Research articles for the 2020-06-28

A pure-jump mean-reverting short rate model
Markus Hess

A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein--Uhlenbeck processes such that the related bond prices possess affine representations. Also the dynamics of the associated instantaneous forward rate is provided and a condition is derived under which the model can be market-consistently calibrated. The analytical tractability of this model is illustrated by the derivation of an explicit plain vanilla option price formula. With view on practical applications, suitable probability distributions are proposed for the driving jump processes. The paper is concluded by presenting a post-crisis extension of the proposed short and forward rate model.

An unsupervised deep learning approach in solving partial-integro differential equations
Ali Hirsa,Weilong Fu

We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow \levy processes, we require to solve PIDEs. In supervised deep learning, pre-calculated labels are used to train neural networks to fit the solution of the PIDE. In an unsupervised deep learning, neural networks are employed as the solution, and the derivatives and the integrals in the PIDE are calculated based on the neural network. By matching the PIDE and its boundary conditions, the neural network gives an accurate solution of the PIDE. Once trained, it would be fast for calculating options values as well as option \texttt{Greeks}.

Bayesian prediction of jumps in large panels of time series data
Angelos Alexopoulos,Petros Dellaportas,Omiros Papaspiliopoulos

We take a new look at the problem of disentangling the volatility and jumps processes in a panel of stock daily returns. We first provide an efficient computational framework that deals with the stochastic volatility model with Poisson-driven jumps in a univariate scenario that offers a competitive inference alternative to the existing implementation tools. This methodology is then extended to a large set of stocks in which it is assumed that the unobserved jump intensities of each stock co-evolve in time through a dynamic factor model. A carefully designed sequential Monte Carlo algorithm provides out-of-sample empirical evidence that our suggested model outperforms, with respect to predictive Bayes factors, models that do not exploit the panel structure of stocks.

Forecasting the effect of COVID-19 on the S&P500
Karina Arias-Calluari,Fernando Alonso-Marroquin,Morteza Nattagh-Najafi,Michael Harré

The outbreak of the novel coronavirus (COVID-19) is considered an exogenous risk, which has caused unprecedented disruptions to financial and economic markets around the globe, leading to one of the fastest U.S. stock market declines in history. However, in the past we have seen the market recover and we can expect the market to recover again, and on this basis we assume the Standard and Poor's 500 (S&P500) index will reach a minimum before rising again in the not-too-distant future. Here we present four forecast models of the S&P500 based on COVID-19 projections of deaths released on 02/04/2020 by the University of Washington and the 2-months consideration since the first confirmed case occured in USA. The decline and recovery in the index is estimated for the following three months. The forecast is a projection of a prediction with fluctuations described by $q$-gaussian distributions. Our forecast was made on the premise that: (a) The prediction is based on a deterministic trend that follows the data available since the initial outbreak of COVID-19, and (b) fluctuations derived from the S&P500 over the last 24 years.

Investor Emotions and Earnings Announcements
Domonkos F. Vamossy

Armed with a decade of social media data, I explore the impact of investor emotions on earnings announcements. In particular, I test whether the emotional content of firm-specific messages posted on social media just prior to a firm's earnings announcement predicts its earnings and announcement returns. I find that investors are typically excited about firms that end up exceeding expectations, yet their enthusiasm results in lower announcement returns. Specifically, a standard deviation increase in excitement is associated with an 7.8 basis points lower announcement return, which translates into an approximately -5.8% annualized loss. My findings confirm that emotions and market dynamics are closely related and highlight the importance of considering investor emotions when assessing a firm's short-term value.

Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model
Michael C. Fu,Bingqing Li,Rongwen Wu,Tianqi Zhang

We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can model volatility clustering and varying mean-reversion speeds of volatility. For pricing European options, we develop a computationally efficient method for obtaining the probability distribution of average integrated variance (AIV), which is key to option pricing under stochastic-volatility-type models. Building upon the efficiency of the European option pricing approach, we are able to price an American-style option, by converting its pricing into the pricing of a portfolio of European options. Our work also provides constructive guidance for analyzing derivatives based on variance, e.g., the variance swap. Numerical results indicate our methods can be implemented very efficiently and accurately.

Status Quo Bias Beats the Decoy Effect and Reverses Attitudes Toward Risk
Miguel Costa-Gomes,Georgios Gerasimou

Inertia and context-dependent choice effects are well-studied classes of behavioural phenomena. While much is known about these effects individually, little is known about whether one of them "dominates" another. Knowledge of any such dominance is important for effective choice architecture and for accurate descriptive modelling. We initiate this empirical investigation with a lab experiment on choice under risk that was designed to test for dominance between *status quo bias* and the *decoy effect*. We find that the former unambiguously prevails over the latter and is powerful enough to make the average subject switch from being risk averse to being risk-seeking. The observed reversal in risk attitudes is explainable by a large class of Kozsegi-Rabin (2006) reference-dependent preferences.

