New binomial model fits all moments to geometric Brownian motion.
problem Discontinuity problem in option pricing.
method Constructs a generalized binomial tree model.
result Resolves discontinuity problem in option pricing.
The study tightens bounds on binomial probabilities and minimums using KL-divergence.
problem Tightening bounds on binomial probabilities and minimums of i.i.d. Binomials.
method Applied Sanov's theorem to derive upper and lower bounds on binomial tail probabilities and minimums, expressed in terms of KL-divergence.
result High probability upper and lower bounds on the minimum of i.i.d. Binomial random variables, finite sample, asymptotically tight.
Efficient Bayesian variable selection for binomial and negative binomial data.
problem Computational challenges in Bayesian variable selection for complex models.
method Tempered Gibbs Sampling and MCMC scheme.
result Demonstrated effectiveness on cancer data with thousands of covariates.
Extends CRR model with q-binomial random walks for asset pricing.
problem Asset pricing with time-varying probabilities and trend parameters.
method Introduces a q-binomial extension of the CRR model with non-self-similar binomial trees.
result Convergence to Black-Scholes formula with rate O(N^(-1/2)).
Paper develops efficient method for probability estimation.
problem Estimating probabilities with high efficiency.
method Adaptive Monte Carlo estimation using truncated inverse binomial sampling.
result Proposed method is orders of magnitude more efficient.
We construct a binomial model for a guaranteed minimum withdrawal benefit (GMWB) rider to a variable annuity (VA) under optimal policyholder behaviour. The binomial model results in explicitly formulated perfect hedging strategies funded using only periodic fee income. We consider the separate perspectives of the insur…
Enhances binomial and trinomial models for equity options pricing.
problem Improving accuracy of equity option pricing models.
method Develops time-dependent binomial model and introduces a risk-neutral trinomial tree.
result Equates moments of pricing tree increments to geometric Brownian motion.
Correction for Error estimates for binomial approximations of game options [math.PR/0607123]
Improved binomial model for American put prices with error analysis.
problem Improving the accuracy of American put price approximations.
method Binomial approximation in the Black-Scholes model with consideration of continuous dividend yield.
result Error in approximation is O((lnn)α/n), where α depends on interest rate and dividend yield. Develops a binomial model in categorical probability spaces.
problem Valuation of financial claims in non-standard filtrations.
method Introduces generalized filtrations in a categorical setting.
result Validates financial claim valuations in new filtrations.
Using techniques from the theories of convex polytopes, lattice paths, and indirect influences on directed manifolds, we construct continuous analogues for the binomial coefficients and the Catalan numbers. Our approach for constructing these analogues can be applied to a wide variety of combinatorial sequences. As an …
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…
New spectral method learns DNA methylation models efficiently.
problem Learning parameters of Binomial HMMs for DNA methylation data.
method Feature-map based approach exploiting Binomial HMM properties.
result The new algorithm provides theoretical guarantees and performs well on real data.
Transformer learns to estimate negative binomial parameters efficiently.
problem Parameter estimation for over-dispersed count data in large screens.
method Pre-trained transformer trained on synthetic data generation to invert parameter to count transformation.
result Method of moments provides faster, more efficient, and better-calibrated estimates.
We construct algorithms via binomial approximations for computation of prices of game put options and obtain estimates of approximation errors.
In the present paper we show that the Binomial-tree approach for pricing, hedging, and risk assessment of Convertible bonds in the framework of the Tsiveriotis-Fernandes model has serious drawbacks. Key words: Convertible bonds, Binomial tree, Tsiveriotis-Fernandes model, Convertible bond pricing, Convertible bond Gree…
The paper models stock returns using q-Gaussians and negative binomials.
problem Modeling stock return distributions and pricing options.
method Proposes a generalized jump-diffusion model and uses q-Gaussians and negative binomial distributions. result An explicit option pricing formula is derived.
The paper resolves a counterexample showing convergence of expected utility in binomial models.
problem The convergence of expected utility under binomial models was previously shown to fail in certain cases.
method The paper provides a positive result on convergence using fine estimates from the Central Limit Theorem.
result A general positive result of convergence of expected utility is provided in symmetric binomial models.
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…
We justify and give error estimates for binomial approximations of game (Israeli) options in the Black--Scholes market with Lipschitz continuous path dependent payoffs which are new also for usual American style options. We show also that rational (optimal) exercise times and hedging self-financing portfolios of binomi…
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.
Develops a new filtration for asset pricing models.
problem Models of financial asset pricing need to account for information loss.
method Introduces a generalized filtration to represent information loss.
result Validates the new filtration in a binomial asset pricing model.
