We consider a network of banks that optimally choose a strategy of asset liquidations and borrowing in order to cover short term obligations. The borrowing is done in the form of collateralized repurchase agreements, the haircut level of which depends on the total liquidations of all the banks. Similarly the fire-sale price of the asset obtained by each of the banks depends on the amount of assets liquidated by the bank itself and by other banks. By nature of this setup, banks' behavior is considered as a Nash equilibrium. This paper provides two forms for market clearing to occur: through a common closing price and through an application of the limit order book. The main results of this work are providing sufficient conditions for existence and uniqueness of the clearing solutions (i.e., liquidations, borrowing, fire sale prices, and haircut levels).

Accurately estimating the effectiveness of stay-at-home orders (SHOs) on reducing social contact and disease spread is crucial for mitigating pandemics. Leveraging individual-level location data for 10 million smartphones, we observe that by April 30th---when nine in ten Americans were under a SHO---daily movement had fallen 70% from pre-COVID levels. One-quarter of this decline is causally attributable to SHOs, with wide demographic differences in compliance, most notably by political affiliation. Likely Trump voters reduce movement by 9% following a local SHO, compared to a 21% reduction among their Clinton-voting neighbors, who face similar exposure risks and identical government orders. Linking social distancing behavior with an epidemic model, we estimate that reductions in movement have causally reduced SARS-CoV-2 transmission rates by 49%.

We derive generalizations of Dupire formula to the cases of general stochastic drift and/or stochastic local volatility. First, we handle a case in which the drift is given as difference of two stochastic short rates. Such a setting is natural in foreign exchange context where the short rates correspond to the short rates of the two currencies, equity single-currency context with stochastic dividend yield, or commodity context with stochastic convenience yield. We present the formula both in a call surface formulation as well as total implied variance formulation where the latter avoids calendar spread arbitrage by construction. We provide derivations for the case where both short rates are given as single factor processes and present the limits for a single stochastic rate or all deterministic short rates. The limits agree with published results. Then we derive a formulation that allows a more general stochastic drift and diffusion including one or more stochastic local volatility terms. In the general setting, our derivation allows the computation and calibration of the leverage function for stochastic local volatility models.

We propose an actionable calibration procedure for general Quadratic Hawkes models of order book events (market orders, limit orders, cancellations). One of the main features of such models is to encode not only the influence of past events on future events but also, crucially, the influence of past price changes on such events. We show that the empirically calibrated quadratic kernel is well described by a diagonal contribution (that captures past realised volatility), plus a rank-one "Zumbach" contribution (that captures the effect of past trends). We find that the Zumbach kernel is a power-law of time, as are all other feedback kernels. As in many previous studies, the rate of truly exogenous events is found to be a small fraction of the total event rate. These two features suggest that the system is close to a critical point -- in the sense that stronger feedback kernels would lead to instabilities.

Green hydrogen can decarbonize transportation, but also help to integrate variable renewable energy sources if its production is sufficiently flexible in time. Using an open-source co-optimization model of the power sector and four supply chains for hydrogen at filling stations, we find a trade-off between energy efficiency and temporal flexibility: for lower shares of renewables and hydrogen, more energy-efficient decentralized electrolysis is optimal. For higher shares of renewables and/or hydrogen, more flexible centralized hydrogen supply chains gain importance as they allow disentangling hydrogen production from demand via storage. Liquid hydrogen emerges as particularly beneficial, followed by liquid organic hydrogen carriers and gaseous hydrogen. Centralized hydrogen supply chains can deliver substantial power sector co-benefits, mainly through reduced renewable surplus generation. Energy modelers and system planners should consider the flexibility characteristics of hydrogen supply chains in more detail when assessing the role of green hydrogen in future energy transition scenarios.

When pricing options, there may be different views on the instantaneous mean return of the underlying price process. According to Black (1972), where there exist heterogeneous views on the instantaneous mean return, this will result in arbitrage opportunities. Behavioral finance proponents argue that such heterogenous views are likely to occur and this will not impact option pricing models proposed by rational dynamic asset pricing theory and will not give rise to volatility smiles. To rectify this, a leading advocate of behavioral finance has proposed a behavioral option pricing model. As there may be unexplored links between the behavioral and rational approaches to option pricing, in this paper we revisit Shefrin (2008) option pricing model as an example and suggest one approach to modify this behavioral finance option pricing formula to be consistent with rational dynamic asset pricing theory by introducing arbitrage transaction costs which offset the gains from arbitrage trades.

We continue a series of papers where prices of the barrier options written on the underlying, which dynamics follows some one factor stochastic model with time-dependent coefficients and the barrier, are obtained in semi-closed form, see (Carr and Itkin, 2020, Itkin and Muravey, 2020). This paper extends this methodology to the CIR model for zero-coupon bonds, and to the CEV model for stocks which are used as the corresponding underlying for the barrier options. We describe two approaches. One is generalization of the method of heat potentials for the heat equation to the Bessel process, so we call it the method of Bessel potentials. We also propose a general scheme how to construct the potential method for any linear differential operator with time-independent coefficients. The second one is the method of generalized integral transform, which is also extended to the Bessel process. In all cases, a semi-closed solution means that first, we need to solve numerically a linear Volterra equation of the second kind, and then the option price is represented as a one-dimensional integral. We demonstrate that computationally our method is more efficient than both the backward and forward finite difference methods while providing better accuracy and stability. Also, it is shown that both method don't duplicate but rather compliment each other, as one provides very accurate results at small maturities, and the other one - at high maturities.

