arXiv subjects

Giacomo Bormetti

Publications and source records attributed to Giacomo Bormetti.

At least 19 recordsLinked to original sources

arXiv2025

Why is the estimation of metaorder impact with public market data so challenging?

Estimating market impact and transaction costs of large trades (metaorders) is a very important topic in finance. However, using models of price and trade based on public market data provide average price trajectories which are qualitatively different from what is observed during real metaorder executions: the price increases linearly, rather than in a concave way, during the execution and the amount of reversion after its end is very limited. We claim that this is a generic phenomenon due to the fact that even sophisticated statistical models are unable to correctly describe the origin of the autocorrelation of the order flow. We propose a modified Transient Impact Model which provides more realistic trajectories by assuming that only a fraction of the metaorder trading triggers market order flow. Interestingly, in our model there is a critical condition on the kernels of the price and order flow equations in which market impact becomes permanent.

q-fin.TR↗

arXiv2025

Joint deep calibration of the 4-factor PDV model

Joint calibration to SPX and VIX market data is a delicate task that requires sophisticated modeling and incurs significant computational costs. The latter is especially true when pricing of volatility derivatives hinges on nested Monte Carlo simulation. One such example is the 4-factor Markov Path-Dependent Volatility (PDV) model of Guyon and Lekeufack (2023). Nonetheless, its realism has earned it considerable attention in recent years. Gazzani and Guyon (2025) marked a relevant contribution by learning the VIX as a random variable, i.e., a measurable function of the model parameters and the Markovian factors. A neural network replaces the inner simulation and makes the joint calibration problem accessible. However, the minimization loop remains slow due to expensive outer simulation. The present paper overcomes this limitation by learning SPX implied volatilities, VIX futures, and VIX call option prices. The pricing functions reduce to simple matrix-vector products that can be evaluated on the fly, shrinking calibration times to just a few seconds.

q-fin.CP↗

arXiv2025

Pricing Carbon Allowance Options on Futures: Insights from High-Frequency Data

Leveraging a unique dataset of carbon futures option prices traded on the ICE market from December 2015 until December 2020, we present the results from an unprecedented calibration exercise. Within a multifactor stochastic volatility framework with jumps, we employ a three-dimensional pricing kernel compensating for equity and variance components' risk to derive an analytically tractable and numerically practical approach to pricing. To the best of our knowledge, we are the first to provide an estimate of the equity and variance risk premia for the carbon futures option market. We gain insights into daily option and futures dynamics by exploiting the information from tick-by-tick futures trade data. Decomposing the realized measure of futures volatility into continuous and jump components, we employ them as auxiliary variables for estimating futures dynamics via indirect inference. Our approach provides a realistic description of carbon futures price, volatility, and jump dynamics and an insightful understanding of the carbon option market.

q-fin.PR↗

arXiv2024

Score-Driven Exponential Random Graphs: A New Class of Time-Varying Parameter Models for Dynamical Networks

Motivated by the increasing abundance of data describing real-world networks that exhibit dynamical features, we propose an extension of the Exponential Random Graph Models (ERGMs) that accommodates the time variation of its parameters. Inspired by the fast-growing literature on Dynamic Conditional Score models, each parameter evolves according to an updating rule driven by the score of the ERGM distribution. We demonstrate the flexibility of score-driven ERGMs (SD-ERGMs) as data-generating processes and filters and show the advantages of the dynamic version over the static one. We discuss two applications to temporal networks from financial and political systems. First, we consider the prediction of future links in the Italian interbank credit network. Second, we show that the SD-ERGM allows discriminating between static or time-varying parameters when used to model the U.S. Congress co-voting network dynamics.

stat.AP↗

arXiv2024

Deep calibration with random grids

We propose a neural network-based approach to calibrating stochastic volatility models, which combines the pioneering grid approach by Horvath et al. (2021) with the pointwise two-stage calibration of Bayer et al. (2018) and Liu et al. (2019). Our methodology inherits robustness from the former while not suffering from the need for interpolation/extrapolation techniques, a clear advantage ensured by the pointwise approach. The crucial point to the entire procedure is the generation of implied volatility surfaces on random grids, which one dispenses to the network in the training phase. We support the validity of our calibration technique with several empirical and Monte Carlo experiments for the rough Bergomi and Heston models under a simple but effective parametrization of the forward variance curve. The approach paves the way for valuable applications in financial engineering - for instance, pricing under local stochastic volatility models - and extensions to the fast-growing field of path-dependent volatility models.

