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Stability and convergence of Galerkin schemes for parabolic equations with application to Kolmogorov pricing equations in time-inhomogeneous Lévy models Journal of Computational Finance (IF 1.417) Pub Date : 2022-01-01 Maximillian Gaß,Kathrin Glau
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Pricing barrier options with deep backward stochastic differential equation methods Journal of Computational Finance (IF 1.417) Pub Date : 2022-01-01 Narayan Ganesan,Yajie Yu,Bernhard Hientzsch
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Automatic differentiation for diffusion operator integral variance reduction Journal of Computational Finance (IF 1.417) Pub Date : 2022-01-01 Johan Auster
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Branching diffusions with jumps, and valuation with systemic counterparties Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Christoph Belak,Daniel Hoffmann,Frank Seifried
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Fast pricing of American options under variance gamma Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Weilong Fu,Ali Hirsa
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process that is constructed by replacing the calendar time with the gamma time in a Brownian motion with drift, resulting in a time-changed Brownian motion. In the case of the Black–Merton–Scholes model, there exist fast approximation methods for pricing American options. However
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Expansion method for pricing foreign exchange options under stochastic volatility and interest rates Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Kenji Nagami
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The effects of transaction costs and illiquidity on the prices of volatility derivatives Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Mehzabeen Dilloo,Yannick Tangman
The prices of assets differ when considering transaction costs and their illiquidity, thus affecting their returns. As volatility derivatives such as variance swaps, gamma swaps, corridor variance swaps and volatility swaps depend on the expected values of these returns, we develop a high-order algorithm so that differences in the fair values of the volatility derivatives under different transaction
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Gradient boosting for quantitative finance Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Jesse Davis,Laurens Devos,Sofie Reyners,Wim Schoutens
In this paper, we discuss how tree-based machine learning techniques can be used in the context of derivatives pricing. Gradient boosted regression trees are employed to learn the pricing map for a couple of classical, time-consuming problems in quantitative finance. In particular, we illustrate this methodology by reducing computation times for pricing exotic derivative products and American options
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An artificial neural network representation of the SABR stochastic volatility model Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 William McGhee
In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate integration scheme of McGhee [2011] as well as a two factor finite difference scheme. The resulting ANN calculates
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Pricing American options under negative rates Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Jherek Healy
This paper defines the criteria under which the early exercise of an American option is never optimal, whether under positive or negative rates, and gives a short analysis of the various shapes of the exercise region under negative interest rates. It then presents a new integral equation, which establishes the option price and the two early-exercise boundaries under negative rates, and shows how to
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A simple and robust approach for expected shortfall estimation Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Zhibin Pan,Tao Pang,Yang Zhao
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Calibration of local-stochastic and path-dependent volatility models to vanilla and no-touch options Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Alan Bain,Matthieu Mariapragassam,Christoph Reisinger
We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al. (2016), which allows fast computation of up-and-out call prices for the complete set of strikes, barriers and maturities. It also utilises a novel two-states particle
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Probabilistic machine learning for local volatility Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Martin Tegnér,Stephen Roberts
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Rainbows and transforms: semi-analytic formulas Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Norberto Laghi
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A review of tree-based approaches to solving forward–backward stochastic differential equations Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Long Teng
In this work, we study solving (decoupled) forward-backward stochastic differential equations (FBSDEs) numerically using the regression trees. Based on the general theta-discretization for the time-integrands, we show how to efficiently use regression tree-based methods to solve the resulting conditional expectations. Several numerical experiments including high-dimensional problems are provided to
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Quantization-based Bermudan option pricing in the foreign exchange world Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Jean-Michel Fayolle,Vincent Lemaire,Thibaut Montes
