1,721,083 research outputs found
Trend detection under erroneous observations: application to quantitative financial strategies
No full textIn this paper, we show how to handle the problem of trend detection, in the context of financial strategies, when the data is potentially erroneous. We focus on the case of a filtering method based on wavelets. This is used, for instance, to build an estimator of a given security at a future time horizon, or to construct trading signals based on extreme variations from the trend. We study how the erroneous observation of past data is incorporated into the filter method and, therefore, into the estimator built with it. The techniques of error calculus with Dirichlet forms are applied to see how the errors affect the estimation: they define an expansion of the estimator in terms of its first- and second-order moments, interpreted as statistical variance/covariance and bias
Alternative to beta coefficients in the context of diffusions
No full textWe develop an alternative to the beta coefficient of the CAPM theory. We show the link between this notion and the Wiener chaos expansion of the underlying processes. In the setting of Markov diffusions, we define the drift-neutral beta, which is the quantity of benchmark such that the resulting portfolio is immune to an infinitesimal change of drift on the Brownian motion driving the benchmark. Our approach yields a coefficient which in many practical cases depends on the initial values of both the portfolio and its benchmark. It can also be used to take into account extreme risks and not only the variance. We study several classical diffusion processes and give a full analysis in the case of Jacobi processes. Examples with credit indices show the efficiency of the method in hedging a portfolio
A Gamma Ornstein–Uhlenbeck model driven by a Hawkes process
Full text linkWe propose an extension of the Γ -OU Barndorff-Nielsen and Shephard model taking into account jump clustering phenomena. We assume that the intensity process of the Hawkes driver coincides, up to a constant, with the variance process. By applying the theory of continuous-state branching processes with immigration, we prove existence and uniqueness of strong solutions of the SDE governing the asset price dynamics. We propose a measure change of self-exciting Esscher type in order to describe the relation between the risk-neutral and the historical dynamics, showing that the Γ -OU Hawkes framework is stable under this probability change. By exploiting the affine features of the model we provide an explicit form for the Laplace transform of the asset log-return, for its quadratic variation and for the ergodic distribution of the variance process. We show that the proposed model exhibits a larger flexibility in comparison with the Γ -OU model, in spite of the same number of parameters required. We calibrate the model on market vanilla option prices via characteristic function inversion techniques, we study the price sensitivities and propose an exact simulation scheme. The main financial achievement is that implied volatility of options written on VIX is upward shaped due to the self-exciting property of Hawkes processes, in contrast with the usual downward slope exhibited by the Γ -OU Barndorff-Nielsen and Shephard model
Optimal investment in markets with over and under-reaction to Information
No full textIn this paper we introduce a jump-diffusion model of shot-noise type for stock prices, taking into account over and under-reaction of the market to incoming news. We work in a partial information setting, by supposing that standard investors do not have access to the market direction, the drift, (modeled via a random variable) after a jump. We focus on the expected (logarithmic) utility maximization problem by providing the optimal investment strategy in explicit form, both under full (i.e., from the insider point of view, aware of the right kind of market reaction at any time) and under partial information (i.e., from the standard investor viewpoint, who needs to infer the kind of market reaction from data). We test our results on market data relative to Enron and Ahold. The three main contributions of this paper are: the introduction of a new market model dealing with over and under-reaction to news, the explicit computation of the optimal filter dynamics using an original approach combining enlargement of filtrations with Innovation Theory and the application of the optimal portfolio allocation rule to market data
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Hawkes-driven stochastic volatility models: goodness-of-fit testing of alternative intensity specifications with S &P500 data
No full textWe introduce a novel stochastic volatility model with price and volatility co-jumps driven by Hawkes processes and develop a feasible maximum-likelihood procedure to estimate the parameters driving the jump intensity. Using S &P500 high-frequency prices over the period May 2007-August 2021, we then perform a goodness-of-fit test of alternative jump intensity specifications and find that the hypothesis of the intensity being linear in the asset volatility provides the relatively best fit, thereby suggesting that jumps have a self-exciting nature
An optimal dividend and investment control problem under debt constraints
No full textThis paper concerns the problem of determining an optimal control on the dividend and investment policy of a firm under debt constraints. We allow the company to make investment by increasing its outstanding indebtedness, which would impact its capital structure and risk profile, thus resulting in higher interest rate debts. Moreover, a high level of debt is also a challenging constraint to any firm, as it is the threshold below which the firm value should never go to avoid bankruptcy. It is equally possible for the firm to divest parts of its business in order to decrease its financial debt owed to creditors. In addition, the firm may favor investment by postponing or reducing any dividend distribution to shareholders. We formulate this problem as a combined singular and multiswitching control problem and use a viscosity solution approach to get qualitative descriptions of the solution. We further enrich our studies with a complete resolution of the problem in the two-regime case and provide some numerical illustrations
A Time-Domain Computer Simulator of the Nonlinear Response of Semiconductor Optical Amplifiers
No full textWe present a computer simulator of semiconductor optical amplifiers, The nonlinear input-output response of the device is characterized in terms of a complex gain, representing the accumulated gain and wavevector change of the propagating field across the active waveguide. We account for the gain saturation induced by stimulated recombination and by the perturbation of the carrier quasi-equilibrium distribution within the bands. A rigorous elimination of the spatial coordinate allows us to reduce the description of the amplifier dynamics to the solution of a set of ordinary differential equation for the complex gain. If the waveguide internal loss is negligible, the spatial inhomogeneity of the complex gain is implicitly yet exactly taken into account by the reduced model. The accuracy of the reduced model is the same for models based on the direct solution of the set of partial differential equations describing the interaction between the optical held and the active semiconductor waveguide, but the model is computationally much simpler. To preserve the input-output characteristics of the model, we include the amplified spontaneous emission noise in the device description by an equivalent signal applied to the device input and amplified by the saturated gain. At the expense of a minor increase of the program complexity, the waveguide internal loss may also be included. We report on the comparison between the output of the simulator and the results of four-wave mixing experiments in various pump-signal configurations. Good agreement is obtained
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