q-fin.PR↗

arXiv2023

Robust Recursive Filtering and Smoothing

Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the observation density. The main advantages of the methodology can be summarized as follows: (i) it relaxes the critical assumption of a Gaussian prior distribution for the latent states underlying such approaches; (ii) can be applied to a general class of state-space models including univariate and multivariate location, scale and count data models; (iii) has a very simple structure based on forward-backward recursions similar to the Kalman filter and smoother; (iv) allows a straightforward computation of confidence bands around the state estimates reflecting the combination of parameter and filtering uncertainty. We show through an extensive Monte Carlo study that the mean square loss with respect to exact simulation-based methods is small in a wide range of scenarios. We finally illustrate empirically the application of the methodology to the estimation of stochastic volatility and correlations in financial time-series.

stat.ME↗

arXiv2022

Score Driven Generalized Fitness Model for Sparse and Weighted Temporal Networks

While the vast majority of the literature on models for temporal networks focuses on binary graphs, often one can associate a weight to each link. In such cases the data are better described by a weighted, or valued, network. An important well known fact is that real world weighted networks are typically sparse. We propose a novel time varying parameter model for sparse and weighted temporal networks as a combination of the fitness model, appropriately extended, and the score driven framework. We consider a zero augmented generalized linear model to handle the weights and an observation driven approach to describe time varying parameters. The result is a flexible approach where the probability of a link to exist is independent from its expected weight. This represents a crucial difference with alternative specifications proposed in the recent literature, with relevant implications for the flexibility of the model. Our approach also accommodates for the dependence of the network dynamics on external variables. We present a link forecasting analysis to data describing the overnight exposures in the Euro interbank market and investigate whether the influence of EONIA rates on the interbank network dynamics has changed over time.

stat.AP↗

arXiv2022

A Lucas Critique Compliant SVAR model with Observation-driven Time-varying Parameters

We propose an observation-driven time-varying SVAR model where, in agreement with the Lucas Critique, structural shocks drive both the evolution of the macro variables and the dynamics of the VAR parameters. Contrary to existing approaches where parameters follow a stochastic process with random and exogenous shocks, our observation-driven specification allows the evolution of the parameters to be driven by realized past structural shocks, thus opening the possibility to gauge the impact of observed shocks and hypothetical policy interventions on the future evolution of the economic system.

econ.EM↗

arXiv2021

The SINC way: A fast and accurate approach to Fourier pricing

The goal of this paper is to investigate the method outlined by one of us (PR) in Cherubini et al. (2009) to compute option prices. We name it the SINC approach. While the COS method by Fang and Osterlee (2009) leverages the Fourier-cosine expansion of truncated densities, the SINC approach builds on the Shannon Sampling Theorem revisited for functions with bounded support. We provide several results which were missing in the early derivation: i) a rigorous proof of the convergence of the SINC formula to the correct option price when the support grows and the number of Fourier frequencies increases; ii) ready to implement formulas for put, Cash-or-Nothing, and Asset-or-Nothing options; iii) a systematic comparison with the COS formula for several log-price models; iv) a numerical challenge against alternative Fast Fourier specifications, such as Carr and Madan (1999) and Lewis (2000); v) an extensive pricing exercise under the rough Heston model of Jaisson and Rosenbaum (2015); vi) formulas to evaluate numerically the moments of a truncated density. The advantages of the SINC approach are numerous. When compared to benchmark methodologies, SINC provides the most accurate and fast pricing computation. The method naturally lends itself to price all options in a smile concurrently by means of Fast Fourier techniques, boosting fast calibration. Pricing requires to resort only to odd moments in the Fourier space. A previous version of this manuscript circulated with the title `Rough Heston: The SINC way'.

