International Journal of Theoretical and Applied Finance

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 the demand of consumers, and are subject to financial risks. Following the methodology of [J. Cvitanić, D. Possamaï & N. Touzi (2018) Dynamic programming approach to principal–agent problems, Finance and Stochastics 22(1), 1–37], we propose an optimal contract, from the perspective of consumers, which complements the revenue capacity owners achieved from the spot energy market, and incentivizes both parties to perform an optimal level of investment 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.

Using neural networks, we compute bounds on the prices of multi-asset derivatives given information on prices of related payoffs. As a main example, we focus on European basket options and include information on the prices of other similar options, such as spread options and/or basket options on subindices. We show that, in most cases, adding further constraints gives rise to bounds that are considerably tighter. Our approach follows the literature on constrained optimal transport and, in particular, builds on the work of Eckstein & Kupper (2018) [Computation of optimal transport and related hedging problems via penalization and neural networks, Appl. Math. Optimiz. 1–29].

One of the most characteristic features of the global financial network is its inherently complex and intertwined structure. From the perspective of systemic risk it is important to understand the influence of this network structure on default contagion. Using sparse random graphs to model the financial network, asymptotic methods turned out to be powerful for the purpose of analytically describing the contagion process and making statements about resilience. So far, however, such methods have been limited to so-called rank-one models in which, informally speaking, the only parameter for the skeleton of the network is the degree sequence and the contagion process can be described by a one-dimensional fixed-point equation. Such networks fail to account for the possibility of a pronounced block structure such as core/periphery or a network composed of different connected blocks for different countries. We present a much more general model here, where we distinguish vertices (institutions) of different types and let edge probabilities and exposures depend on the types of both, the receiving and the sending vertex, plus additional parameters. Our main result allows one to compute explicitly the systemic damage caused by some initial local shock event, and we derive a complete characterization of resilient and nonresilient financial systems. This is the first instance that default contagion is rigorously studied in a model outside the class of rank-one models and several technical challenges arise. In contrast to previous work, in which networks could be classified as resilient or nonresilient independently of the distribution of the shock, information about the shock becomes important in our model and a more refined resilience condition arises. Among other applications of our theory we derive resilience conditions for the global network based on subnetwork conditions only.

This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of studies. We first show that the optimal solution, in general, is not a constant function. We give the optimal conditions for a vector function to be the solution, and hence give the conditions for a plug-in solution (replacing the unknown mean and variance by certain estimates based on past values) to be optimal. After showing that the plug-in solutions are sub-optimal in general, we propose gradient-ascent algorithms to solve the functional optimization for mean–variance portfolio management with theorems for convergence provided. Simulations and empirical studies show that our approach can perform significantly better than the plug-in approach.

When prices reflect all available information, they oscillate around an equilibrium level. This oscillation is the result of the temporary market impact caused by waves of buyers and sellers. This price behavior can be approximated through an Ornstein–Uhlenbeck (OU) process. Market makers provide liquidity in an attempt to monetize this oscillation. They enter a long position when a security is priced below its estimated equilibrium level, and they enter a short position when a security is priced above its estimated equilibrium level. They hold that position until one of three outcomes occur: (1) they achieve the targeted profit; (2) they experience a maximum tolerated loss; (3) the position is held beyond a maximum tolerated horizon. All market makers are confronted with the problem of defining profit-taking and stop-out levels. More generally, all execution traders acting on behalf of a client must determine at what levels an order must be fulfilled. Those optimal levels can be determined by maximizing the trader’s Sharpe ratio in the context of OU processes via Monte Carlo experiments [M. López de Prado (2018) Advances in Financial Machine Learning. Hoboken, NJ, USA: John Wiley & Sons]. This paper develops an analytical framework and derives those optimal levels by using the method of heat potentials [A. Lipton & V. Kaushansky (2018) On the first hitting time density of an Ornstein–Uhlenbeck process, arXiv:1810.02390; A. Lipton & V. Kaushansky (2020a) On the first hitting time density for a reducible diffusion process, Quantitative Finance, doi:10.1080/14697688.2020.1713394].

This paper presents a new approximation method for pricing multi-asset continuous single-barrier options. Barrier options are frequently traded, and it is necessary for practitioners to evaluate these precisely and quickly, both for competitiveness, and for risk management. However, it is a difficult task under local stochastic volatility models. To the best of our knowledge, this paper is the first to provide an analytical approximation for continuous barrier options prices in a multi-asset environment. In numerical experiments, we examine the validity of the formula by using parameters calibrated to EURUSD European options.

In this paper, the objective is to study the continuous mean–variance portfolio selection with a no-short-selling constraint and obtain a time-consistent solution. We assume that there is a self-financing portfolio with wealth process $X_t^u$, in which $u\ge 0$ represents the fraction of wealth invested in the risk asset under the short selling prohibition. We investigate the mean–variance optimal constrained problem defined by obtaining the supremum over all admissible controls of the difference between the expectation of the value process at some designated terminal time $T$ and a positive constant times the variance of $X_T^u$. To envisage the quadratic nonlinearity introduced by the variance, the method of Lagrangian multipliers reduces the nonlinear problem into a set of linear problems which can be solved by applying the Hamilton–Jacobi–Bellman equation and change of variables formula with local time on curves. Solving the HJB system provides the time-inconsistent solution and from there, we derive the time-consistent optimal control.