A Stochastic Volatility Model With Realized Measures for Option Pricing

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options

Analysis of Bank Leverage via Dynamical Systems and Deep Neural Networks

We consider a model of a simple financial system consisting of a leveraged investor that invests in a risky asset and manages risk by using value-at-risk (VaR). The VaR is estimated by using past data via an adaptive expectation scheme. We show that the leverage dynamics can be described by a dynamical system of slow-fast type associated with a unimodal map on [0,1] with an addi-tive heteroscedastic noise whose variance is related to the portfolio rebalancing frequency to target leverage. In absence of noise the model is purely deterministic and the parameter space splits into two regions: (i) a region with a globally attracting fixed point or a 2-cycle; (ii) a dynamical core region, where the map could exhibit chaotic behavior. Whenever the model is randomly perturbed, we prove the existence of a unique stationary density with bounded variation, the stochastic stability of the process, and the almost certain existence and continuity of the Lyapunov exponent for the stationary measure. We then use deep neural networks to estimate map parameters from a short time series. Using this method, we estimate the model in a large dataset of US commercial banks over the period 2001--2014. We find that the parameters of a substantial fraction of banks lie in the dynamical core, and their leverage time series are consistent with a chaotic behavior. We also present evidence that the time series of the leverage of large banks tend to exhibit chaoticity more frequently than those of small banks

Unimodal maps perturbed by heteroscedastic noise: an application to a financial systems

We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate the stability of the associated Markov chain, show the weak convergence of the unique stationary measure to the invariant measure of the map, and show that the average Lyapunov exponent depends continuously on the Markov chain parameters. Representing the Markov chain in terms of random transformation enables us to state and prove the Central Limit Theorem, the large deviation principle, and the Berry-Ess\`een inequality. We perform a multifractal analysis for the invariant and the stationary measures, and we prove Gumbel's law for the Markov chain with an extreme index equal to 1. In addition, we present an example linked to the financial concept of systemic risk and leverage cycle, and we use the model to investigate the finite sample properties of our asymptotic results.Comment: 31 pages, 8 figure

Kelly betting with quantum payoff: A continuous variable approach

The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which model losses and winning events. The resulting stochastic evolution of the quantum memory resembles the dynamics of random lasing which we characterize within the theoretical setting of Bosonic Gaussian channels. As in the classical Kelly Criterion for optimal betting, we define the asymptotic doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of Gaussian density matrices (i.e. displaced, squeezed thermal Gibbs states) revealing that the best option for the gambler is to devote all their initial resources into coherent state amplitude

Testicular masses in association with Adrenogenital syndrome: US findings

Adrenogenital syndrome (AGS) is the result of inborn enzymatic defects in the synthesis of steroid hormones. The production of cortisol is deficient and that of adrenocorticotropic hormone is increased. Sometimes male patients have clinically detectable testicular lesions, known as testicular tumors of AGS (TTAGS). From 1985 to 1991, scrotal ultrasonography (US) was performed in 30 consecutive pubertal and postpubertal patients with AGS to investigate the prevalence and US characteristics of TTAGS. Eight of 30 patients had a testicular lesion (27%); six of the eight lesions were clinically undetected. The mean diameter of the lesions was 16.44 mm (range, 2-28 mm). The lesions were hypoechoic in all cases, with well-defined margins in six cases. The nodules were multifocal in all patients and bilateral in six (75%). If testicular lesions are present in a patient with AGS, TTAGS are likely, and frequent US monitoring is adequate for diagnostic evaluation

Elasto-Plastic Strain Concentration Factors in Finite Thickness Plates

The paper presents a comparison of a detailed finite element modelling of elastoplastic strains at a notch root with experimental Moire interferometric data. The three-dimensional nature of the local constraint at a notch root for elastic or elastoplastic material behaviour is confirmed. The elastoplastic analysis shows that the stress concentration factor ratio from the mid-plane and the surface is practically insensitive to the actual sigma-epsilon relationship when the nominal stress achieves the yield stress

Adding Cycles into the Neoclassical Growth Model

We propose a stochastic Solow growth model where a cyclical component is added to the total factor productivity process. Theoretically, an important feature of the model is that its main equation takes a state space representation where key parameters can be estimated via an unobserved component approach without involving capital stock measures. In addition, the dynamic properties of the model are mostly unaffected by the newly introduced cyclical component. Empirically, our novel framework is consistent with secular U.S. empirical evidenc

The continuous-time limit of score-driven volatility models

We provide general conditions under which a class of discrete-time volatility models driven by the score of the conditional density converges in distribution to a stochastic differential equation as the interval between observations goes to zero. We show that the form of the diffusion limit depends on: (i) the link function, (ii) the conditional second moment of the score, (iii) the normalization of the score. Interestingly, the properties of the stochastic differential equation are strictly entangled with those of the discrete-time counterpart. Score-driven models with fat-tailed densities lead to continuous-time processes with finite volatility of volatility, as opposed to fat-tailed models with a GARCH update, for which the volatility of volatility is explosive. We examine in simulations the implications of such results on approximate estimation and filtering of diffusion processes. An extension to models with a time-varying conditional mean and to conditional covariance models is also developed