q-fin.PR↗

arXiv2020

A tale of two sentiment scales: Disentangling short-run and long-run components in multivariate sentiment dynamics

We propose a novel approach to sentiment data filtering for a portfolio of assets. In our framework, a dynamic factor model drives the evolution of the observed sentiment and allows to identify two distinct components: a long-term component, modeled as a random walk, and a short-term component driven by a stationary VAR(1) process. Our model encompasses alternative approaches available in literature and can be readily estimated by means of Kalman filtering and expectation maximization. This feature makes it convenient when the cross-sectional dimension of the portfolio increases. By applying the model to a portfolio of Dow Jones stocks, we find that the long term component co-integrates with the market principal factor, while the short term one captures transient swings of the market associated with the idiosyncratic components and captures the correlation structure of returns. Using quantile regressions, we assess the significance of the contemporaneous and lagged explanatory power of sentiment on returns finding strong statistical evidence when extreme returns, especially negative ones, are considered. Finally, the lagged relation is exploited in a portfolio allocation exercise.

q-fin.GN↗

arXiv2020

Deep learning Profit & Loss

Building the future profit and loss (P&L) distribution of a portfolio holding, among other assets, highly non-linear and path-dependent derivatives is a challenging task. We provide a simple machinery where more and more assets could be accounted for in a simple and semi-automatic fashion. We resort to a variation of the Least Square Monte Carlo algorithm where interpolation of the continuation value of the portfolio is done with a feed forward neural network. This approach has several appealing features not all of them will be fully discussed in the paper. Neural networks are extremely flexible regressors. We do not need to worry about the fact that for multi assets payoff, the exercise surface could be non connected. Neither we have to search for smart regressors. The idea is to use, regardless of the complexity of the payoff, only the underlying processes. Neural networks with many outputs can interpolate every single assets in the portfolio generated by a single Monte Carlo simulation. This is an essential feature to account for the P&L distribution of the whole portfolio when the dependence structure between the different assets is very strong like the case where one has contingent claims written on the same underlying.

q-fin.RM↗

arXiv2019

A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: an Application to High-Frequency Covariance Dynamics

The analysis of the intraday dynamics of correlations among high-frequency returns is challenging due to the presence of asynchronous trading and market microstructure noise. Both effects may lead to significant data reduction and may severely underestimate correlations if traditional methods for low-frequency data are employed. We propose to model intraday log-prices through a multivariate local-level model with score-driven covariance matrices and to treat asynchronicity as a missing value problem. The main advantages of this approach are: (i) all available data are used when filtering correlations, (ii) market microstructure noise is taken into account, (iii) estimation is performed through standard maximum likelihood methods. Our empirical analysis, performed on 1-second NYSE data, shows that opening hours are dominated by idiosyncratic risk and that a market factor progressively emerges in the second part of the day. The method can be used as a nowcasting tool for high-frequency data, allowing to study the real-time response of covariances to macro-news announcements and to build intraday portfolios with very short optimization horizons.

q-fin.TR↗

arXiv2016

Linear models for the impact of order flow on prices II. The Mixture Transition Distribution model

Modeling the impact of the order flow on asset prices is of primary importance to understand the behavior of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be obtained when one incorporates the impact of past returns on the future order flow. However, impact models presented in Part I consider the order flow as an exogenous process, only characterized by its two-point correlations. This assumption seriously limits the forecasting ability of the model. Here we attempt to model directly the stream of discrete events with a so-called Mixture Transition Distribution (MTD) framework, introduced originally by Raftery (1985). We distinguish between price-changing and non price-changing events and combine them with the order sign in order to reduce the order flow dynamics to the dynamics of a four-state discrete random variable. The MTD represents a parsimonious approximation of a full high-order Markov chain. The new approach captures with adequate realism the conditional correlation functions between signed events for both small and large tick stocks and signature plots. From a methodological viewpoint, we discuss a novel and flexible way to calibrate a large class of MTD models with a very large number of parameters. In spite of this large number of parameters, an out-of-sample analysis confirms that the model does not overfit the data.

