1,980 research outputs found

    A neural network-based framework for financial model calibration

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    A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal values of the model parameters is formulated as training hidden neurons within a machine learning framework, based on available financial option prices. The framework consists of two parts: a forward pass in which we train the weights of the ANN off-line, valuing options under many different asset model parameter settings; and a backward pass, in which we evaluate the trained ANN-solver on-line, aiming to find the weights of the neurons in the input layer. The rapid on-line learning of implied volatility by ANNs, in combination with the use of an adapted parallel global optimization method, tackles the computation bottleneck and provides a fast and reliable technique for calibrating model parameters while avoiding, as much as possible, getting stuck in local minima. Numerical experiments confirm that this machine-learning framework can be employed to calibrate parameters of high-dimensional stochastic volatility models efficiently and accurately.Comment: 34 pages, 9 figures, 11 table

    On Pricing of Discrete Asian and Lookback Options under the Heston Model

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    We propose a new, data-driven approach for efficient pricing of - fixed- and float-strike - discrete arithmetic Asian and Lookback options when the underlying process is driven by the Heston model dynamics. The method proposed in this article constitutes an extension of our previous work, where the problem of sampling from time-integrated stochastic bridges was addressed. The model relies on the Seven-League scheme, where artificial neural networks are employed to "learn" the distribution of the random variable of interest utilizing stochastic collocation points. The method results in a robust procedure for Monte Carlo pricing. Furthermore, semi-analytic formulae for option pricing are provided in a simplified, yet general, framework. The model guarantees high accuracy and a reduction of the computational time up to thousands of times compared to classical Monte Carlo pricing schemes

    Cheapest-to-Deliver Collateral: A Common Factor Approach

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    The collateral choice option gives the collateral posting party the opportunity to switch between different collateral currencies which is well-known to impact the asset price. Quantification of the option's value is of practical importance but remains challenging under the assumption of stochastic rates, as it is determined by an intractable distribution which requires involved approximations. Indeed, many practitioners still rely on deterministic spreads between the rates for valuation. We develop a scalable and stable stochastic model of the collateral spreads under the assumption of conditional independence. This allows for a common factor approximation which admits analytical results from which further estimators are obtained. We show that in modelling the spreads between collateral rates, a second order model yields accurate results for the value of the collateral choice option. The model remains precise for a wide range of model parameters and is numerically efficient even for a large number of collateral currencies.Comment: 23 pages, 4 figures, 4 table

    On Randomization of Affine Diffusion Processes with Application to Pricing of Options on VIX and S&P 500

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    The class of Affine (Jump) Diffusion (AD) has, due to its closed form characteristic function (ChF), gained tremendous popularity among practitioners and researchers. However, there is clear evidence that a linearity constraint is insufficient for precise and consistent option pricing. Any non-affine model must pass the strict requirement of quick calibration -- which is often challenging. We focus here on Randomized AD (RAnD) models, i.e., we allow for exogenous stochasticity of the model parameters. Randomization of a pricing model occurs outside the affine model and, therefore, forms a generalization that relaxes the affinity constraints. The method is generic and can apply to any model parameter. It relies on the existence of moments of the so-called randomizer- a random variable for the stochastic parameter. The RAnD model allows flexibility while benefiting from fast calibration and well-established, large-step Monte Carlo simulation, often available for AD processes. The article will discuss theoretical and practical aspects of the RAnD method, like derivations of the corresponding ChF, simulation, and computations of sensitivities. We will also illustrate the advantages of the randomized stochastic volatility models in the consistent pricing of options on the S&P 500 and VIX

    Randomization of Short-Rate Models, Analytic Pricing and Flexibility in Controlling Implied Volatilities

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    We focus on extending existing short-rate models, enabling control of the generated implied volatility while preserving analyticity. We achieve this goal by applying the Randomized Affine Diffusion (RAnD) method to the class of short-rate processes under the Heath-Jarrow-Morton framework. Under arbitrage-free conditions, the model parameters can be exogenously stochastic, thus facilitating additional degrees of freedom that enhance the calibration procedure. We show that with the randomized short-rate models, the shapes of implied volatility can be controlled and significantly improve the quality of the model calibration, even for standard 1D variants. In particular, we illustrate that randomization applied to the Hull-White model leads to dynamics of the local volatility type, with the prices for standard volatility-sensitive derivatives explicitly available. The randomized Hull-White (rHW) model offers an almost perfect calibration fit to the swaption implied volatilities

    Persistent left superior vena cava with an absent right superior vena cava in a 72-year-old male with multivessel coronary artery disease

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    Congenital anomalies of systemic veins are usually asymptomatic and foundincidentally during ultrasonography, computed tomography (CT) or magneticresonance examinations performed for other clinical indications. Persistent leftsuperior vena cava (PLSVC) with absent right superior vena cava (RSVC) is thecongenital aberration in the thoracic venous system which occurs in only 0.09%to 0.13% of patients who have congenital heart defects. In this paper, we presentthe extremely rare case of a 72-year-old male with PLSVC associated withan absence of RSVC, referred for coronary CT angiography. Multidetector CTangiography is a powerful tool for the detection of venous anomalies, which isessential before invasive procedures such as the implantation of pacemakers
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