), 245–276], Cheang and Garces [Cheang, GHL and Garces LPDM (2020). Representation of exchange option prices under stochastic volatility jump-diffusion dynamics. Quantitative Finance, 20(2), 291–310], Cufaro Petroni and Sabino [Cufaro Petroni, N and Sabino P (2020). Pricing exchange options with correlated jump diffusion processes. Quantitate Finance, 20(11), 1811–1823], and Ma et al. [Ma, Y, Pan D and Wang T (2020). Exchange options under clustered jump dynamics. Quantitative Finance, 20(6), 949–967]. Although the authors argue that they explored stock jumps under Hawkes processes, those processes are the Poisson process in their applications. Thus, they studied Hawkes processes in-between two assets while this study explores Hawkes process within any asset. Furthermore, the Poisson process can be flipped into Hawkes process and vice versa. In terms of hedging, this study uses specific Greeks (rho and phi) while some of the mentioned studies used other Greeks (Delta, Theta, Vega, and Gamma). Moreover, hedging is carried out under static and dynamic environments. The results illustrate that the jumpy Margrabe option can be extended to complex barrier option and waiting to invest option. In addition, hedging strategies are robust both under static and dynamic environments.


2021 ◽  
Vol 105 ◽  
pp. 104416
Author(s):  
Lu-ning Zhang ◽  
Jian-wei Liu ◽  
Zhi-yan Song ◽  
Xin Zuo
Keyword(s):  

Author(s):  
Heyuan Wang ◽  
Shun Li ◽  
Tengjiao Wang ◽  
Jiayi Zheng

Stock trend prediction is a challenging task due to the non-stationary dynamics and complex market dependencies. Existing methods usually regard each stock as isolated for prediction, or simply detect their correlations based on a fixed predefined graph structure. Genuinely, stock associations stem from diverse aspects, the underlying relation signals should be implicit in comprehensive graphs. On the other hand, the RNN network is mainly used to model stock historical data, while is hard to capture fine-granular volatility patterns implied in different time spans. In this paper, we propose a novel Hierarchical Adaptive Temporal-Relational Network (HATR) to characterize and predict stock evolutions. By stacking dilated causal convolutions and gating paths, short- and long-term transition features are gradually grasped from multi-scale local compositions of stock trading sequences. Particularly, a dual attention mechanism with Hawkes process and target-specific query is proposed to detect significant temporal points and scales conditioned on individual stock traits. Furthermore, we develop a multi-graph interaction module which consolidates prior domain knowledge and data-driven adaptive learning to capture interdependencies among stocks. All components are integrated seamlessly in a unified end-to-end framework. Experiments on three real-world stock market datasets validate the effectiveness of our model.


2021 ◽  
Vol 64 (9) ◽  
Author(s):  
Xiao Ding ◽  
Jihao Shi ◽  
Junwen Duan ◽  
Bing Qin ◽  
Ting Liu
Keyword(s):  

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