The theme in this paper is the recombining binomial tree to price American put option when the underlying stock follows constant elasticity of variance(CEV) process. Recombining nodes of binomial tree are decided from finite difference scheme to emulate CEV process and the tree has a linear complexity. Also it is deriv…
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48 results for “Recombining tree”
A New Trinomial Recombination Tree Algorithm and Its Applications
Paper develops a new method for game options in local volatility models.
problem Optimal stopping in one-dimensional diffusion with general coefficients.
method Skorokhod embedding to construct recombining tree approximations.
result Construct nearly optimal stopping times with convergence rates.
Gaussian Recombining Split Treeq-fin.CP
A new tree model, GRST, improves option pricing without log-normality assumptions.
problem Limitations of CRR binomial trees in valuing securities with early exercise characteristics.
method Gaussian Recombining Split Tree (GRST) that generates a discrete probability mass function approximating a Gaussian distribution.
result Option prices from GRST align closely with market prices.
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processe…
Recombinant binomial trees are binary trees where each non-leaf node has two child nodes, but adjacent parents share a common child node. Such trees arise in finance when pricing an option. For example, valuation of a European option can be carried out by evaluating the expected value of asset payoffs with respect to r…
Site-specific recombination is an enzymatic process where two sites of precise sequence and orientation along a circle come together, are cleaved, and the ends are recombined. Site-specific recombination on a knotted substrate produces another knot or a two-component link depending on the relative orientation of the si…
Site-specific recombination on supercoiled circular DNA molecules can yield a variety of knots and catenanes. Twist knots are some of the most common conformations of these products and they can act as substrates for further rounds of site-specific recombination. They are also one of the simplest families of knots and …
In this paper a multi-factor generalization of Ho-Lee model is proposed. In sharp contrast to the classical Ho-Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is stationary to be compatible with principal component analysis. Based on…
A high-order recombination algorithm for weak approximation of stochastic differential equationsmath.PR
Paper develops a high-order recombination algorithm for financial modeling.
problem Creating accurate approximations of stochastic differential equations in finance.
method High-order recombination method applied to practical financial problems.
result Algorithm effectively avoids explosive growth in support cardinality for high-order approximations.
We introduce an evolutionary algorithm called recombinator--means for optimizing the highly non-convex kmeans problem. Its defining feature is that its crossover step involves all the members of the current generation, stochastically recombining them with a repurposed variant of the -means++ seeding algorithm. Th…
Implied Probabilities and Volatility in Credit Risk: A Merton-Based Approach with Binomial Treesq-fin.RM
The study models credit risk using Merton's framework and binomial trees.
problem Credit risk pricing and implied volatility estimation.
method Calibrated using Merton's structural model, with asset volatility derived from Black-Scholes-Merton. Implied mean return and probability surfaces constructed using a recombining binomial tree.
result Established a practical method for constructing implied credit surfaces.
In Divide & Recombine (D&R), big data are divided into subsets, each analytic method is applied to subsets, and the outputs are recombined. This enables deep analysis and practical computational performance. An innovate D\&R procedure is proposed to compute likelihood functions of data-model (DM) parameters for big dat…
We develop a topological model of site-specific recombination that applies to substrates which are the connected sum of two torus links of the form . Then we use our model to prove that all knots and links that can be produced by site-specific recombination on such substrates are contained in one of two…
Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysisq-fin.MF
We develop a trinomial tree model for pricing perpetual derivatives and European options.
problem Pricing perpetual derivatives and European options in a market with two risky assets and a perpetual derivative of one of them.
method We introduce a recombining trinomial tree model, consider a market with two risky assets and a perpetual derivative, and use a replicating portfolio to price options and generate relationships between risk-neutral and real-world parameters.
result We develop implied parameter surfaces for real-world parameters in the model using historical data.
We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small crossing number. We demonstrate these band surgeries for knots and links with small cr…
New RL approach builds short ancestral recombination graphs.
problem Building short ancestral recombination graphs (ARGs).
method Reinforcement Learning applied to genetic sequences.
result RL can build ARGs as short as heuristic algorithms.
We extend the tangle model, originally developed by Ernst and Sumners, to include composite knots. We show that, for any prime tangle, there are no rational tangle attachments of distance greater than one that first yield a 4-plat and then a connected sum of 4-plats. This is done by building on results on exceptional D…
When firms want to buy back their own shares, they have a choice between several alternatives. If they often carry out open market repurchase, they also increasingly rely on banks through complex buyback contracts involving option components, e.g. accelerated share repurchase contracts, VWAP-minus profit-sharing contra…
Market portfolio decomposed into body and tail legs
problem Separation of market portfolio into body and tail legs
method Dynamic value-weighted body and tail legs
result Recombination identity holds for all models
Study decomposes market portfolio into body and tail legs, revealing systematic differences.
problem Understanding the relationship between body and tail components in market portfolios.
method Decomposes CRSP market portfolio into body and tail legs, analyzes their recombination identity.
result Recombination identity holds for all models but not for all, indicating systematic differences.
Betti Numbers of Prodsimplicial Complexes for Directed Graphs with Applications to Word Reductionsmath.CO
Study of Betti numbers in prodsimplicial complexes for directed graphs, focusing on DNA recombination.
problem Analyzing Betti numbers in directed graphs for DNA recombination.
method Custom prodsimplicial complexes for acyclic directed graphs, investigating Betti numbers.
result Investigated Betti numbers and cycles in prodsimplicial complexes for DNA recombination.
