Different approaches to defining dynamic market risk measures are available in the literature. Most are focused or derived from probability theory, economic behavior or dynamic programming. Here, we propose an approach to define and implement dynamic market risk measures based on recursion and state economy representation. The proposed approach is to be implementable and to inherit properties from static market risk measures.
In this paper we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insuance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation we obtain asymptotic results for systemic conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. These results allow us to assess the influence of an individual institution on the systemic or market risk and vice versa through a collection of conditional systemic risk …
We consider the risk sharing problem for capital requirements induced by capital adequacy tests and security markets. The agents involved in the sharing procedure may be heterogeneous in that they apply varying capital adequacy tests and have access to different security markets. We discuss conditions under which there exists a representative agent. Thereafter, we study two frameworks of capital adequacy more closely, polyhedral constraints and distribution based constraints. We prove existence of optimal risk allocations and equilibria within these frameworks and elaborate on their robustness…
The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions for the existence of optimal and asymptotic optimal allocations. We will show that, similar to a market with convex preferences, in a non-convex framework with distortion risk measures the boundedness of the optimal risk allocation problem depends only on the preferences. Second, we consider the same optimal allocation problem by adding a further assumption …
We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term $ρ$-arbitrage for a risk measure $ρ$. We show how to determine analytically whether such $ρ$-arbitrage portfolios exist in complete markets and in the Markowitz model. We also consider realistic numerical examples of incomplete markets and determine whether expected shortfall constraints are ineffective in these markets. We find that the answer depends heavily upon the pro…
We develop a method to decompose the PnL of a portfolio of assets into four parts: (a) PnL due to FX rate changes, (b) PnL due to interest rate changes, (c) carry gain due to time passing, (d) PnL due to residual market risk changes (credit risk, liquidity risk, volatility risk etc.). We demonstrate the usefulness of our approach by decomposing the performance of an FX- and interest rate-hedged negative basis position in our fund XAIA Credit Basis II, and we apply the methodology to decompose the performance of our fund XAIA Credit Debt Capital in the first quarter of 2022 into PnL contributio…
We compare two models of corporate default by calculating the Jeffreys-Kullback-Leibler divergence between their predicted default probabilities when asset correlations are either high or low. Our main results show that the divergence between the two models increases in highly correlated, volatile, and large markets, but that it is closer to zero in small markets, when asset correlations are low and firms are highly leveraged. These findings suggest that during periods of financial instability the single-and multi-factor models of corporate default will generate increasingly inconsistent predi…
By treating the financial market as a thermodynamic system, we establish a one-to-one correspondence between thermodynamic variables and economic quantities. Measured by the expected loss under the worst-case scenario, financial risk caused by model uncertainty is regarded as a result of the interaction between financial market and external information sources. This forms a thermodynamic picture in which a closed system interacts with an external reservoir, reaching its equilibrium at the worst-case scenario. The severity of the worst-case scenario depends on the rate of heat dissipation, caus…
We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance reduction methods for Monte Carlo simulation of portfolio market risk, there is no paper discussing combining the randomized quasi-Monte Carlo method with variance reduction techniques. In this paper, we combine the randomized quasi-Monte Carlo method with importance sampling and stratified importance sampling. Numerical results for realistic portfolio examples s…
This paper proposes a new integrated variance estimator based on order statistics within the framework of jump-diffusion models. Its ability to disentangle the integrated variance from the total process quadratic variation is confirmed by both simulated and empirical tests. For practical purposes, we introduce an iterative algorithm to estimate the time-varying volatility and the occurred jumps of log-return time series. Such estimates enable the definition of a new market risk model for the Value at Risk forecasting. We show empirically that this procedure outperforms the standard historical …
To find a trade-off between profitability and prudence, financial practitioners need to choose appropriate risk measures. Two key points are: Firstly, investors' risk attitudes under uncertainty conditions should be an important reference for risk measures. Secondly, risk attitudes are not absolute. For different market performance, investors have different risk attitudes. We proposed a new risk measure named SlideVaR which sufficiently reflects the different subjective attitudes of investors and the impact of market changes on investors' attitudes. We proposed the concept of risk-tail region …
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate risk measures is constructed via a recent Lagrange duality for set optimization. In particular, it is shown that a shortfall risk measure can be written as an intersection over a family of divergence risk measures indexed by a scalarization parameter. Examples include set-valued ver…
Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the instantaneous arbitrage capability generated by the market itself. The asset and market portfolio dynamics have a quantum mechanical description, which is constructed by quantizing the deterministic version of the stochastic Lagrangian system describing a market…
Since the quasiconvex risk measures is a bigger class than the well known convex risk measures, the study of quasiconvex risk measures makes sense especially in the financial markets with volatility. In this paper, we will study the quasiconvex risk measures defined on a special space $L^{p(\cdot)}$ where the variable exponent $p(\cdot)$ is no longer a given real number like the space $L^{p}$, but a random variable, which reflects the possible volatility of the financial markets. The dual representation for this quasiconvex risk measures will also provided.
