Research articles for the 2020-09-01

A Principal-Agent approach to Capacity Remuneration Mechanisms
Clémence Alasseur,Heythem Farhat,Marcelo Saguan

We propose to study electricity capacity remuneration mechanism design through a Principal-Agent approach. The Principal represents the aggregation of electricity consumers (or a representative entity), subject to the physical risk of shortage, and the Agent represents the electricity capacity owners, who invest in capacity and produce electricity to satisfy consumers' demand, and are subject to financial risks. Following the methodology of Cvitanic et al. (2017), we propose an optimal contract, from consumers' perspective, which complements the revenue capacity owners achieved from the spot energy market, and incentivizes both parties to perform an optimal level of investments while sharing the physical and financial risks. Numerical results provide insights on the necessity of a capacity remuneration mechanism and also show how this is especially true when the level of uncertainties on demand or production side increases.

Contingent Convertible Bonds in Financial Networks
Giovanni Calice,Carlo Sala,Daniele Tantari

We study the role of contingent convertible bonds (CoCos) in a network of interconnected banks. We first confirm the phase transitions documented by Acemoglu et al. (2015) in absence of CoCos, thus revealing that the structure of the interbank network is of fundamental importance for the effectiveness of CoCos as a financial stability enhancing mechanism. Furthermore, we show that in the presence of a moderate financial shock lightly interconnected financial networks are more robust than highly interconnected networks, and can possibly be the optimal choice for both CoCos issuers and buyers. Finally our results show that, under some network structures, the presence of CoCos can increase (and not reduce) financial fragility, because of the occurring of unneeded triggers and consequential suboptimal conversions that damage CoCos investors.

High-Resolution Poverty Maps in Sub-Saharan Africa
Kamwoo Lee,Jeanine Braithwaite

Up-to-date poverty maps are an important tool for policymakers, but until now, have been prohibitively expensive to produce. We propose a generalizable prediction methodology to produce poverty maps at the village level using geospatial data and machine learning algorithms. We tested the proposed method for 25 Sub-Saharan African countries and validated them against survey data. The proposed method can increase the validity of both single country and cross-country estimations leading to higher precision in poverty maps of the 25 countries than previously available. More importantly, our cross-country estimation enables the creation of poverty maps when it is not practical or cost-effective to field new national household surveys, as is the case with many Sub-Saharan African countries and other low- and middle-income countries.

Interacting Regional Policies in Containing a Disease
Arun G. Chandrasekhar,Paul Goldsmith-Pinkham,Matthew O. Jackson,Samuel Thau

Regional quarantine policies, in which a portion of a population surrounding infections are locked down, are an important tool to contain disease. However, jurisdictional governments -- such as cities, counties, states, and countries -- act with minimal coordination across borders. We show that a regional quarantine policy's effectiveness depends upon whether (i) the network of interactions satisfies a balanced-growth condition, (ii) infections have a short delay in detection, and (iii) the government has control over and knowledge of the necessary parts of the network (no leakage of behaviors). As these conditions generally fail to be satisfied, especially when interactions cross borders, we show that substantial improvements are possible if governments are proactive: triggering quarantines in reaction to neighbors' infection rates, in some cases even before infections are detected internally. We also show that even a few lax governments -- those that wait for nontrivial internal infection rates before quarantining -- impose substantial costs on the whole system. Our results illustrate the importance of understanding contagion across policy borders and offer a starting point in designing proactive policies for decentralized jurisdictions.

Optimal Border Control during the Re-opening Phase of the COVID-19 Pandemic
Zhen Zhu,Enzo Weber,Till Strohsal,Duaa Serhan

Most of the existing literature on the current pandemic focuses on approaches to model the outbreak and spreading of COVID-19. This paper proposes a generalized Markov-Switching approach, the SUIHR model, designed to study border control policies and contact tracing against COVID-19 in a period where countries start to re-open. We offer the following contributions. First, the SUIHR model can include multiple entities, reflecting different government bodies with different containment measures. Second, constraints as, for example, new case targets and medical resource limits can be imposed in a linear programming framework. Third, in contrast to most SIR models, we focus on the spreading of infectious people without symptoms instead of the spreading of people who are already showing symptoms. We find that even if a country has closed its borders completely, domestic contact tracing is not enough to go back to normal life. Countries having successfully controlled the virus can keep it under check as long as imported risk is not growing, meaning they can lift travel restrictions with similar countries. However, opening borders towards countries with less controlled infection dynamics would require a mandatory quarantine or a strict test on arrival.

Optimal Hedging in Incomplete Markets
George Bouzianis,Lane P. Hughston

We consider the problem of optimal hedging in an incomplete market with an established pricing kernel. In such a market, prices are uniquely determined, but perfect hedges are usually not available. We work in the rather general setting of a L\'evy-Ito market, where assets are driven jointly by an $n$-dimensional Brownian motion and an independent Poisson random measure on an $n$-dimensional state space. Given a position in need of hedging and the instruments available as hedges, we demonstrate the existence of an optimal hedge portfolio, where optimality is defined by use of an expected least squared-error criterion over a specified time frame, and where the numeraire with respect to which the hedge is optimized is taken to be the benchmark process associated with the designated pricing kernel.

Pseudo-Hermiticity, and Removing the Brownian Motion from Finance
Will Hicks

In this article we apply the methods of quantum mechanics to the study of the financial markets. Specifically, we discuss the Pseudo-Hermiticity of the Hamiltonian operators associated to the typical partial differential equations of Mathematical Finance (such as the Black-Scholes equation) and how this relates to the non-arbitrage condition.

We propose that one can use a Schrodinger equation to derive the probabilistic behaviour of the financial market, and discuss the benefits of doing so. This presents an alternative approach to replace the use of standard diffusion processes (for example a Brownian motion or Wiener process).

We go on to study the method using the Bohmian approach to quantum mechanics. We consider how to interpret the equations for pseudo-Hermitian systems, and highlight the crucial role played by the quantum potential function.

Rough Heston: the SINC way
Fabio Baschetti,Giacomo Bormetti,Silvia Romagnoli,Pietro Rossi

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 named 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 important results which were missing in the early derivation: i) a rigorous proof of the converge of the SINC formula to the correct option price when the support growths 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 in several settings; 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.

XVA Analysis From the Balance Sheet
Claudio Albanese,Stephane Crepey,Rodney Hoskinson,Bouazza Saadeddine

XVAs denote various counterparty risk related valuation adjustments that are applied to financial derivatives since the 2007--09 crisis. We root a cost-of-capital XVA strategy in a balance sheet perspective which is key in identifying the economic meaning of the XVA terms. Our approach is first detailed in a static setup that is solved explicitly. It is then plugged in the dynamic and trade incremental context of a real derivative banking portfolio. The corresponding cost-of-capital XVA strategy ensures to bank shareholders a submartingale equity process corresponding to a target hurdle rate on their capital at risk, consistently between and throughout deals. Set on a forward/backward SDE formulation, this strategy can be solved efficiently using GPU computing combined with deep learning regression methods in a whole bank balance sheet context. A numerical case study emphasizes the workability and added value of the ensuing pathwise XVA computations.