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Daniele Marazzina

Publications and source records attributed to Daniele Marazzina.

10 recordsLinked to original sources
arXiv2026

Pricing and Hedging Financial Derivatives in Merger\&Acquisition Deals with Price Impact

We investigate the optimal execution of contracts that are used in merger\&acquisition deals. We consider cash-settled and physically delivered contracts between a broker and a counterpart. Contracts are linear (total returns swaps), nonlinear (collar contracts) or Asian type (TWAP based contracts). We derive the optimal execution strategy and the optimal fee through indifference utility arguments allowing for linear market effects of trades. We show that linear cash-settled contracts are more expensive and more exposed to manipulation/statistical arbitrages by the broker. Also nonlinear and Asian type contracts are exposed to these phenomena.

q-fin.MF↗
arXiv2025

Sovereign Debt Default and Climate Risk

We explore the interplay between sovereign debt default/renegotiation and environmental factors (e.g., pollution from land use, natural resource exploitation). Pollution contributes to the likelihood of natural disasters and influences economic growth rates. The country can default on its debt at any time while also deciding whether to invest in pollution abatement. The framework provides insights into the credit spreads of sovereign bonds and explains the observed relationship between bond spread and a country's climate vulnerability. Through calibration for developing and low-income countries, we demonstrate that there is limited incentive for these countries to address climate risk, and the sensitivity of bond spreads to climate vulnerability remains modest. Climate risk does not play a relevant role on the decision to default on sovereign debt. Financial support for climate abatement expenditures can effectively foster climate adaptation actions, instead renegotiation conditional upon pollution abatement does not produce any effect.

econ.GN↗
arXiv2023

Hawkes-based cryptocurrency forecasting via Limit Order Book data

Accurately forecasting the direction of financial returns poses a formidable challenge, given the inherent unpredictability of financial time series. The task becomes even more arduous when applied to cryptocurrency returns, given the chaotic and intricately complex nature of crypto markets. In this study, we present a novel prediction algorithm using limit order book (LOB) data rooted in the Hawkes model, a category of point processes. Coupled with a continuous output error (COE) model, our approach offers a precise forecast of return signs by leveraging predictions of future financial interactions. Capitalizing on the non-uniformly sampled structure of the original time series, our strategy surpasses benchmark models in both prediction accuracy and cumulative profit when implemented in a trading environment. The efficacy of our approach is validated through Monte Carlo simulations across 50 scenarios. The research draws on LOB measurements from a centralized cryptocurrency exchange where the stablecoin Tether is exchanged against the U.S. dollar.

q-fin.ST↗
arXiv2021

Sensitivity of Optimal Retirement Problem to Liquidity Constraints

In this work we analytically solve an optimal retirement problem, in which the agent optimally allocates the risky investment, consumption and leisure rate to maximise a gain function characterised by a power utility function of consumption and leisure, through the duality method. We impose different liquidity constraints over different time spans and conduct a sensitivity analysis to discover the effect of this kind of constraint.

q-fin.PM↗
arXiv2021

Effect of Labour Income on the Optimal Bankruptcy Problem

In this paper we deal with the optimal bankruptcy problem for an agent who can optimally allocate her consumption rate, the amount of capital invested in the risky asset as well as her leisure time. In our framework, the agent is endowed by an initial debt, and she is required to repay her debt continuously. Declaring bankruptcy, the debt repayment is exempted at the cost of a wealth shrinkage. We implement the duality method to solve the problem analytically and conduct a sensitivity analysis to the cost and benefit parameters of bankruptcy. Introducing the flexible leisure/working rate, and therefore the labour income, into the bankruptcy model, we investigate its effect on the optimal strategies.

q-fin.PM↗
arXiv2021

Pricing methods for $α$-quantile and perpetual early exercise options based on Spitzer identities

We present new numerical schemes for pricing perpetual Bermudan and American options as well as $α$-quantile options. This includes a new direct calculation of the optimal exercise barrier for early-exercise options. Our approach is based on the Spitzer identities for general Lévy processes and on the Wiener-Hopf method. Our direct calculation of the price of $α$-quantile options combines for the first time the Dassios-Port-Wendel identity and the Spitzer identities for the extrema of processes. Our results show that the new pricing methods provide excellent error convergence with respect to computational time when implemented with a range of Lévy processes.

q-fin.CP↗
arXiv2021

Solution of Wiener-Hopf and Fredholm integral equations by fast Hilbert and Fourier transforms

We present numerical methods based on the fast Fourier transform (FFT) to solve convolution integral equations on a semi-infinite interval (Wiener-Hopf equation) or on a finite interval (Fredholm equation). We extend and improve a FFT-based method for the Wiener-Hopf equation due to Henery, expressing it in terms of the Hilbert transform, and computing the latter in a more sophisticated way with sinc functions. We then generalise our method to the Fredholm equation reformulating it as two coupled Wiener-Hopf equations and solving them iteratively. We provide numerical tests and open-source code.

math.NA↗
arXiv2020

Hilbert transform, spectral filters and option pricing

We show how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities, which give the distribution of the maximum or the minimum of a random path, or the joint distribution at maturity with the extrema staying below or above barriers. We use as examples the methods by Feng and Linetsky (2008) and Fusai, Germano and Marazzina (2016) to price discretely monitored barrier options where the underlying asset price is modelled by an exponential Lévy process. Both methods show exponential convergence with respect to the number of grid points in most cases, but are limited to polynomial convergence under certain conditions. We relate these rates of convergence to the Gibbs phenomenon for Fourier transforms and achieve improved results with spectral filtering.

q-fin.CP↗
arXiv2017

Fluctuation identities with continuous monitoring and their application to price barrier options

We present a numerical scheme to calculate fluctuation identities for exponential Lévy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities are given in the Fourier-Laplace domain and require numerical inverse transforms. Thus we cover a gap in the literature that has mainly studied the discrete monitoring case; indeed, there are no existing numerical methods that deal with the continuous case. As a motivating application we price continuously monitored barrier options with the underlying asset modelled by an exponential Lévy process. We perform a detailed error analysis of the method and develop error bounds to show how the performance is limited by the truncation error of the sinc-based fast Hilbert transform used for the Wiener-Hopf factorisation. By comparing the results for our new technique with those for the discretely monitored case (which is in the Fourier-$z$ domain) as the monitoring time step approaches zero, we show that the error convergence with continuous monitoring represents a limit for the discretely monitored scheme.

q-fin.CP↗