This paper proposes two numerical solution based on Product Optimal Quantization for the pricing of Foreign Exchange (FX) linked long term Bermudan options e.g. Bermudan Power Reverse Dual Currency options, where we take into account stochastic domestic and foreign interest rates on top of stochastic FX rate, hence we consider a 3-factor model. For these two numerical methods, we give an estimation
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Deep learning for discrete-time hedging in incomplete markets Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Simon Fecamp,Joseph Mikael,Xavier Warin
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The CTMC–Heston model: calibration and exotic option pricing with SWIFT Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Álvaro Leitao,J Kirkby,Luis Ortiz-Gracia
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Penalty methods for bilateral XVA pricing in European and American contingent claims by a partial differential equation model Journal of Computational Finance (IF 1.417) Pub Date : 2021-01-01 Yuwei Chen,Christina Christara
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Finding the nearest covariance matrix: the foreign exchange market case Journal of Computational Finance (IF 1.417) Pub Date : 2020-11-01 Aleksey Minabutdinov,Ilya Manaev,Maxim Bouev
We consider the problem of finding a valid covariance matrix in the foreign exchange market given an initial nonpositively semidefinite (non-PSD) estimate of such a matrix. The common no-arbitrage assumption imposes additional linear constraints on such matrixes, inevitably making them singular. As a result, even the most advanced numerical techniques will predictably balk at a seemingly standard optimization
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Pricing multiple barrier derivatives under stochastic volatility Journal of Computational Finance (IF 1.417) Pub Date : 2020-11-01 Marcos Escobar,Sven Panz,Rudi Zagst
This work generalizes existing one- and two-dimensional pricing formulas with an equal number of barriers to a setting of n dimensions and up to two barriers in the presence of stochastic volatility. This allows for the consideration of multidimensional single-barrier derivatives with, for example, a collateral triggered by a barrier default of the issuing company. We introduce stochastic volatility
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Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach Journal of Computational Finance (IF 1.417) Pub Date : 2020-11-01 Jerome Lelong
In this work, we propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process. Our approach is based on a modification of the well-known Longstaff Schwartz algorithm, in which we basically replace the standard least square regression by a Wiener chaos expansion. Not only does it allow us to deal with a non Markovian
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Monte Carlo pathwise sensitivities for barrier options Journal of Computational Finance (IF 1.417) Pub Date : 2020-04-27 Thomas Gerstner, Bastian Harrach, Daniel Roth
The Monte Carlo pathwise sensitivities approach is well established for smooth payoff functions. In this work, we present a new Monte Carlo algorithm that is able to calculate the pathwise sensitivities for discontinuous payoff functions. Our main tool is to combine the one-step survival idea of Glasserman and Staum with the stable differentiation approach of Alm, Harrach, Harrach and Keller. As an
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Option pricing in exponential Lévy models with transaction costs Journal of Computational Finance (IF 1.417) Pub Date : 2020-04-27 Nicola Cantarutti, Manuel Guerra, Joao Guerra, Maria do Rosario Grossinho
We present an approach for pricing a European call option in presence of proportional transaction costs, when the stock price follows a general exponential L\'evy process. The model is a generalization of the celebrated work of Davis, Panas and Zariphopoulou (1993), where the value of the option is obtained using the concept of utility indifference price. This requires to solve two stochastic singular
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An adaptive Monte Carlo approach for pricing Parisian options with general boundaries Journal of Computational Finance (IF 1.417) Pub Date : 2020-04-01 Sercan Gűr
We propose a new, flexible framework using Monte Carlo methods to price Parisian options not only with constant boundaries but also with general curved boundaries. The proposed approach also enables a direct simulation of the Parisian time, namely the first time when a Parisian contract is triggered. Further, we employ an adaptive control variable method to improve the accuracy of the Monte Carlo simulation
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Numerical simulation and applications of the convection–diffusion–reaction equation with the radial basis function in a finite-difference mode Journal of Computational Finance (IF 1.417) Pub Date : 2020-04-01 Reza Mollapourasl,Majid Haghi,Alfa Heryudono
This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of convection–diffusion–reaction type. These are known as the radial-basis-function generated finite-difference method and the Hermite finite-difference method. The convergence and stability of these schemes are investigated numerically
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Numerical techniques for the Heston collocated volatility model Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Fabien Le Floc’h,Cornelis Oosterlee
In the collocating volatility (CLV) model, the stochastic collocation technique is used as a convenient representation of the terminal distribution of the market option prices. A specific dynamic is added in the form of a stochastic driver process, which allows more control over the prices of forward starting options. This is reminiscent of the Markov functional models. (Grzelak uses a single-factor
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A shrinking horizon optimal liquidation framework with lower partial moments criteria Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Hassan Anis,Roy H.Kwon
