136,047 research outputs found

    Derivative pricing under the possibility of long memory in the supOU stochastic volatility model

    Get PDF
    We consider the supOU stochastic volatility model which is able to exhibit long-range dependence. For this model we give conditions for the discounted stock price to be a martingale, calculate the characteristic function, give a strip where it is analytic and discuss the use of Fourier pricing techniques. Finally, we present a concrete specification with polynomially decaying autocorrelations and calibrate it to observed market prices of plain vanilla options

    A NEW MODEL FOR STOCK PRICE MOVEMENTS

    Get PDF
    This paper presents a new alternative diffusion model for asset price movements. In contrast to the popular approach of Brownian Motion it proposes Deterministic Diffusion for the modelling of stock price movements. These diffusion processes are a new area of physical research and can be created by the chaotic behaviour of rather simple piecewise linear maps, but can also occur in chaotic deterministic systems like the famous Lorenz system. The motivation for the investigation on Deterministic Diffusion processes as suitable model for the behaviour of stock prices is, that their time series can obey mostly observed stylized facts of real world stock market time series. They can show fat tails of empirical log returns in union with timevarying volatility i.e. heteroscedasticity as well as slowly decaying autocorrelations of squared log returns i.e. long range dependence. These phenomena cannot be explained by a geometric Brownian Motion and have been the largest criticism to the lognormal random walk. In this paper it will be shown that Deterministic Diffusion models can obey those empirical observed stylized facts and the implications of these alternative diffusion processes on economic theory with respect to market efficiency and option pricing are discussed.Deterministic Diffusion, Stock Pricing, Fat Tails, Heteroscedasticity, Long Range Dependence, Option Pricing

    Long Memory Persistence in the Factor of Implied Volatility Dynamics

    Get PDF
    The volatility implied by observed market prices as a function of the strike and time to maturity form an Implied Volatility Surface (IV S). Practical applications require reducing the dimension and characterize its dynamics through a small number of factors. Such dimension reduction is summarized by a Dynamic Semiparametric Factor Model (DSFM) that characterizes the IV S itself and their movements across time by a multivariate time series of factor loadings. This paper focuses on investigating long range dependence in the factor loadings series. Our result reveals that shocks to volatility persist for a very long time, affecting significantly stock prices. For appropriate representation of the series dynamics and the possibility of improved forecasting, we model the long memory in levels and absolute returns using the class of fractional integrated volatility models that provide flexible structure to capture the slow decaying autocorrelation function reasonably well.Implied Volatility, Dynamic Semiparametric Factor Modeling, Long Memory, Fractional Integrated Volatility Models.

    Robust option replication for a Black-Scholes model extended with nondeterministic trends

    Get PDF
    Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model. This memory or nondeterministic trend behavior is often seen as a reflection of market sentiments and causes that the historical volatility estimator becomes unreliable in practice. We propose an extension of the Black and Scholes model by adding a term to the original Wiener term involving a smoother process which accounts for these effects. The problem of arbitrage will be discussed. Using a generalized stochastic integration theory [8], we show that it is possible to construct a self financing replicating portfolio for a European option without any further knowledge of the extension and that, as a consequence, the classical concept of volatility needs to be re-interpreted. AMS subject classifications: 60H05, 60H10, 90A09

    Excess Volatility and Herding in an Artificial Financial Market: Analytical Approach and Estimation

    Get PDF
    Several agent-based models have been proposed in the economic literature to explain the key stylized facts of financial data: heteroscedasticity, fat tails of returns and long-range dependence of volatility. Agentbased models view these empirical regularities as emerging properties of interacting groups of boundedly rational agents in financial markets. The complexity of these interacting agent models has largely constrained their analytical treatment, limiting their analysis mainly to Monte Carlo simulations. In order to overcome this limitation, we introduce a ‘minimalist’ model of an artificial financial market, along the lines of our previous contributions, based on herding behavior among two types of traders. The simplicity of the model allows for an almost complete analytical characterization of both conditional and unconditional statistical properties of prices and returns. Moreover, the underlying parameters of the model can be estimated directly, which permits an assessment of its goodness-of-fit for empirical data. While the performance of the model for domestic stock markets has been the focus of a previous contribution, in this paper we report results for selected exchange rates against the US dollar.Herd Behavior; Speculative Dynamics; Fat Tails; Volatility Clustering.

    Some stylized facts of the Bitcoin market

    Get PDF
    In recent years a new type of tradable assets appeared, generically known as cryptocurrencies. Among them, the most widespread is Bitcoin. Given its novelty, this paper investigates some statistical properties of the Bitcoin market. This study compares Bitcoin and standard currencies dynamics and focuses on the analysis of returns at different time scales. We test the presence of long memory in return time series from 2011 to 2017, using transaction data from one Bitcoin platform. We compute the Hurst exponent by means of the Detrended Fluctuation Analysis method, using a sliding window in order to measure long range dependence. We detect that Hurst exponents changes significantly during the first years of existence of Bitcoin, tending to stabilize in recent times. Additionally, multiscale analysis shows a similar behavior of the Hurst exponent, implying a self-similar process.Comment: 17 pages, 6 figures. arXiv admin note: text overlap with arXiv:1605.0670

    Some stylized facts of the Bitcoin market

    Get PDF
    In recent years a new type of tradable assets appeared, generically known as cryptocurrencies. Among them, the most widespread is Bitcoin. Given its novelty, this paper investigates some statistical properties of the Bitcoin market. This study compares Bitcoin and standard currencies dynamics and focuses on the analysis of returns at different time scales. We test the presence of long memory in return time series from 2011 to 2017, using transaction data from one Bitcoin platform. We compute the Hurst exponent by means of the Detrended Fluctuation Analysis method, using a sliding window in order to measure long range dependence. We detect that Hurst exponents changes significantly during the first years of existence of Bitcoin, tending to stabilize in recent times. Additionally, multiscale analysis shows a similar behavior of the Hurst exponent, implying a self-similar process.Fil: Fernández, Aurelio. Universitat Rovira I Virgili; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Basgall, María José. Universidad Nacional de la Plata. Facultad de Informatica. Instituto de Investigación En Informatica Lidi; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hasperué, Waldo. Universidad Nacional de la Plata. Facultad de Informatica. Instituto de Investigación En Informatica Lidi; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Naiouf, Ricardo Marcelo. Universidad Nacional de la Plata. Facultad de Informatica. Instituto de Investigación En Informatica Lidi; Argentin
    corecore