Systemic Optimal Risk Transfer Equilibrium
Francesca Biagini,Alessandro Doldi,Jean-Pierre Fouque,Marco Frittelli,Thilo Meyer-Brandis

We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the B\"uhlmann's classical notion of an Equilibrium Risk Exchange. We provide sufficient general assumptions that guarantee existence, uniqueness, and Pareto optimality of such a SORTE. In both the B\"uhlmann and the SORTE definition, each agent is behaving rationally by maximizing his/her expected utility given a budget constraint. The two approaches differ by the budget constraints. In B\"uhlmann's definition the vector that assigns the budget constraint is given a priori. On the contrary, in the SORTE approach, the vector that assigns the budget constraint is endogenously determined by solving a systemic utility maximization. SORTE gives priority to the systemic aspects of the problem, in order to optimize the overall systemic performance, rather than to individual rationality.

Systems of ergodic BSDEs arising in regime switching forward performance processes
Ying Hu,Gechun Liang,Shanjian Tang

We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a regime switching market. In addition, we develop a connection between the solution of the ergodic BSDE system and the long-term growth rate of classical utility maximization problems, and use the ergodic BSDE system to study the large time behavior of PDE systems with quadratic growth Hamiltonians.

The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks
Jean-Bernard Chatelain,Kirsten Ralf

With non-controllable auto-regressive shocks, the welfare of Ramsey optimal policy is the solution of a single Riccati equation of a linear quadratic regulator. The existing theory by Hansen and Sargent (2007) refers to an additional Sylvester equation but miss another equation for computing the block matrix weighting the square of non-controllable variables in the welfare function. There is no need to simulate impulse response functions over a long period, to compute period loss functions and to sum their discounted value over this long period, as currently done so far. Welfare is computed for the case of the new-Keynesian Phillips curve with an auto-regressive cost-push shock. JEL classification numbers: C61, C62, C73, E47, E52, E61, E63.

The non-universality of wealth distribution tails near wealth condensation criticality
Sam L. Polk,Bruce M. Boghosian

In this work, we modify the Affine Wealth Model of wealth distributions to examine the effects of nonconstant redistribution on the very wealthy. Previous studies of this model, restricted to flat redistribution schemes, have demonstrated the presence of a phase transition to a partially wealth-condensed state, or "partial oligarchy", at the critical value of an order parameter. These studies have also indicated the presence of an exponential tail in wealth distribution precisely at criticality. Away from criticality, the tail was observed to be Gaussian. In this work, we generalize the flat redistribution within the Affine Wealth Model to allow for an essentially arbitrary redistribution policy. We show that the exponential tail observed near criticality in prior work is in fact a special case of a much broader class of critical, slower-than-Gaussian decays that depend sensitively on the corresponding asymptotic behavior of the progressive redistribution model used. We thereby demonstrate that the functional form of the tail of the wealth distribution of a near-critical society is not universal in nature, but rather is entirely determined by the specifics of public policy decisions. This is significant because most major economies today are observed to be near-critical.

Time-consistent conditional expectation under probability distortion
Jin Ma,Ting-Kam Leonard Wong,Jianfeng Zhang

We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic setting is time-inconsistency, that is, the usual "tower property" fails. By localizing the probability distortion and restricting to a smaller class of random variables, we introduce a so-called distorted probability and construct a conditional expectation in such a way that it coincides with the original nonlinear expectation at time zero, but has a time-consistent dynamics in the sense that the tower property remains valid. Furthermore, we show that in the continuous time model this conditional expectation corresponds to a parabolic differential equation whose coefficient involves the law of the underlying diffusion. This work is the first step towards a new understanding of nonlinear expectations under probability distortion, and will potentially be a helpful tool for solving time-inconsistent stochastic optimization problems.

Variance and interest rate risk in unit-linked insurance policies
David R. Baños,Marc Lagunas-Merino,Salvador Ortiz-Latorre

One of the risks derived from selling long term policies that any insurance company has, arises from interest rates. In this paper we consider a general class of stochastic volatility models written in forward variance form. We also deal with stochastic interest rates to obtain the risk-free price for unit-linked life insurance contracts, as well as providing a perfect hedging strategy by completing the market. We conclude with a simulation experiment, where we price unit-linked policies using Norwegian mortality rates. In addition we compare prices for the classical Black-Scholes model against the Heston stochastic volatility model with a Vasicek interest rate model.