arXiv research

Develops a martingale expansion for stochastic volatility models.

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…

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

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

Neural networks solve SPDEs using Wiener chaos expansion.

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…

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, …

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…

Study local expansions of continuous-time processes using Ito signature properties.

New analysis of stochastic approximation with non-expansive mappings.

In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox-Ingersoll-Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of …

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

We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation parameter between the underlying asset and volatility process…

In the compagnion paper [Marginal density expansions for diffusions and stochastic volatility, part I] we discussed density expansions for multidimensional diffusions $(X^1,...,X^d)$, at fixed time $T$ and projected to their first $l$ coordinates, in the small noise regime. Global conditions were found which replace th…

We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do…

New method estimates SDE parameters efficiently using WCE and SGD.

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

Paper introduces cubature method for stochastic Volterra equations.

This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate the validity of our app…

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 method for European option pricing faster and more robust.

A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is also given as a corollary.…

AL-SPCE improves reliability analysis for complex systems with active learning and SPCE.

A new fast method simulates stochastic volatility models.

Paper presents new expansions for option pricing with cash dividends.

We obtain a first order extension of the large deviation estimates in the Gärtner-Ellis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order one to that of the original family of measures. The construction of the special fam…

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…

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…

We consider a stochastic volatility model with Lévy jumps for a log-return process $Z=(Z_{t})_{t\geq 0}$ of the form $Z=U+X$, where $U=(U_{t})_{t\geq 0}$ is a classical stochastic volatility process and $X=(X_{t})_{t\geq 0}$ is an independent Lévy process with absolutely continuous Lévy measure $ν$. Small-time expansio…

A new method for creating simpler models from complex ones.

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 apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to deal with the …

In an abstract Wiener space setting, we constract a rigorous mathematical model of the one-loop approximation of the perturbative Chern-Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines.

Paper applies theorem to find optimal investment boundary in stochastic capacity expansion.

Combines Gaussian processes and polynomial chaos for stochastic control.

This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the relevant conditional distri…

The proposed model is aimed to reveal important patterns in the behavior of a simplified financial system. The patterns could be detected as regular cycles consisting of debt bubbles and crises. Financial cycles have a well defined structure and form periodic sequences along the axis of credit expansion while retaining…

In this paper we study the pricing of exchange options when underlying assets have stochastic volatility and stochastic correlation. An approximation using a closed-form approximation based on a Taylor expansion of the conditional price is proposed. Numerical results are illustrated for exchanges between WTI and Brent …

We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion aroun…

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expan…

Maximal concentration bounds for stochastic approximation with heavy-tailed noise.

Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games, and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data efficient Deep-Q-learning method…

In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion technique for the underlying volatility process, we derive explicit expression f…

New method analyzes volatility models for option prices, especially in rough volatility.

Study examines USD exchange rate dynamics using Kramers-Moyal expansion.

Study short-maturity Asian option pricing in LSV models using large deviations theory.

The study examines numerical aspects of Karhunen-Loève expansions for stochastic processes.

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 …