A novel quasi-multi-period model for optimal position liquidation in the presence of both temporary and permanent market impact is proposed. Two main features distinguish the proposed approach from alternatives. First, a shrinking horizon framework is implemented to update intraday parameters by incorporating new incoming information while maintaining standard non-anticipativity constraints. The method
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A Libor market model including credit risk under the real-world measure Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Sara Dutra Lopes,Carlos V´azquez
We present a methodology to generate future scenarios of interest rates for different credit ratings under a real-world probability measure. More precisely, we explain how to perform simulations of the real-world forward rates for different rating classes by generalizing the multidimensional shifted lognormal London Interbank Offered Rate market model to account for credit ratings and a specification
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On extensions of the Barone-Adesi and Whaley method to price American-type options Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Ludovic Mathys
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Neural networks for option pricing and hedging: a literature review Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Johannes Ruf,Weiguan Wang
Neural networks have been used as a nonparametric method for option pricing and hedging since the early 1990s. Far over a hundred papers have been published on this topic. This note intends to provide a comprehensive review. Papers are compared in terms of input features, output variables, benchmark models, performance measures, data partition methods, and underlying assets. Furthermore, related work
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High-order approximations to call option prices in the Heston model Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Marc Lagunas-Merino,Raúl Merino,Josep Vives,Archil Gulisashvili
In the present paper, a decomposition formula for the call price due to Alòs is transformed into a Taylor-type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of the call price found in a recent paper by Als, Gatheral and Rodoičić. We use the new decomposition to obtain various approximations to the call price
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Second-order Monte Carlo sensitivities in linear or constant time Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Roberto Daluiso
We consider the problem of efficiently computing the full matrix of second-order sensitivities of a Monte Carlo price when the number of inputs is large. Specifically, we analyze and compare methods with run times of at most O(NT), where N is the dimension of the input and T is the time required to compute the price. Since none of the alternatives from previous literature appears to be satisfactory
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Pricing American call options using the Black–Scholes equation with a nonlinear volatility function Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Maria do Rosario Grossinho,Yaser Fagan Kord,Daniel Sevcovic
In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a numerical method for pricing American style call options by means of transformation of the free boundary problem for a nonlinear Black-Scholes equation into the so-called
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Introducing two mixing fractions to a lognormal local-stochastic volatility model Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Bowie Owens,Zili Zhu,Geoffrey Lee
A single parameter, termed the mixing fraction, is used to calibrate current local stochastic volatility (LSV) models to traded exotic prices as well as vanilla options. This single parameter has been multiplied by both the volatility-of-volatility parameter and the correlation between spot and volatility of the original stochastic volatility model. In this paper, we introduce two mixing fractions
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Extremal risk management: expected shortfall value verification using the bootstrap method Journal of Computational Finance (IF 1.417) Pub Date : 2020-01-01 Marta Malecka
In this paper, we refer to the axiomatic theory of risk and investigate the problem of formal verification of the expected shortfall (ES) model based on a sample ES. Recognizing the infeasibility of parametric methods, we explore the bootstrap technique, which, unlike the current value-at-risk model-based (VaR model-based) Basel III testing framework, permits the creation of more powerful sample ES-based
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One-dimensional Markov-functional models driven by a non-Gaussian driver Journal of Computational Finance (IF 1.417) Pub Date : 2019-12-01 Jaka Gogala
The class of Markov-functional models (MFMs) provides a framework that can be used to define interest-rate models of finite dimension calibrated to any arbitrage-free formula for caplet or swaption prices. Because of their computational efficiency, one-factor MFMs are of particular interest. So far, the literature has focused on models driven by a Gaussian process. The aim of this paper is to move
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The Chebyshev method for the implied volatility Journal of Computational Finance (IF 1.417) Pub Date : 2019-12-01 Christian Pötz
The implied volatility is a crucial element of any financial toolbox, since it is used for quoting and the hedging of options as well as for model calibration. In contrast to the Black-Scholes formula its inverse, the implied volatility, is not explicitly available and numerical approximation is required. We propose a bivariate interpolation of the implied volatility surface based on Chebyshev polynomials