Detecting and recovering labels in binomial logistic mixtures is challenging due to an information gap.
problem Detecting and recovering labels in binomial logistic mixtures
method Propose two feasibility-aware inference procedures
result Avoid misleading component selections and improve label probability calibration
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. …
PSO optimizes model parameters in nonstandard distributions.
problem Estimating model parameters in nonstandard distributions using existing algorithms.
method Particle Swarm Optimization (PSO) as an alternative optimization routine.
result PSO produces more optimal or convergent results than existing algorithms.
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.
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in learning theory and generalization bounds for unbounded loss functions.
Two approaches improve parameter learning in various mixture models.
problem Parameter learning in mixture models.
method Complex-analytic and algebraic-combinatorial methods.
result Improved sample sufficiency for parameter estimation in specific mixture models.
Proves integrality of knot invariants using number theory.
problem Integrality of BPS invariants of knots.
method Number theoretic proof involving binomial coefficients and Möbius function.
result Proves divisibility properties of knot invariants.
New framework for portfolio management using binomial markets and game theory.
problem Investment behavior in competitive and incomplete markets.
method Introduces PRFPP framework, constructs and analyzes for both finite and mean field games.
result Relative performance concerns do not always lead to more risky asset investment.
Proved a combinatorial conjecture in machine learning.
problem None explicitly stated in the abstract.
method Binomial and multinomial sums identities.
result Proved a combinatorial conjecture.
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.
Bayesian optimization for binomial outputs with multifidelity.
problem Optimizing functions with binomial outputs that don't fit Gaussian process assumptions.
method General Gaussian process model for binomial data, Expected Improvement acquisition function, heuristic sample selection.
result Improves optimization performance for binomial target functions.
We show that prices and shortfall risks of game (Israeli) barrier options in a sequence of binomial approximations of the Black--Scholes (BS) market converge to the corresponding quantities for similar game barrier options in the BS market with path dependent payoffs and the speed of convergence is estimated, as well. …
BKP R package models spatially varying binomial probabilities efficiently.
problem Modeling spatially varying binomial probabilities efficiently.
method Beta Kernel Process (BKP) combining localized kernel-weighted likelihoods with conjugate beta priors.
result Closed-form posterior inference without requiring latent variables or intensive MCMC sampling.
We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corresponding Black--Scholes market considering Lipschitz continuous path-dependent payoffs for both discrete- and continuous-time cases. These results are new also for usual American style option…
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partitio…
Parallelizes computation of expected values in binomial trees for financial option pricing.
problem High computational cost of evaluating expected values in binomial trees.
method Parallelizes the calculation of expected values into an 'embarrassingly parallel' problem and uses a parallel Monte Carlo method.
result Parallelization and Monte Carlo methods reduce computational cost and variance.
Develops methods to construct exchangeable sequences of random multisets.
problem Creating models for random multisets with unknown base measures.
method Uses exchangeable sequences of point processes and conditional-i.i.d. negative binomial processes.
result Provides constructions for negative binomial processes with random base measures.
Derives Black-Scholes model without stochastic calculus or PDEs.
problem Deriving the Black-Scholes model without advanced math.
method Continuum limit of Binomial tree approach.
result Derives Black-Scholes model and exchange-option generalization.
NegBio-VAE models neural spike counts with negative binomial distribution.
problem Limited biological plausibility of continuous latent variables in VAEs for neural spike modeling.
method Proposes a negative binomial latent-variable model with a dispersion parameter for overdispersed spike count modeling.
result NegBio-VAE outperforms competing models in reconstruction and generation tasks.
The paper introduces ESG valuation in option pricing using binomial trees.
problem Option pricing with ESG considerations and discrete compounding.
method Replicating binomial trees with ESG valuation and discrete compounding.
result The approach enhances yield and reflects market history.
NBMF improves recommendation precision by modeling count data dispersion.
problem Predicting user preferences in recommender systems with over-dispersed data.
method NBMF extends PF with a multiplicative term to handle over-dispersion, skipping binarization.
result NBMF predicts user tastes more accurately than Poisson matrix factorization.
A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency for a covariate present in a sample to both repeat itself and excite related ones…
New copulas fit asymmetric data for risk management.
problem Fitting asymmetric data to copulas.
method Data-driven constructive approach to partition-of-unity copulas.
result Solution for fitting Bernstein-, negative binomial, and Poisson copulas to asymmetric data.
Enhances binomial model with machine learning for microstructure effects.
problem Traditional binomial models ignore market microstructure effects like bid-ask spreads.
method Augments binomial tree with Random Forest classifiers trained on market data.
result Achieves 88.25% AUC in forecasting price movements using real-world data.
Study on risk model with claims, dividends, and random probabilities.
problem Analyzing a risk model with claims, delayed claims, and randomized dividends.
method Discrete time Compound Beta-Binomial Risk Model with recursive expressions for Gerber-Shiu function.
result Recursive relations for ruin-related quantities obtained.
We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process (NBP)…