The COVID-19 pandemic has caused a massive economic shock across the world due to business interruptions and shutdowns from social-distancing measures. To evaluate the socio-economic impact of COVID-19 on individuals, a micro-economic model is developed to estimate the direct impact of distancing on household income, savings, consumption, and poverty. The model assumes two periods: a crisis period during which some individuals experience a drop in income and can use their precautionary savings to maintain consumption; and a recovery period, when households save to replenish their depleted savings to pre-crisis level. The San Francisco Bay Area is used as a case study, and the impacts of a lockdown are quantified, accounting for the effects of unemployment insurance (UI) and the CARES Act federal stimulus. Assuming a shelter-in-place period of three months, the poverty rate would temporarily increase from 17.1% to 25.9% in the Bay Area in the absence of social protection, and the lowest income earners would suffer the most in relative terms. If fully implemented, the combination of UI and CARES could keep the increase in poverty close to zero, and reduce the average recovery time, for individuals who suffer an income loss, from 11.8 to 6.7 months. However, the severity of the economic impact is spatially heterogeneous, and certain communities are more affected than the average and could take more than a year to recover. Overall, this model is a first step in quantifying the household-level impacts of COVID-19 at a regional scale. This study can be extended to explore the impact of indirect macroeconomic effects, the role of uncertainty in households' decision-making and the potential effect of simultaneous exogenous shocks (e.g., natural disasters).

We establish several closed pricing formula for various path-independent payoffs, under an exponential L\'evy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools from Mellin transform theory as well as from multidimensional complex analysis. Particular focus is made on the symmetric process, but extension to the asymmetric process is also provided. Speed of convergence and comparison with numerical methods (Fourier transform, quadrature approximations, Monte Carlo simulations) are also discussed; notable feature is the accelerated convergence of the series for short term options, which constitutes an interesting improvement of numerical Fourier inversion techniques.

Strong social distancing restrictions have been crucial to controlling the COVID-19 outbreak thus far, and the next question is when and how to relax these restrictions. A sequential timing of relaxing restrictions across groups is explored in order to identify policies that simultaneously reduce health risks and economic stagnation relative to current policies. The goal will be to mitigate health risks, particularly among the most fragile sub-populations, while also managing the deleterious effect of restrictions on economic activity. The results of this paper show that a properly constructed sequential release of age-defined subgroups from strict social distancing protocols can lead to lower overall fatality rates than the simultaneous release of all individuals after a lockdown. The optimal release policy, in terms of minimizing overall death rate, must be sequential in nature, and it is important to properly time each step of the staggered release. This model allows for testing of various timing choices for staggered release policies, which can provide insights that may be helpful in the design, testing, and planning of disease management policies for the ongoing COVID-19 pandemic and future outbreaks.

Consider a financial market with nonnegative semimartingales which does not need to have a num\'{e}raire. We are interested in the absence of arbitrage in the sense that no self-financing portfolio gives rise to arbitrage opportunities, where we are allowed to add a savings account to the market. We will prove that in this sense the market is free of arbitrage if and only if there exists an equivalent local martingale deflator which is a multiplicative special semimartingale. In this case, the additional savings account relates to the finite variation part of the multiplicative decomposition of the deflator. By focusing on self-financing portfolios, this result clarifies links between previous results in the literature and makes the respective concepts more realistic.

The magnitude of the coronavirus disease (COVID-19) pandemic has an enormous impact on the social life and the economic activities in almost every country in the world. Besides the biological and epidemiological factors, a multitude of social and economic criteria also govern the extent of the coronavirus disease spread in the population. Consequently, there is an active debate regarding the critical socio-economic determinants that contribute to the resulting pandemic. In this paper, we contribute towards the resolution of the debate by leveraging Bayesian model averaging techniques and country level data to investigate the potential of 29 determinants, describing a diverse set of socio-economic characteristics, in explaining the coronavirus pandemic outcome. We show that the true empirical model behind the coronavirus outcome is constituted only of few determinants, but the extent to which each determinant is able to provide a credible explanation varies between countries due to their heterogeneous socio-economic characteristics. To understand the relationship between the potential determinants in the specification of the true model, we develop the coronavirus determinants Jointness space. In this space, two determinants are connected with each other if they are able to jointly explain the coronavirus outcome. As constructed, the obtained map acts as a bridge between theoretical investigations and empirical observations, and offers an alternate view for the joint importance of the socio-economic determinants when used for developing policies aimed at preventing future epidemic crises.

This seemed impossible to use a theoretically adequate but too sophisticated risk measure called non-ruin capital, whence its widespread (including regulatory documents) replacement with an inadequate, but simple risk measure called Value-at-Risk. Conflicting with the idea by Albert Einstein that "everything should be made as simple as possible, but not simpler", this led to fallacious, and even deceitful (but generally accepted) standards and recommendations. Arguing from the standpoint of mathematical theory of risk, we aim to break this impasse.