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A new approach to the quantification of model risk for practitioners Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Zuzana Krajcovicova,Pedro Pablo Perez-Velasco,Carlos Vazquez
Global regulation obliges financial institutions to manage model risk with the same severity as any other risk. Its quantification is therefore essential to meet these requirements and to ensure an institution’s basic internal operations are able to run smoothly. In this paper, we address the quantification of model risk by calculating the norm of an appropriate function defined on a Riemannian manifold
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The extended SSVI volatility surface Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Sebas Hendriks,Claude Martini
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Fast stochastic forward sensitivities in Monte Carlo simulations using stochastic automatic differentiation (with applications to initial margin valuation adjustments) Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Christian Fries
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Path-dependent American options Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Etienne Chevalier, Vathana Ly Vath, Mohamed Mnif
In this paper, we investigate a path-dependent American option problem and provide an efficient and implementable numerical scheme for the solution of its associated path-dependent variational inequality. We obtain the viscosity characterization of our value function and suggest a monotone, stable and consistent numerical scheme, the convergence of which is proven thanks to the uniqueness property
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Yield curve fitting with artificial intelligence: a comparison of standard fitting methods with artificial intelligence algorithms Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Achim Posthaus
The yield curve is a fundamental input parameter of valuation theories in capital markets. Information about yields can be observed in a discrete form, either directly through traded yield instruments (eg., interest rate swaps) or indirectly through the prices of bonds (eg., government bonds). Capital markets usually create benchmark yield curves for specific and very liquid market instruments, or
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Efficient conservative second-order central-upwind schemes for option-pricing problems Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Omishwary Bhatoo, Arshad Ahmud Iqbal Peer, Eitan Tadmor, Desire Yannick Tangman, Aslam Aly El Faidal Saib
The conservative Kurganov–Tadmor (KT) scheme has been successfully applied to option-pricing problems by Germán I. Ramírez-Espinoza and Matthias Ehrhardt. These included the valuation of European, Asian and nonlinear options as Black–Scholes partial differential equations, written in the conservative form, by simply updating fluxes in the black box approach. In this paper, we describe an improvement
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Calculate tail quantiles of compound distributions Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Azamat Abdymomunov, Filippo Curti, Hayden Kane
We evaluate the performance of different approaches for estimating quantiles of compound distributions, which are widely used for risk quantification in the banking and insurance industries. We focus on three approaches: (1) single-loss approximation (SLA), (2) perturbative expansion correction (PEC) and (3) the fast Fourier transform (FFT). We demonstrate that both the SLA and PEC approaches are accurate
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Variance optimal hedging with application to electricity markets Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Xavier Warin
In Electricity markets, illiquidity, transaction costs and market price characteristics prevent managers to replicate exactly contracts. A residual risk is always present and the hedging strategy depends on a risk criterion chosen. We present an algorithm to hedge a position for a mean variance criterion taking into account the transaction cost and the small depth of the market. We show its effectiveness
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Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Rongju Zhang, Nicolas Langrené, Yu Tian, Zili Zhu, Fima Klebaner, Kais Hamza
In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target representing an investment goal. This strategy favorably shapes the entire probability distribution of returns
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Complexity reduction for calibration to American options Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Olena Burkovska, Kathrin Glau, Mirco Mahlstedt, Barbara Wohlmuth
American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to their higher flexibility compared with European options, the mathematical model involves additional constraints, and a variational inequality is obtained. We use the Heston stochastic volatility model to describe the
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The standard market risk model of the Swiss solvency test: an analytic solution Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Andras Niedermayer
The full standard model of the Swiss solvency test (SST) requires a Monte Carlo simulation to calculate the regulatory target capital. This paper derives an alternative fast Fourier transform-based computational approach for calculating the target capital of the SST that is more than 600 times faster than a Monte Carlo simulation. We also show that the relative computational error of our approach is
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Path independence of exotic options and convergence of binomial approximations Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Guillaume Leduc, Kenneth J. Palmer