Equity risk premium is a central component of every risk and return model in finance and a key input to estimate costs of equity and capital in both corporate finance and valuation. An article by Damodaran examines three broad approaches for estimating the equity risk premium. The first is survey based, it consists in asking common investors or big players like pension fund managers what they require as a premium to invest in equity. The second is to look at the premia earned historically by investing in stocks, as opposed to risk-free investments. The third method tries to extrapolate a marke…
Systemic risks of default contagion in the Russian interbank market are investigated. The analysis is based on considering the bow-tie structure of the weighted oriented graph describing the structure of the interbank loans. A probabilistic model of interbank contagion explicitly taking into account the empirical bow-tie structure reflecting functionality of the corresponding nodes (borrowers, lenders, borrowers and lenders simultaneously), degree distributions and disassortativity of the interbank network under consideration based on empirical data is developed. The characteristics of contagi…
Cryptocurrency, the most controversial and simultaneously the most interesting asset, has attracted many investors and speculators in recent years. The visibly significant market capitalization of cryptos also motivates modern financial instruments such as futures and options. Those will depend on the dynamics, volatility, or even the jumps of cryptos. We provide a comprehensive investigation of the risk dynamics of the Bitcoin Market from a realized volatility perspective. The Bitcoin market is extremely risky in the sense of volatility, entangled jumps, and extensive consecutive jumps, which…
Value at risk and expected shortfall are increasingly popular tail risk measures in the financial risk management field. Both academia and financial institutions are working to improve tail risk forecasts in order to meet the requirements of the Basel Capital Accord; it states that one purpose of risk management and measuring risk accuracy is, since extreme movements cannot always be avoided, financial institutions can prepare for these extreme returns by capital allocation, and putting aside the appropriate amount of capital so as to avoid default in times of extreme price or index movements.…
Management of systemic risk in financial markets is traditionally associated with setting (higher) capital requirements for market participants. There are indications that while equity ratios have been increased massively since the financial crisis, systemic risk levels might not have lowered, but even increased. It has been shown that systemic risk is to a large extent related to the underlying network topology of financial exposures. A natural question arising is how much systemic risk can be eliminated by optimally rearranging these networks and without increasing capital requirements. Over…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature of our approach is that we embed portfolio constraints and transaction costs into the securities market. As a consequence, we have to dispense with the property of translation invariance, which plays a key role in the classical theory. We provide a comprehensive analysis of relevant properties such as star shapedness, positive homogeneity, convexity, quasic…
We develop a risk-neutral spot and equity option market simulator for a single underlying, under which the joint market process is a martingale. We leverage an efficient low-dimensional representation of the market which preserves no static arbitrage, and employ neural spline flows to simulate samples which are free from conditional drifts and are highly realistic in the sense that among all possible risk-neutral simulators, the obtained risk-neutral simulator is the closest to the historical data with respect to the Kullback-Leibler divergence. Numerical experiments demonstrate the effectiven…
In this paper, we examine the capacity of an arbitrage-free neural-SDE market model to produce realistic scenarios for the joint dynamics of multiple European options on a single underlying. We subsequently demonstrate its use as a risk simulation engine for option portfolios. Through backtesting analysis, we show that our models are more computationally efficient and accurate for evaluating the Value-at-Risk (VaR) of option portfolios, with better coverage performance and less procyclicality than standard filtered historical simulation approaches.
We propose the Hawkes flocking model that assesses systemic risk in high-frequency processes at the two perspectives -- endogeneity and interactivity. We examine the futures markets of WTI crude oil and gasoline for the past decade, and perform a comparative analysis with conditional value-at-risk as a benchmark measure. In terms of high-frequency structure, we derive the empirical findings. The endogenous systemic risk in WTI was significantly higher than that in gasoline, and the level at which gasoline affects WTI was constantly higher than in the opposite case. Moreover, although the relat…
