arXiv subjects

Nils Bertschinger

Publications and source records attributed to Nils Bertschinger.

At least 19 recordsLinked to original sources

arXiv2022

Equilibria and Convergence in Fire Sale Games

The complex interactions between algorithmic trading agents can have a severe influence on the functioning of our economy, as witnessed by recent banking crises and trading anomalies. A common phenomenon in these situations are fire sales, a contagious process of asset sales that trigger further sales. We study the existence and structure of equilibria in a game-theoretic model of fire sales. We prove that for a wide parameter range (e.g., convex price impact functions), equilibria exist and form a complete lattice. This is contrasted with a non-existence result for concave price impact functions. Moreover, we study the convergence of best-response dynamics towards equilibria when they exist. In general, best-response dynamics may cycle. However, in many settings they are guaranteed to converge to the socially optimal equilibrium when starting from a natural initial state. Moreover, we discuss a simplified variant of the dynamics that is less informationally demanding and converges to the same equilibria. We compare the dynamics in terms of convergence speed.

cs.GT↗

arXiv2021

Cross-ownership as a structural explanation for rising correlations in crisis times

In this paper, we examine the interlinkages among firms through a financial network where cross-holdings on both equity and debt are allowed. We relate mathematically the correlation among equities with the unconditional correlation of the assets, the values of their business assets and the sensitivity of the network, particularly the $Δ$-Greek. We noticed also this relation is independent of the Equities level. Besides, for the two-firms case, we analytically demonstrate that the equities correlation is always higher than the correlation of the assets; showing this issue by numerical illustrations. Finally, we study the relation between equity correlations and asset prices, where the model arrives to an increase in the former due to a fall in the assets.

q-fin.MF↗

arXiv2021

The sub-fractional CEV model

The sub-fractional Brownian motion (sfBm) is a stochastic process, characterized by non-stationarity in their increments and long-range dependency, considered as an intermediate step between the standard Brownian motion (Bm) and the fractional Brownian motion (fBm). The mixed process, a linear combination between a Bm and an independent sfBm, called mixed sub-fractional Brownian motion (msfBm), keeps the features of the sfBm adding the semi-martingale property for H>3/4, is a suitable candidate to use in price fluctuation modeling, in particular for option pricing. In this note, we arrive at the European Call price under the Constant Elasticity of Variance (CEV) model driven by a mixed sub-fractional Brownian motion. Empirical tests show the capacity of the proposed model to capture the temporal structure of option prices across different maturities.

q-fin.MF↗

arXiv2020

Bayesian Quantile Matching Estimation

Due to increased awareness of data protection and corresponding laws many data, especially involving sensitive personal information, are not publicly accessible. Accordingly, many data collecting agencies only release aggregated data, e.g. providing the mean and selected quantiles of population distributions. Yet, research and scientific understanding, e.g. for medical diagnostics or policy advice, often relies on data access. To overcome this tension, we propose a Bayesian method for learning from quantile information. Being based on order statistics of finite samples our method adequately and correctly reflects the uncertainty of empirical quantiles. After outlining the theory, we apply our method to simulated as well as real world examples. In addition, we provide a python-based package that implements the proposed model.

stat.ME↗

arXiv2020

Visual explanation of country specific differences in Covid-19 dynamics

This report provides a visual examination of Covid-19 case and death data. In particular, it shows that country specific differences can too a large extend be explained by two easily interpreted parameters. Namely, the delay between reported cases and deaths and the fraction of cases observed. Furthermore, this allows to lower bound the actual total number of people already infected.

q-bio.PE↗

arXiv2019

Systemic Risk: Fire-Walling Financial Systems Using Network-Based Approaches

The latest financial crisis has painfully revealed the dangers arising from a globally interconnected financial system. Conventional approaches based on the notion of the existence of equilibrium and those which rely on statistical forecasting have seen to be inadequate to describe financial systems in any reasonable way. A more natural approach is to treat financial systems as complex networks of claims and obligations between various financial institutions present in an economy. The generic framework of complex networks has been successfully applied across several disciplines, e.g., explaining cascading failures in power transmission systems and epidemic spreading. Here we review various network models addressing financial contagion via direct inter-bank contracts and indirectly via overlapping portfolios of financial institutions. In particular, we discuss the implications of the "robust-yet-fragile" nature of financial networks for cost-effective regulation of systemic risk.

