The impact of co-jumps in the oil sector

We study the dynamics of the oil sector using a new multivariate stochastic volatility model with a structure of common factors subjected to jumps in mean and conditional variance. This model contributes to the literature allowing the estimation of spillover effects between assets in a multivariate framework through joint jumps (co-jumps), identifying the permanent and transitory effects through a structure defined by Bernoulli processes. The jump structure introduced in the article can be interpreted as a regime-switching model with an endogenous number of states, avoiding the difficulties associated with models with a fixed number of regimes. We apply the model to oil prices and stock prices of integrated oil companies. The jump structure allows dating the relevant events in the oil sector in the period 2000–2019. The period analyzed encompasses important events in the oil market such as the price escalation in 2008 and the falling prices in 2014. We also apply the model to estimate risk management measures and portfolio allocation and perform a comparison with other multivariate models of conditional volatility, showing the good properties of the model in these applications.     

Exchange options under clustered jump dynamics

Exchange options are one of the most popular exotic options, and have important implications for many common financial arrangements and for implied beta as a measure of systematic risk. In this study, we extend the existing literature on exchange options to allow for clustered jump contagion dynamics in each single asset, as well as across assets, using the Hawkes jump-diffusion model. We derive the analytical pricing formulae, the Greeks, and the optimal hedging strategy via Fourier transforms. Using an illustrative numerical analysis, we present the relationship between the exchange option price and clustered jump intensities and jump sizes in the underlying assets. We discuss the managerial insights on financial arrangements with exchange option characteristics. Furthermore, we discuss the implications of incorporating clustered jumps into the estimation of implied beta with exchange options, in which the applications can be insightful and useful in finance practice.     

Analysis of order book flows using a non-parametric estimation of the branching ratio matrix

We introduce a new non-parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this method by applying it to high-frequency order book data from the EUREX exchange. We show that it is able to uncover (or recover) various relationships between all the first-level order book events associated with some asset when mapped to a 12-dimensional process. We then scale up the model so as to account for events on two assets simultaneously and we discuss the joint high-frequency dynamics.     

Systemic Risk and International Portfolio Choice

Returns on international equities are characterized by jumps; moreover, these jumps tend to occur at the same time across countries leading to systemic risk. We capture these stylized facts using a multivariate system of jump‐diffusion processes where the arrival of jumps is simultaneous across assets. We then determine an investor's optimal portfolio for this model of returns. Systemic risk has two effects: One, it reduces the gains from diversification and two, it penalizes investors for holding levered positions. We find that the loss resulting from diminished diversification is small, while that from holding very highly levered positions is large.     

Modelling microstructure noise with mutually exciting point processes

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By suitably coupling the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable us to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro–Bund and Euro–Bobl in several situations.     

Modelling illiquidity spillovers with Hawkes processes: an application to the sovereign bond market

Modelling the dynamics of (il)liquidity across assets is an important yet complicated task, especially when considering significant deteriorations of liquidity conditions. Here, we propose a peak-over-threshold method to identify abrupt liquidity drops from limit order book data and we model the time-series of these illiquidity events across multiple assets as a multivariate Hawkes process. This allows us to quantify both the self-excitation of extreme changes of liquidity in the same asset (illiquidity spirals) and the cross-excitation across different assets (illiquidity spillovers). Applying the method to the MTS sovereign bond market, we find significant evidence for both illiquidity spillovers and spirals. The proportion of shocks explained by illiquidity spillovers roughly doubles from 2011 to 2015, suggesting an increased synchronization of extreme illiquidity across assets.     

A self-exciting switching jump diffusion: properties,calibration and hitting time

A way to model the clustering of jumps in asset prices consists in combining a diffusion process with a jump Hawkes process in the dynamics of the asset prices. This article proposes a new alternative model based on regime switching processes, referred to as a self-exciting switching jump diffusion (SESJD) model. In this model, jumps in the asset prices are synchronized with changes of states of a hidden Markov chain. The matrix of transition probabilities of this chain is designed in order to approximate the dynamics of a Hawkes process. This model presents several advantages compared to other jump clustering models. Firstly, the SESJD model is easy to fit to time series since estimation can be performed with an enhanced Hamilton filter. Secondly, the model explains various forms of option volatility smiles. Thirdly, several properties about the hitting times of the SESJD model can be inferred by using a fluid embedding technique, which leads to closed form expressions for some financial derivatives, like perpetual binary options.     