The protein recombinase can change the knot type of circular DNA. The action of a recombinase converting one knot into another knot is normally mathematically modeled by band surgery. Band surgeries on a 2-bridge knot N((4mn-1)/(2m)) yielding a (2,2k)-torus link are characterized. We apply this and other rational tangl…
We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of the underlying asset. The algorithm computes the prices on recombining binomial trees, and is designed for modern multi-core processors. Although parallel option pricing…
A new data-level recombination strategy improves RGB-D salient object detection.
problem RGB-D salient object detection struggles with depth information.
method Proposes a novel data-level recombination strategy to fuse RGB and depth data before feature extraction.
result Achieves a new state-of-the-art performance in RGB-D salient object detection.
Parallelized Bayesian quadrature improves sample efficiency and inference.
problem Efficient Bayesian inference and model evidence calculation.
method Batch Bayesian quadrature with kernel recombination for parallel sampling.
result Empirically, outperforms state-of-the-art methods in various datasets.
Improved kernel quadrature with convex weights using subsampling.
problem Constructing quadrature rules with small worst-case error.
method Combining spectral properties of the kernel with recombination results.
result Effective algorithms for constructing convex quadrature rules with i.i.d. samples.
The paper develops a valuation framework for GLWB-LTC contracts with Levy dynamics and stochastic interest rates.
problem Valuation of GLWB-LTC contracts with financial guarantees, longevity protection, and health-contingent LTC payments.
method Coupling a recombining Hull-White trinomial tree with an IMEX finite difference scheme, incorporating a seven-state health model.
result Hybrid tree-IMEX method delivers stable long-maturity prices consistent with simulation benchmarks.
Recent progress in applying machine learning for jet physics has been built upon an analogy between calorimeters and images. In this work, we present a novel class of recursive neural networks built instead upon an analogy between QCD and natural languages. In the analogy, four-momenta are like words and the clustering…
Learning to Evolvecs.NE
Evolution and learning are two of the fundamental mechanisms by which life adapts in order to survive and to transcend limitations. These biological phenomena inspired successful computational methods such as evolutionary algorithms and deep learning. Evolution relies on random mutations and on random genetic recombina…
We give a short topological proof for Rubermans Theorem about mutation and volume, using the Maskit combination theorem and the homology of the linear group.
The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such r…
We develop a model characterizing all possible knots and links arising from recombination starting with a twist knot substrate, extending previous work of Buck and Flapan. We show that all knot or link products fall into three well-understood families of knots and links, and prove that given a positive integer , the…
Humans are able to perform a myriad of sophisticated tasks by drawing upon skills acquired through prior experience. For autonomous agents to have this capability, they must be able to extract reusable skills from past experience that can be recombined in new ways for subsequent tasks. Furthermore, when controlling com…
We develop a topological model of knots and links arising from a single (or multiple processive) round(s) of recombination starting with an unknot, unlink, or (2,m)-torus knot or link substrate. We show that all knotted or linked products fall into a single family, and prove that the size of this family grows linearly …
LSTM based language models are an important part of modern LVCSR systems as they significantly improve performance over traditional backoff language models. Incorporating them efficiently into decoding has been notoriously difficult. In this paper we present an approach based on a combination of one-pass decoding and l…
In plant and animal breeding studies a distinction is made between the genetic value (additive + epistatic genetic effects) and the breeding value (additive genetic effects) of an individual since it is expected that some of the epistatic genetic effects will be lost due to recombination. In this paper, we argue that t…
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale representations are presented for short (seller's) and long (buyer's) positions in an Americ…
This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the calculus of continued fractions. We characterize the class of strongly invertib…
We consider visual domains in which a class label specifies the content of an image, and class-irrelevant properties that differentiate instances constitute the style. We present a domain-independent method that permits the open-ended recombination of style of one image with the content of another. Open ended simply me…
Hydro storage system optimization is becoming one of the most challenging tasks in Energy Finance. While currently the state-of-the-art of the commercial software in the industry implements mainly linear models, we would like to introduce risk aversion and a generic utility function. At the same time, we aim to develop…
New training method for ReLU networks achieves optimal weight size for memorization.
problem Approximate memorization of arbitrary real labels with neural networks.
method Complex recombination training procedure for ReLU networks.
result Approximate memorization with nearly optimal weight size and neuron count.
SwISS improves scalability of Bayesian inference for large datasets.
problem Scalability issues in Bayesian inference for large datasets.
method Divide-and-conquer approach with SwISS for recombining sub-posterior samples.
result SwISS accurately approximates the original posterior distribution.
New model separates objects in scenes, enabling novel arrangements and depth.
problem Lack of modular, compositional scene modeling in generative models.
method Ensemble of generative models (experts) compete for explaining different parts of a scene.
result Model generates scenes with novel object arrangement and depth ordering.
Locally epistatic genomic relationship matrices for genomic association, prediction and selectionstat.AP
As the amount and complexity of genetic information increases it is necessary that we explore some efficient ways of handling these data. This study takes the "divide and conquer" approach for analyzing high dimensional genomic data. Our aims include reducing the dimensionality of the problem that has to be dealt one a…
Wittgenstein's Rule Following evolves datasets by extrapolating structural descriptors.
problem Generating meaningful continuations of evolving datasets.
method Wittgenstein's Rule Following (WRF) uses structural descriptors to extrapolate trajectories and average historical descriptors.
result WRF can generate meaningful continuations of evolving datasets.
Fusion of transformer networks using optimal transport for improved performance.
problem Improving performance of transformer-based models through fusion.
method Exploiting optimal transport for soft alignment of transformer components.
result Consistently outperforms vanilla fusion and individual parent models.
From tangle fractions to DNAmath.GT
This paper is an introduction to rational tangles, rational knots and links and their applications to DNA. The paper can be read as an introduction to our more technical papers on rational tangles (math.GT/0311499) and on rational knots (math.GT/0212011). The present paper includes a self-contained account of the tangl…