q-fin.TR↗

arXiv2016

Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact

Market impact is a key concept in the study of financial markets and several models have been proposed in the literature so far. The Transient Impact Model (TIM) posits that the price at high frequency time scales is a linear combination of the signs of the past executed market orders, weighted by a so-called propagator function. An alternative description -- the History Dependent Impact Model (HDIM) -- assumes that the deviation between the realised order sign and its expected level impacts the price linearly and permanently. The two models, however, should be extended since prices are a priori influenced not only by the past order flow, but also by the past realisation of returns themselves. In this paper, we propose a two-event framework, where price-changing and non price-changing events are considered separately. Two-event propagator models provide a remarkable improvement of the description of the market impact, especially for large tick stocks, where the events of price changes are very rare and very informative. Specifically the extended approach captures the excess anti-correlation between past returns and subsequent order flow which is missing in one-event models. Our results document the superior performances of the HDIMs even though only in minor relative terms compared to TIMs. This is somewhat surprising, because HDIMs are well grounded theoretically, while TIMs are, strictly speaking, inconsistent.

q-fin.TR↗

arXiv2015

Coupling news sentiment with web browsing data improves prediction of intra-day price dynamics

The new digital revolution of big data is deeply changing our capability of understanding society and forecasting the outcome of many social and economic systems. Unfortunately, information can be very heterogeneous in the importance, relevance, and surprise it conveys, affecting severely the predictive power of semantic and statistical methods. Here we show that the aggregation of web users' behavior can be elicited to overcome this problem in a hard to predict complex system, namely the financial market. Specifically, our in-sample analysis shows that the combined use of sentiment analysis of news and browsing activity of users of Yahoo! Finance greatly helps forecasting intra-day and daily price changes of a set of 100 highly capitalized US stocks traded in the period 2012-2013. Sentiment analysis or browsing activity when taken alone have very small or no predictive power. Conversely, when considering a "news signal" where in a given time interval we compute the average sentiment of the clicked news, weighted by the number of clicks, we show that for nearly 50% of the companies such signal Granger-causes hourly price returns. Our result indicates a "wisdom-of-the-crowd" effect that allows to exploit users' activity to identify and weigh properly the relevant and surprising news, enhancing considerably the forecasting power of the news sentiment.

q-fin.ST↗

arXiv2015

A backward Monte Carlo approach to exotic option pricing

We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a discrete multinomial tree. The crucial feature of our approach is that -- in a similar spirit to the Brownian Bridge -- each random path runs backward from a terminal fixed point to the initial spot price. We characterize the tree in two alternative ways: in terms of the optimal grids originating from the Recursive Marginal Quantization algorithm and following an approach inspired by the finite difference approximation of the diffusion's infinitesimal generator. We assess the reliability of the new methodology comparing the performance of both approaches and benchmarking them with competitor Monte Carlo methods.

q-fin.CP↗

arXiv2015

Multi-curve HJM modelling for risk management

We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for a finite number of time-to-maturity buckets, we propose a modelling framework which is inherently discrete. In particular, we show how to approximate the HJM continuous time description of the multi-curve dynamics by a Vector Autoregressive process of order one. The resulting dynamics lends itself to a feasible estimation of the model volatility-correlation structure and market risk-premia. Then, resorting to the Principal Component Analysis we further simplify the dynamics reducing the number of covariance components. Applying the constant volatility version of our model on a sample of curves from the Euro area, we demonstrate its forecasting ability through an out-of-sample test.

q-fin.RM↗

arXiv2015

Impact of Multiple Curve Dynamics in Credit Valuation Adjustments under Collateralization

We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that spot Libor rates are to be treated as market primitives rather than being defined by no-arbitrage relationships. We formulate a consistent realistic dynamics for the different rates emerging from our analysis and compare the resulting model performances to simpler models used in the industry. We include the often neglected margin period of risk, showing how this feature may increase the impact of different rates dynamics on valuation. We point out limitations of multiple curve models with deterministic basis considering valuation of particularly sensitive products such as basis swaps. We stress that a proper wrong way risk analysis for such products requires a model with a stochastic basis and we show numerical results confirming this fact.

q-fin.PR↗