Pricing of European basket call option with n-assets and a bond is discussed in this paper, where all prices of n-assets and the bond are driven by Exponential Ornstein-Uhlenbeck processes. The close-form of European basket option pricing formula is derived. Utilizing with 1-order differential approximate numerical sol…
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48 results for “European baskets”
Lower Bound Approximation to Basket Option Values for Local Volatility Jump-Diffusion Modelsq-fin.PR
In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. If the local volatility function is time independent then there i…
Study bounds for European basket call options in a discrete-time market model with price jumps.
problem Bounding the prices of European basket call options in a market model with price jumps.
method Computed bounds using a binomial model and proved that the lower bound coincides with Jensen's bound.
result The upper bound of the price interval of European basket call options can be computed by restricting to a binomial model.
The paper develops Hawkes-based models for LOB and applies them to European, spread, and basket option pricing.
problem Developing accurate models for pricing options in the context of limit order books (LOB).
method Introduces multivariate Hawkes processes and their limit theorems, applies to European, spread, and basket options.
result Hawkes-based models provide more market forecast information than classical models.
We present a new high-order compact scheme for the multi-dimensional Black-Scholes model with application to European Put options on a basket of two underlying assets. The scheme is second-order accurate in time and fourth-order accurate in space. Numerical examples confirm that a standard second-order finite differenc…
Generative model prices basket options efficiently.
problem Real-time pricing of basket options with varying market inputs.
method Truncated path signatures and Mixture Density Networks (MDN) for learning the terminal density.
result The model produces small pricing errors and matches Monte Carlo simulations closely.
We consider the problem of computing upper and lower bounds on the price of a European basket call option, given prices on other similar baskets. Although this problem is very hard to solve exactly in the general case, we show that in some instances the upper and lower bounds can be computed via simple closed-form expr…
The Pricing of Vanilla Options with Cash Dividends as a Classic Vanilla Basket Option Problemq-fin.PR
This paper uses basket option formulas to price vanilla options with discrete dividends.
problem Pricing vanilla options on stocks with discrete cash dividends.
method Uses existing basket option formulas for European options on a single asset with cash dividends in the piecewise lognormal model.
result Explains the use of basket option formulas for a specific problem in the piecewise lognormal model.
Using neural networks, we compute bounds on the prices of multi-asset derivatives given information on prices of related payoffs. As a main example, we focus on European basket options and include information on the prices of other similar options, such as spread options and/or basket options on subindices. We show tha…
In this paper we propose an efficient method to compute the price of multi-asset American options, based on Machine Learning, Monte Carlo simulations and variance reduction technique. Specifically, the options we consider are written on a basket of assets, each of them following a Black-Scholes dynamics. In the wake of…
Closed-form pricing method for multi-asset options.
problem Pricing multi-asset contingent claims in an incomplete market.
method Proving extremal martingale measures and constructing algorithms for bounds and hedging.
result Closed-form formulas for no-arbitrage price intervals and hedging strategies.
Analytical pricing formulas and Greeks are obtained for European and American basket put options using Mellin transforms. We assume assets are driven by geometric Brownian motion which exhibit correlation and pay a continuous dividend rate. A novel approach to numerical Mellin inversion is achieved via the fast Fourier…
This paper provides formulas for minimum cost super-hedging in a multi-asset binomial market.
problem Finding minimum cost super-hedging strategies in a multi-asset, incomplete market model.
method Explicit formulas for minimum cost super-hedging strategies for various European type multi-asset contingent claims.
result Explicit formulas for non-negative local residuals of super-hedging strategies.
Hedging strategies and minimal variance portfolios for European and exotic options in a Levy marketq-fin.PM
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European optio…
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by Lévy processes, extending earlier works which focused on the Black-Scholes and continuous stochastic volatility models. Usin…
In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of financial derivatives. We present a significantly improved RBF-FD scheme and successfull…
Tensor network surrogate for efficient option pricing in large portfolios.
problem Large-scale portfolio revaluation problems in market risk management.
method Tensor-train (TT) approximation for high-dimensional price surfaces, direct inference using Laplacian kernel and TT representations.
result Tensor surrogate achieves lower test error and faster evaluation times compared to standard GPR.