A multivariate jump-driven financial asset model

We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behaviour of a series of stocks or indexes and to study a multi-firm, value-based default model. Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a stochastic time-change technique and provide the details for a Gamma change. The main feature of the model is the fact that—opposite to other, non-jointly Gaussian settings—its risk-neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.     

美元指数与原油价格暴涨暴跌的交互刺激研究

采用具有相互刺激特征的Hawkes过程探究美元指数与原油价格暴涨暴跌的交互刺激作用。结果表明:在暴涨暴跌幅度均服从广义帕累托分布的基础上, Hawkes过程对美元指数与原油价格的暴涨暴跌均拟合得较好;美元指数和原油价格的暴涨暴跌具有明显的自我刺激效应,且原油价格的暴涨暴跌会单向刺激美元指数暴涨暴跌的发生,即交叉刺激效应具有非对称性。同时,实证发现Hawkes过程对美元指数与原油价格的暴涨暴跌的预测能力要优于泊松过程。     

Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics

We present a modified version of the non parametric Hawkes kernel estimation procedure studied in Bacry and Muzy [arXiv:1401.0903, 2014] that is adapted to slowly decreasing kernels. We show on numerical simulations involving a reasonable number of events that this method allows us to estimate faithfully a power-law decreasing kernel over at least six decades. We then propose a eight-dimensional Hawkes model for all events associated with the first level of some asset order book. Applying our estimation procedure to this model, allows us to uncover the main properties of the coupled dynamics of trade, limit and cancel orders in relationship with the mid-price variations.     

Asset Allocation with a High Dimensional Latent Factor Stochastic Volatility Model

We investigate the implications of time-varying expected returnand volatility on asset allocation in a high dimensional setting.We propose a dynamic factor multivariate stochastic volatility(DFMSV) model that allows the first two moments of returns tovary over time for a large number of assets. We then evaluatethe economic significance of the DFMSV model by examining theperformance of various dynamic portfolio strategies chosen bymean-variance investors in a universe of 36 stocks. We findthat the DFMSV dynamic strategies significantly outperform variousbenchmark strategies out of sample. This outperformance is robustto different performance measures, investor’s objectivefunctions, time periods, and assets.     

A slightly depressing jump model: intraday volatility pattern simulation

Hawkes processes have been finding more applications in diverse areas of science, engineering and quantitative finance. In multi-frequency finance various phenomena have been observed, such as shocks, crashes, volatility clustering, turbulent flows and contagion. Hawkes processes have been proposed to model those challenging phenomena appearing across asset prices in various exchanges. The original Hawkes process is an intensity-based model for series of events with path dependence and self-exciting or mutual-exciting mechanisms. This paper introduces a slightly depressing process to model the reverse phenomenon of self-exciting mechanisms. Such a process models the decline in the intensity of jumps observed in market regimes. The proposed birth-immigration-death process captures the decline in jump intensity observed at the start of a daily trading regime while the classical immigration-birth process models an increase in jump intensity towards the close of daily trading. Each of these processes can be expressed as a special case of a simple bivariate Hawkes process.     

Liquidity Dynamics Around Jumps: The Evidence from the Warsaw Stock Exchange

The aim of our study is to examine the dynamics of trading volume and the number of trades around jumps detected in intraday stock returns. We detect jumps in equally spaced 10-minute returns for most liquid stocks quoted on the Warsaw Stock Exchange within one-year sample period. We match jumps with macroeconomic and firm specific news. We find that only the minority of jumps is associated with public information releases, whereas the majority of them is motivated by liquidity shocks observed in the spreads, volume, and the number of trades. Our findings show that jumps are related to the inability of the market to absorb new and big orders. Liquidity shocks in volatility, volume, and quoted spread are the key drivers accompanying the occurrence of the jumps. Finally, the introduction of a faster and more efficient trading system improves the liquidity by increasing the depth of the market.     

