Related papers: A new self-exciting jump-diffusion process for opt…
We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the…
Efficient sampling for the conditional time integrated variance process in the Heston stochastic volatility model is key to the simulation of the stock price based on its exact distribution. We construct a new series expansion for this…
We introduce the Hyperedge-triggered Hawkes (HTH) process for inferring higher-order interaction structure in multi-cellular systems from asynchronous event-time data. Beyond standard pairwise excitation, the HTH intensity includes a term…
Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…
We introduce a novel and efficient simulation scheme for Hawkes processes on a fixed time grid, leveraging their affine Volterra structure. The key idea is to first simulate the integrated intensity and the counting process using Inverse…
In energy markets, joint historical and implied calibration is of paramount importance for practitioners, yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from…
A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al (2011, CUP) to derive a first order approximation of the…
This work introduces a self and mutually exciting point process that embeds flexible residuals and intensity with discretely Markovian dynamics. By allowing the integration of diverse residual distributions, this model serves as an…
In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of…
This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point…
The HEat modulated Infinite DImensional Heston (HEIDIH) model and its numerical approximation are introduced and analyzed. This model falls into the general framework of infinite dimensional Heston stochastic volatility models of (F.E.…
In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…
We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying…
We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to…
Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of high…
We reconcile rough volatility models and jump models using a class of reversionary Heston models with fast mean reversions and large vol-of-vols. Starting from hyper-rough Heston models with a Hurst index $H \in (-1/2,1/2)$, we derive a…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
This study develops an integrated stochastic modeling framework for pricing short and medium-maturity equity options and assessing interest-rate risk using the Heston (1993), Bates (1996), and CIR (1985) models. We calibrate the Heston…
In this paper, authors successfully construct a new algorithm for the new higher order scheme of weak approximation of SDEs. The algorithm presented here is based on [1][2]. Although this algorithm shares some features with the algorithm…