This paper examines pricing and hedging strategies for cross-currency equity protection swaps.
problem Dynamic requirements from EPS buyers in cross-currency equity protection swaps.
method Detailed analysis of two hedging paradigms, including separate and aggregated returns, with consideration of different types of returns.
result Proposes various hedging strategies with practical implications for EPS providers and investors.
Pricing Exotic Options in a Path Integral Approachcond-mat.other
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we det…
Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. These flat plumbing basket surface can be presented by a sequential presentation known as flat plumbing basket code first found by Furihata, Hirasawa and Kobayashi. The minimum number of flat plumbings to obtain…
Quantum state preparation framework speeds up basket option pricing.
problem Limited practical benefit of quantum amplitude estimation due to state-preparation depth.
method Structure-aware tensor-train rank-based variational state preparation.
result State-preparation depth scaling replaced with linear scaling, maintaining low basket-pricing errors.
Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. In present article, we study links of the flat plumbing basket numbers or less using a special presentation of the flat plumbing basket surfaces. We find a complete classification theorem of links of the fla…
We define the basket number, the flat plumbing number and the flat plumbing basket number of a link. Then we provide some upperbounds for these plumbing numbers by using Seifert's algorithm. We study the relation between these plumbing numbers and the genera of links.
A flat plumbing basket is a Seifert surface consisting of a disk and bands contained in distinct pages of the disk open book decomposition of the 3-sphere. In this paper, we examine close connections between flat plumbing baskets and the contact structure supported by the open book. As an application we give lower boun…
Basket Options with Volatility Skew: Calibrating a Local Volatility Model by Sample Rearrangementq-fin.CP
Method calibrates basket options using rearranged samples from constituent processes.
problem Calibrate basket options with non-linear dependency structure.
method Propose a method to extract dependency structure from market data through systematic sampling rearrangement, then calibrate a local volatility model.
result Efficiently calibrates basket options with near-perfect accuracy.
A flat plumbing basket is a surface consisting a disk and finitely many bands which are contained in distinct pages of the trivial open book decomposition of . In this paper, we construct a Legendrian link from a flat plumbing basket, and we describe a relation among the self-linking number, the Thursto…
Pricing basket options with the first three moments of the basket: log-normal models and beyondq-fin.PR
Paper improves basket option pricing for log-normal models.
problem Challenges in pricing basket options with negative weights.
method Moment matching and solving a unary cubic equation.
result Highly accurate closed form solution for basket options.
The paper solves the skewness problem in high-dimensional basket options.
problem Inconsistent skewness between individual stock options and basket options on an index.
method Developed an effective local volatility model and calibrated the basket to the index smile using a jump-diffusion model.
result The method resolves the skewness issue, matching the index smile in basket option prices.
Develops M2 model for next-basket recommendation considering user preferences, item popularity, and transition patterns.
problem Next-basket recommendation problem considering user preferences, item popularity, and transition patterns.
method Mixed model with preferences, popularities, and transitions (M2) using ed-Trans for transition patterns among items.
result Significantly outperforms state-of-the-art methods on all datasets in all tasks, with up to 22.1% improvement.
New method uses tensor networks to price multi-asset options efficiently.
problem Pricing multi-asset options via classical full-grid solvers is computationally infeasible due to the curse of dimensionality.
method Quantized tensor trains (QTT) transform the d-asset Black-Scholes PDE into a tractable high-dimensional problem.
result Full-grid prices and Greeks for correlated basket and max-min options in three to five dimensions can be computed with high accuracy.
Complementary products recommendation is an important problem in e-commerce. Such recommendations increase the average order price and the number of products in baskets. Complementary products are typically inferred from basket data. In this study, we propose the BB2vec model. The BB2vec model learns vector representat…
The study analyzes the differences between physical and risk-neutral correlation estimates for equity baskets.
problem Analyzing the differences between physical and risk-neutral correlation estimates for equity baskets.
method Assumed equicorrelation, reduced dimensionality, approximated ICS from implied volatilities, analyzed dynamics using dynamic semiparametric factor model.
result Proposed profitability improvement schemes based on implied correlation forecasts.