q-fin.TR↗

arXiv2019

Flow Allocation Games

We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game, we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges. Given the strategy choices of all agents, a maximal circulation that adheres to the chosen allocation strategies evolves in the network. Each agent wants to maximize the amount of flow through her node. Flow allocation games can be used to express strategic incentives of clearing in financial networks. We provide a cumulative set of results on the existence and computational complexity of pure Nash and strong equilibria, as well as tight bounds on the (strong) prices of anarchy and stability. Our results show an interesting dichotomy: Ranking strategies over individual flow units allow to obtain optimal strong equilibria for many objective functions. In contrast, more intuitive ranking strategies over edges can give rise to unfavorable incentive properties.

cs.GT↗

arXiv2019

Rotation Invariant Householder Parameterization for Bayesian PCA

We consider probabilistic PCA and related factor models from a Bayesian perspective. These models are in general not identifiable as the likelihood has a rotational symmetry. This gives rise to complicated posterior distributions with continuous subspaces of equal density and thus hinders efficiency of inference as well as interpretation of obtained parameters. In particular, posterior averages over factor loadings become meaningless and only model predictions are unambiguous. Here, we propose a parameterization based on Householder transformations, which remove the rotational symmetry of the posterior. Furthermore, by relying on results from random matrix theory, we establish the parameter distribution which leaves the model unchanged compared to the original rotationally symmetric formulation. In particular, we avoid the need to compute the Jacobian determinant of the parameter transformation. This allows us to efficiently implement probabilistic PCA in a rotation invariant fashion in any state of the art toolbox. Here, we implemented our model in the probabilistic programming language Stan and illustrate it on several examples.

stat.ML↗

arXiv2019

Applications of Gaussian Process Latent Variable Models in Finance

Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we propose a novel covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM). Our estimator can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Furthermore, our Bayesian treatment naturally shrinks the sample covariance matrix towards a more structured matrix given by the prior and thereby systematically reduces estimation errors. Finally, we discuss some financial applications of the GP-LVM.

cs.CE↗

arXiv2018

Systemic Greeks: Measuring risk in financial networks

Since the latest financial crisis, the idea of systemic risk has received considerable interest. In particular, contagion effects arising from cross-holdings between interconnected financial firms have been studied extensively. Drawing inspiration from the field of complex networks, these attempts are largely unaware of models and theories for credit risk of individual firms. Here, we note that recent network valuation models extend the seminal structural risk model of Merton (1974). Furthermore, we formally compute sensitivities to various risk factors -- commonly known as Greeks -- in a network context. In particular, we propose the network $Δ$ as a quantitative measure of systemic risk and illustrate our findings on some numerical examples.

q-fin.RM↗

arXiv2018

Reality-check for Econophysics: Likelihood-based fitting of physics-inspired market models to empirical data

The statistical description and modeling of volatility plays a prominent role in econometrics, risk management and finance. GARCH and stochastic volatility models have been extensively studied and are routinely fitted to market data, albeit providing a phenomenological description only. In contrast, the field of econophysics starts from the premise that modern economies consist of a vast number of individual actors with heterogeneous expectations and incentives. In turn explaining observed market statistics as emerging from the collective dynamics of many actors following heterogeneous, yet simple, rather mechanistic rules. While such models generate volatility dynamics qualitatively matching several stylized facts and thus illustrate the possible role of different mechanisms, such as chartist trading, herding behavior etc., rigorous and quantitative statistical fits are still mostly lacking. Here, we show how Stan, a modern probabilistic programming language for Bayesian modeling, can be used to fit several models from econophysics. In contrast to the method of moment matching, which is currently popular, our fits are purely likelihood based with many advantages, including systematic model comparison and principled generation of model predictions conditional on the observed price history. In particular, we investigate models by Vikram & Sinha and Franke & Westerhoff, and provide a quantitative comparison with standard econometric models.

cs.CE↗

arXiv2017

On extractable shared information

We consider the problem of quantifying the information shared by a pair of random variables $X_{1},X_{2}$ about another variable $S$. We propose a new measure of shared information, called extractable shared information, that is left monotonic; that is, the information shared about $S$ is bounded from below by the information shared about $f(S)$ for any function $f$. We show that our measure leads to a new nonnegative decomposition of the mutual information $I(S;X_1X_2)$ into shared, complementary and unique components. We study properties of this decomposition and show that a left monotonic shared information is not compatible with a Blackwell interpretation of unique information. We also discuss whether it is possible to have a decomposition in which both shared and unique information are left monotonic.

