Quantitative Finance
New submissions
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New submissions for Fri, 22 Jun 18
 [1] arXiv:1806.07983 [pdf, other]

Title: Nonlocal Diffusions and The Quantum BlackScholes Equation: Modelling the Market Fear FactorAuthors: Will HicksComments: 21 pages, 3 figuresSubjects: Mathematical Finance (qfin.MF)
In this paper, we establish a link between quantum stochastic processes, and nonlocal diffusions. We demonstrate how the noncommutative BlackScholes equation of Accardi & Boukas (Luigi Accardi, Andreas Boukas, 'The Quantum BlackScholes Equation', Jun 2007, available at arXiv:0706.1300v1) can be written in integral form. This enables the application of the MonteCarlo methods adapted to McKean stochastic differential equations (H. P. McKean, 'A class of Markov processes associated with nonlinear parabolic equations', Proc. Natl. Acad. Sci. U.S.A., 56(6):19071911, 1966) for the simulation of solutions. We show how unitary transformations can be applied to classical BlackScholes systems to introduce novel quantum effects. These have a simple economic interpretation as a market `fear factor', whereby recent market turbulence causes an increase in volatility going forward, that is not linked to either the local volatility function or an additional stochastic variable. Lastly, we extend this system to 2 variables, and consider Quantum models for bidoffer spread dynamics.
 [2] arXiv:1806.08005 [pdf, other]

Title: MeanVariance Efficiency of Optimal Power and Logarithmic Utility PortfoliosComments: 25 pages, 3 figuresSubjects: Portfolio Management (qfin.PM)
We derive new results related to the portfolio choice problem for a power and logarithmic utilities. Assuming that the portfolio returns follow a lognormal distribution, the closedform expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal portfolios belong to the set of meanvariance feasible portfolios and establish necessary and sufficient conditions such that they are meanvariance efficient. Furthermore, an application to the stock market is presented and the behavior of the optimal portfolio is discussed for different values of the relative risk aversion coefficient. It turns out that the assumption of lognormality does not seem to be a strong restriction.
 [3] arXiv:1806.08107 [pdf, other]

Title: ArbitrageFree Interpolation in Models of Market Observable Interest RatesAuthors: Erik SchlöglJournalref: Schl\"ogl, E. (2002), ArbitrageFree Interpolation in Models of Market Observable Interest Rates, in K. Sandmann and P. Sch\"onbucher (eds), Advances in Finance and Stochastics, SpringerVerlagSubjects: Mathematical Finance (qfin.MF); Computational Finance (qfin.CP)
Models which postulate lognormal dynamics for interest rates which are compounded according to market conventions, such as forward LIBOR or forward swap rates, can be constructed initially in a discrete tenor framework. Interpolating interest rates between maturities in the discrete tenor structure is equivalent to extending the model to continuous tenor. The present paper sets forth an alternative way of performing this extension; one which preserves the Markovian properties of the discrete tenor models and guarantees the positivity of all interpolated rates.
Crosslists for Fri, 22 Jun 18
 [4] arXiv:1806.08161 (crosslist from math.PR) [pdf, other]

Title: Explicit Asymptotics on First Passage Times of Diffusion ProcessesComments: 31 pages, 16 figuresSubjects: Probability (math.PR); Numerical Analysis (math.NA); Mathematical Finance (qfin.MF)
We introduce a unified framework for solving first passage times of timehomogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closedform solutions for probability densities of singlesided level crossing problem. The framework is applicable to diffusion processes with continuous drift functions, and a recursive system in the frequency domain has been provided. Besides, we derive a probabilistic representation for error estimation. The representation can be used to evaluate deviations in perturbed density functions. In the present paper, we apply the framework to OrnsteinUhlenbeck and Bessel processes to find closedform approximations for their first passage times; another successful application is given by the exponentialShiryaev process. Numerical results are provided at the end of this paper.
Replacements for Fri, 22 Jun 18
 [5] arXiv:1606.06111 (replaced) [pdf, ps, other]

Title: Deviations from universality in the fluctuation behavior of a heterogeneous complex system reveal intrinsic properties of components: The case of the international currency marketComments: 10 pages, 6 figures, final revised versionSubjects: Statistical Finance (qfin.ST); Physics and Society (physics.socph)
 [6] arXiv:1707.05096 (replaced) [pdf, ps, other]

Title: Effective risk aversion in thin risksharing marketsComments: 28 pages, second revised versionSubjects: Mathematical Finance (qfin.MF); Trading and Market Microstructure (qfin.TR)
 [7] arXiv:1709.06296 (replaced) [pdf, other]

Title: LargeScale Portfolio Allocation Under Transaction Costs and Model UncertaintySubjects: Portfolio Management (qfin.PM)
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