Large deviations estimation of the windfall and shortfall probabilities for optimal diversified portfolios

Many investors believe that they can effectively reduce risk by, among other ways, holding large combinations of investment assets. The purpose of this paper is to develop asymptotic approximations of the windfall and shortfall probabilities for an optimal portfolio of risky assets as the number of the assets becomes sufficiently large. We start by providing some heuristics to motivate our problem, then proceed to prove general large deviations theorems. We also present specific results with an application to the multivariate normal case. Both a theoretical analysis of the method and an empirical application justify the diversification tenet of the allocation strategies that many hedge funds and pension funds tend to adopt nowadays.     

A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability

We present a simulation-based method for solving discrete-timeportfolio choice problems involving non-standard preferences,a large number of assets with arbitrary return distribution,and, most importantly, a large number of state variables withpotentially path-dependent or non-stationary dynamics. The methodis flexible enough to accommodate intermediate consumption,portfolio constraints, parameter and model uncertainty, andlearning. We first establish the properties of the method forthe portfolio choice between a stock index and cash when thestock returns are either iid or predictable by the dividendyield. We then explore the problem of an investor who takesinto account the predictability of returns but is uncertainabout the parameters of the data generating process. The investorchooses the portfolio anticipating that future data realizationswill contain useful information to learn about the true parametervalues.     

Contingent Claims on Foreign Assets Following Jump-Diffusion Processes

In this paper we price contingent claims on several foreign assetsthat follow jump-diffusion processes. Discontinuities (jumps) arise dueto the assets' movement in the respective countries, or the exchangerates, or both. We assume the existence of multiple classes (sources)of jumps. Each jump can affect one or more state-variables and is definedby its intensity of arrival and by the joint probability distributionof its magnitude. The existence of jumps gives rise to significant deviationsfrom the joint lognormality assumptions of the multivariate geometricBrownian motion, and affords more flexibility in capturing the empiricallyobserved asymmetry and fat tails in asset returns. Analytic solutionsare provided for the European option on the best of several assets withoutor with exchange rate (quanto-type) protection. A Markov-chainnumerical method that can also handle American claims is given and itsaccuracy is demonstrated. Neglecting the effect of jumps causes seriousmisspricing and leads to erroneous decision-making when purchasing orexercising such options.     

Constant proportion portfolio insurance strategies in contagious markets

Constant Proportion Portfolio Insurance (CPPI) strategies are popular as they allow to gear up the upside potential of a stock index while limiting its downside risk. From the issuer’s perspective it is important to adequately assess the risks associated with the CPPI, both for correct ‘gap’ fee charging and for risk management. The literature on CPPI modelling typically assumes diffusive or Lévy-driven dynamics for the risky asset underlying the strategy. In either case the self-contagious nature of asset prices is not taken into account. In order to account for contagion while preserving analytical tractability, we introduce self-exciting jumps in the underlying dynamics via Hawkes processes. Within this framework we derive the loss probability when trading is performed continuously. Moreover, we estimate measures of the risk involved in the practical implementation of discrete-time rebalancing rules governing the CPPI product. When rebalancing is performed on a frequency less than weekly, failing to take contagion into account will significantly underestimate the risks of the CPPI. Finally, in order to mimic a situation with low liquidity, we impose a daily trading cap on the risky asset and find that the Hawkes process driven models give rise to the highest risk measures even under daily rebalancing.     

The dynamics of squared returns under contemporaneous aggregation of GARCH models

The paper investigates the properties of a portfolio composed of a large number of assets driven by a strong multivariate GARCH(1,1) process with heterogeneous parameters. The aggregate return is shown to be a weak GARCH process with a (possibly large) number of lags, which reflects the moments of the distribution of the individual persistence parameters. The paper describes a consistent estimator of the aggregate return dynamics, based on nonlinear least squares. The proposed aggregation-corrected estimator (ACE) performs very well and outperforms some competing estimators in forecasting the daily variance of U.S. stocks portfolios at different horizons.     

Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market

This paper studies the modelling of large diversified portfolios in a financial market with jump-diffusion risks. The portfolios considered include three categories: equal money-weighted portfolios, risk-minimizing portfolios and market indices. Reduced-form dynamics driven jointly by one Brownian motion and one Poisson process are derived for the asymptotics of such portfolios. We prove that derivatives written on a portfolio can be priced by treating the asymptotic dynamics as the underlying process if the number of assets in the portfolio is sufficiently large. Analytical and Monte Carlo value-at-risk can be computed for the portfolios based on their asymptotic dynamics.