cs.IT↗

arXiv2017

Coarse-graining and the Blackwell order

Suppose we have a pair of information channels, $κ_{1},κ_{2}$, with a common input. The Blackwell order is a partial order over channels that compares $κ_{1}$ and $κ_{2}$ by the maximal expected utility an agent can obtain when decisions are based on the channel outputs. Equivalently, $κ_{1}$ is said to be Blackwell-inferior to $κ_{2}$ if and only if $κ_{1}$ can be constructed by garbling the output of $κ_{2}$. A related partial order stipulates that $κ_{2}$ is more capable than $κ_{1}$ if the mutual information between the input and output is larger for $κ_{2}$ than for $κ_{1}$ for any distribution over inputs. A Blackwell-inferior channel is necessarily less capable. However, examples are known where $κ_{1}$ is less capable than $κ_{2}$ but not Blackwell-inferior. We show that this may even happen when $κ_{1}$ is constructed by coarse-graining the inputs of $κ_{2}$. Such a coarse-graining is a special kind of "pre-garbling" of the channel inputs. This example directly establishes that the expected value of the shared utility function for the coarse-grained channel is larger than it is for the non-coarse-grained channel. This contradicts the intuition that coarse-graining can only destroy information and lead to inferior channels. We also discuss our results in the context of information decompositions.

cs.IT↗

arXiv2016

Uncertainty Estimates in the Heston Model via Fisher Information

We address the information content of European option prices about volatility in terms of the Fisher information matrix. We assume that observed option prices are centred on the theoretical price provided by Heston's model disturbed by additive Gaussian noise. We fit the likelihood function on the components of the VIX, i.e., near- and next-term put and call options on the S&P 500 with more than 23 days and less than 37 days to expiration and non-vanishing bid, and compute their Fisher information matrices from the Greeks in the Heston model. We find that option prices allow reliable estimates of volatility with negligible uncertainty as long as volatility is large enough. Interestingly, if volatility drops below a critical value, inferences from option prices become impossible because Vega, the derivative of a European option w.r.t. volatility, nearly vanishes.

q-fin.ST↗

arXiv2016

Volatility Inference and Return Dependencies in Stochastic Volatility Models

Stochastic volatility models describe stock returns $r_t$ as driven by an unobserved process capturing the random dynamics of volatility $v_t$. The present paper quantifies how much information about volatility $v_t$ and future stock returns can be inferred from past returns in stochastic volatility models in terms of Shannon's mutual information.

q-fin.MF↗

arXiv2015

Inferring Volatility in the Heston Model and its Relatives -- an Information Theoretical Approach

Stochastic volatility models describe asset prices $S_t$ as driven by an unobserved process capturing the random dynamics of volatility $σ_t$. Here, we quantify how much information about $σ_t$ can be inferred from asset prices $S_t$ in terms of Shannon's mutual information $I(S_t : σ_t)$. This motivates a careful numerical and analytical study of information theoretic properties of the Heston model. In addition, we study a general class of discrete time models motivated from a machine learning perspective. In all cases, we find a large uncertainty in volatility estimates for quite fundamental information theoretic reasons.

q-fin.ST↗

arXiv2015

Value of information in noncooperative games

In some games, additional information hurts a player, e.g., in games with first-mover advantage, the second-mover is hurt by seeing the first-mover's move. What properties of a game determine whether it has such negative "value of information" for a particular player? Can a game have negative value of information for all players? To answer such questions, we generalize the definition of marginal utility of a good to define the marginal utility of a parameter vector specifying a game. So rather than analyze the global structure of the relationship between a game's parameter vector and player behavior, as in previous work, we focus on the local structure of that relationship. This allows us to prove that generically, every game can have negative marginal value of information, unless one imposes a priori constraints on allowed changes to the game's parameter vector. We demonstrate these and related results numerically, and discuss their implications.

cs.GT↗

arXiv2014

The Information Theory of Individuality

We consider biological individuality in terms of information theoretic and graphical principles. Our purpose is to extract through an algorithmic decomposition system-environment boundaries supporting individuality. We infer or detect evolved individuals rather than assume that they exist. Given a set of consistent measurements over time, we discover a coarse-grained or quantized description on a system, inducing partitions (which can be nested). Legitimate individual partitions will propagate information from the past into the future, whereas spurious aggregations will not. Individuals are therefore defined in terms of ongoing, bounded information processing units rather than lists of static features or conventional replication-based definitions which tend to fail in the case of cultural change. One virtue of this approach is that it could expand the scope of what we consider adaptive or biological phenomena, particularly in the microscopic and macroscopic regimes of molecular and social phenomena.

q-bio.PE↗