The analysis of the convergence of tree methods for pricing barrier and lookback options has been the subject of numerous publications aimed at describing, quantifying and improving the slow and oscillatory convergence in such methods. For barrier and lookback options, we find path-independent options whose price is exactly that of the original path-dependent option. The usual binomial models converge
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Ensemble models in forecasting financial markets Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Andreas Karathanasopoulos, Mitra Sovan, Chia Chun Lo, Adam Zaremba, Mohammed Osman
In this paper, we study an evolutionary framework for the optimization of various types of neural network structures and parameters. Three different evolutionary algorithms – the genetic algorithm (GA), differential evolution (DE) and the particle swarm optimizer (PSO) – are developed to optimize the structure and the parameters of three different types of neural network: multilayer perceptrons (MLPs)
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Application of the Heath–Platen estimator in the Fong–Vasicek short rate model Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Sema Coskun, Ralf Korn, Sascha Desmettre
Due to the presence of stochastic volatility dynamics, the Fong–Vasicek (FV) short rate model is more complex but also more realistic than the classical Vasicek version. To enhance the numerical tractability of the FV model for the calculation of bond option prices, we suggest using the Heath–Platen (HP) estimator, which performs excellently in the related Heston stochastic volatility model. We show
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The two-dimensional tree–grid method Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Igor Kossaczký, Matthias Ehrhardt, Michael Günther
In this paper, we introduce a novel, explicit, wide-stencil, two-dimensional (2D) tree–grid method for solving stochastic control problems (SCPs) with two space dimensions and one time dimension, or, equivalently, the corresponding Hamilton– Jacobi–Bellman equation. This new method can be seen as a generalization of the tree–grid method for SCPs with one space dimension that was recently developed
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ε-monotone Fourier methods for optimal stochastic control in finance Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Peter A. Forsyth, George Labahn
Stochastic control problems in finance having complex controls inevitably give rise to low order accuracy, usually at most second order. Fourier methods are efficient at advancing the solution between control monitoring dates, but are not monotone. This gives rise to possible violations of arbitrage inequalities. We devise a preprocessing step for Fourier methods which involves projecting the Green's
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A pairwise local correlation model Journal of Computational Finance (IF 1.417) Pub Date : 2019-01-01 Frank Koster, Daniel Oeltz
We develop a local correlation model that uses a given correlation matrix and a generic function g.t ; mi ; mj / to compute the local correlation between any asset–asset pair .i; j / of a basket of underlyings. The arguments mi , mj are spot moneynesses. The generic function is calibrated to fit the implied volatilities of an equity index such as the DAX or EURO STOXX 50. The advantage of this approach
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Bermudan swaption model risk analysis: a local volatility approach Journal of Computational Finance (IF 1.417) Pub Date : 2018-01-01 Juliusz Jablecki
Prices of callable interest rate derivatives, such as Bermudan swaptions, can be strongly affected by our choice of interest rate model as well as its parameterization and calibration strategy. This paper develops a simple way to handle the inherent model uncertainty. The approach is based on analyzing the exercise deferral premium of Bermudan swaptions with exactly two exercise dates in a “minimal”
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Monte Carlo payoff smoothing for pricing autocallable instruments Journal of Computational Finance (IF 1.417) Pub Date : 2018-01-01 Frank Koster,Achim Rehmet
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Hedging of options in the presence of jump clustering Journal of Computational Finance (IF 1.417) Pub Date : 2018-01-01 Donatien Hainaut, Franck Moraux
This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. In the proposed model, the asset is ruled by a jump-diffusion process, wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of the main properties of the process
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American and exotic option pricing with jump diffusions and other Levy processes Journal of Computational Finance (IF 1.417) Pub Date : 2018-01-01 Justin Lars Kirkby
In general, no analytical formulas exist for pricing discretely monitored exotic options, even when a geometric Brownian motion governs the risk-neutral underlying. While specialized numerical algorithms exist for pricing particular contracts, few can be applied universally with consistent success and with general Lévy dynamics. This paper develops a general methodology for pricing early exercise and
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Hybrid finite-difference/pseudospectral methods for the Heston and Heston–Hull–White partial differential equations Journal of Computational Finance (IF 1.417) Pub Date : 2018-01-01 Christian Hendricks, Matthias Ehrhardt, Michael Gunther
We propose a hybrid spatial finite-difference/pseudospectral discretization for European option-pricing problems under the Heston and Heston–Hull–White models. In the direction of the underlying asset, where the payoff profile is nonsmooth, we use a standard central second-order finite-difference scheme, whereas we use a Chebyshev collocation method in the other spatial dimensions. In the time domain