arXiv research

Develops a martingale expansion for stochastic volatility models.

New method models portfolios with leptokurtic risk factors using Gram-Charlier expansions.

The study improves volatility model pricing accuracy with new statistical expansions.

For any strictly positive martingale $S = \exp(X)$ for which $X$ has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log strike. We illustrate the versatility of our expansion by computing t…

We introduce an asymptotic small noise expansion, a so called vol-of-vol expansion, for potentially infinite dimensional and rough stochastic volatility models. Thereby we extend the scope of existing results for finite dimensional models and validate claims for infinite dimensional models. Furthermore we provide new, …

We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kern…

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validat…

We quantify predictive uncertainty using the posterior predictive variance.

Rescaling expansiveness proven for k*-expansive vector fields.

New formulas for pricing Asian and basket options using stochastic expansion.

We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe paramet…

New approximations for Asian basket spread options using stochastic Taylor expansions.

We investigate the analogy between the large N expansion in normal matrix models and the asymptotic expansion of the determinant of the Hilb map, appearing in the study of critical metrics on complex manifolds via projective embeddings. This analogy helps to understand the geometric meaning of the expansion of matrix m…

A new method for creating simpler models from complex ones.

Paper presents new expansions for option pricing with cash dividends.

In the planar limit of the 't Hooft expansion, the Wilson-loop average in 3d Chern-Simons theory (i.e. the HOMFLY polynomial) depends in a very simple way on representation (the Young diagram), so that the (knot-dependent) Ooguri-Vafa partition function becomes a trivial KP tau-function. We study higher genus correctio…

Develops AMITE for analyzing neural network nonlinearities.

Modeling business expansion as a stochastic control problem, the study finds that firms are incentivized to expand but may wait.

We create precise formulas for VIX option implied volatility.

Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptot…

The paper derives expansions for Green's operators and resolvents using Hadamard methods.

Cumulant expansion is used to derive accurate closed-form approximation for Monthly Sum Options in case of constant volatility model. Payoff of Monthly Sum Option is based on sum of $N$ caped (and probably floored) returns. It is noticed, that $1/\sqrt{N}$ can be used as a small parameter in Edgeworth expansion. First …

In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its asymptotic variance. Our …

New method for CMS derivatives pricing using Watanabe's expansions.

TaylorPODA uses Taylor expansions to improve feature attributions for opaque models.

The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian …

We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. …

Study shows non-convergence of short-maturity expansion in SABR model.

In this note, we derive the characteristic function expansion for logarithm of the underlying asset price in corrected Heston model as proposed by Fouque and Lorig.

New test for point processes without strong model assumptions.

This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option pricing. As an application, w…

Due to the isotropy $d$-dimensional hyperbolic space, there exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator. On the $R$-radius hyperboloid model of $d$-dimensional hyperbolic geometry with $R>0$ and $d\ge 2$, we compute azimuthal Fourier expansions for a fundamental so…

New theory explains how strong models can learn from weak ones.

Taylor expansions improve reinforcement learning policies.

Analytic torsion expansions for symmetric and complex homogeneous spaces.

Ensembles dynamic models using random feature approximations.

In this article, we consider a Markov process X, starting from x and solving a stochastic differential equation, which is driven by a Brownian motion and an independent pure jump component exhibiting state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability …

Proved cyclotomic expansion for double twist knots' HOMFLY-PT invariants.

Study of hypersurfaces with specific expansion properties.

A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices …

A new method builds sparse polynomial chaos expansions for models with dependent inputs.

Some expansion methods have been proposed for approximately pricing options which has no exact closed formula. Benhamou et al. (2010) presents the smart expansion method that directly expands the expectation value of payoff function with respect to the volatility of volatility, then uses it to price options in the stoc…

It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment $s_+$ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility at large strikes: $σ_{BS}( k,T)^{2}T\sim Ψ(s_+-1) \times k$ (Roger Lee's moment…

Expanding the rough Heston model in $H$

The paper calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.

We consider first order expansions of convex penalized estimators in high-dimensional regression problems with random designs. Our setting includes linear regression and logistic regression as special cases. For a given penalty function $h$ and the corresponding penalized estimator $\hatβ$, we construct a quantity $η$,…

Are expansions and recessions more likely to end as their magnitude increases? In this paper we apply parametric hazard models to investigate this issue in a sample of 16 countries from 1881 to 2000. For the total sample we find evidence of positive magnitude dependence for recessions, while for expansions we are not a…