With growing consumer adoption of online grocery shopping through platforms such as Amazon Fresh, Instacart, and Walmart Grocery, there is a pressing business need to provide relevant recommendations throughout the customer journey. In this paper, we introduce a production within-basket grocery recommendation system, R…
The existence of basket, flat plumbing and flat plumbing basket surfaces of a link was first proven from a braid representative of the link. In the present article, we show the existence of such surfaces from an induced graph of the link. Consequently, we define the basket number, flat plumbing number and flat plumbing…
New formulas for pricing Asian and basket options using stochastic expansion.
problem Pricing Asian and basket options under time-dependent parameters.
method Stochastic Taylor expansion around a log-normal proxy model.
result Highly accurate approximations for Asian options and vanilla options with discrete dividends.
New approximations for Asian basket spread options using stochastic Taylor expansions.
problem Pricing Asian basket spread options under the Black-Scholes model.
method Stochastic Taylor expansion applied to a log-normal proxy model.
result Highly accurate approximations for Asian and spread options, without numerical integration.
The paper suggests using derivatives instead of stocks for better utility and risk management.
problem The use of stocks in portfolio construction is challenged.
method The study uses the Black--Scholes--Merton setting to demonstrate the benefits of derivatives for maximizing utility and minimizing risk.
result Two derivatives are sufficient to maximize utility and minimize risk exposure in a two-asset portfolio.
Paper improves CDO calibration using Magnus Expansion and Deep Learning.
problem Calibrating CDO to iTraxx market data.
method Large basket approximation, SPDE, Magnus expansion, Deep Learning.
result Highly accurate calibration to market data.
Basket links are shown to be isotopic to .
problem Understanding isotopy of basket links to torus links.
method Using symmetrized Seifert form congruence to matrix.
result Basket links are isotopic to .
The matrix rate of returnphysics.soc-ph
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous a…
Numerical valuation of American basket options via partial differential complementarity problemsmath.NA
Study efficient numerical methods for American basket options.
problem Valuation of American basket options.
method Partial differential complementarity problems (PDCPs) and efficient discretization.
result Approximations of American basket options are close and converge favourably.
Deep neural operators learn complex probabilistic models efficiently.
problem Learning complex probabilistic models with global Lipschitz conditions.
method Deep neural-operator framework under global Lipschitz conditions.
result Explicit network-size bounds for universal approximation of probabilistic models.
Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real-time. Simultaneously we observe an increase in model sophistication on the one hand and growing demands on the quality of risk management on the other. To address the resulting computational challenges, it is nat…
The possibility that the collective dynamics of a set of stocks could lead to a specific basket violating the efficient market hypothesis is investigated. Precisely, we show that it is systematically possible to form a basket with a non-trivial autocorrelation structure when the examined time scales are at the order of…
This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for solving the problem become prohibitively costly due to the curse of dimensionalit…
The flat plumbing basket presentation of a link is introduced by Furihata, Hirasawa and Kobayashi. In this paper, we show that the pass-equivalence and an equivalence introduced by using the flat plumbing basket presentation are the same relation. Furthermore, we obtain an evaluation of the minimal number of bands used…
The article models financial asset returns using Gaussian mixtures and EVT-based copulas to price equity options.
problem Modeling financial asset returns and pricing equity options considering extreme values.
method Modeling marginal distributions with Gaussian mixtures and joint dependence structure with EVT-based copulas.
result The approach accurately prices various equity options on Atos and Dassault Systems actions.
Recommender systems (RS) help users navigate large sets of items in the search for "interesting" ones. One approach to RS is Collaborative Filtering (CF), which is based on the idea that similar users are interested in similar items. Most model-based approaches to CF seek to train a machine-learning/data-mining model b…