A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The BBF, SABR, and rough SABR formulas provide nearly arbitrage-free implied vol approximations.
This paper improves SABR/LMM for better practical use in global banks.
A new method calculates accurate SABR model option prices and deltas.
Derives a rough SABR formula for short maturities.
Extends SABR model for pricing RFR caplets.
Derives formulae linking SABR model parameters to ATM and option prices.
Develops a novel SABR DNN for accurate volatility surface calibration.
The SABR model is a benchmark stochastic volatility model in interest rate markets, which has received much attention in the past decade. Its popularity arose from a tractable asymptotic expansion for implied volatility, derived by heat kernel methods. As markets moved to historically low rates, this expansion appeared…
Enhanced SABR model captures complex volatility smiles in Chinese financial options.
Lower bound found for volatility swap in SABR model.
Study uses SABR model to create implied volatilities from sparse quotes.
We derive variance-optimal hedging strategies for SABR and rough Bergomi models.
We refine the analysis of hedging strategies for options under the SABR model carried out in [2]. In particular, we provide a theoretical justification of the empirical observation made in [2] that the modified delta ("Bartlett's delta") introduced there provides a more accurate and robust hedging strategy than the con…
Efficiently calibrates SABR/LIBOR models to real market caplets and swaptions data.
Improved option pricing for SABR model using Gauss-Hermite quadrature.
We discuss a semi-analytical method for solving SABR-type equations based on path integrals. In this approach, one set of variables is integrated analytically while the second set is integrated numerically via Monte-Carlo. This method, known in the literature as Conditional Monte-Carlo, leads to compact expressions fun…
Hybrid method improves SABR implied volatility approximation.
VolNP learns IVS from sparse quotes via meta-learning and SABR priors.
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such a model is less studied in the literature. We show i…
Efficiently simulates SABR model with novel sampling methods.
The SABR model is shortly presented and the volatility swap explained. The fair value for a volatility swap is then computed using the usual theory in financial mathematics. An analytical solution using confluent hypergeometric functions is found. The solution is then verified using Rama Cont's functional calculus.
We propose a deterministic numerical method for pricing vanilla options under the SABR stochastic volatility model, based on a finite element discretization of the Kolmogorov pricing equations via non-symmetric Dirichlet forms. Our pricing method is valid under mild assumptions on parameter configurations of the proces…
Matrix approximation method for Bachelier option pricing and Greeks under stochastic volatility models
New method for pricing barrier options in time-dependent λ-SABR model.
In this article, we show how the scaling symmetry of the SABR model can be utilized to efficiently price European options. For special kinds of payoffs, the complexity of the problem is reduced by one dimension. For more generic payoffs, instead of solving the 1+2 dimensional SABR PDE, it is sufficient to solve u…
Extensive neural networks eliminate the need for SABR pricing formulas.
In this short note, using our geometric method introduced in a previous paper \cite{phl} and initiated by \cite{ave}, we derive an asymptotic swaption implied volatility at the first-order for a general stochastic volatility Libor Market Model. This formula is useful to quickly calibrate a model to a full swaption matr…
This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error i…
Study on VIX options pricing in SABR model, showing infinite prices due to volatility explosion.
We describe a high performance parallel implementation of a derivative pricing model, within which we introduce a new parallel method for the calibration of the industry standard SABR (stochastic-αβρ) stochastic volatility model using three strike inputs. SABR calibration involves a non-linear three dimensional minimis…
We use commutator techniques and calculations in solvable Lie groups to investigate certain evolution Partial Differential Equations (PDEs for short) that arise in the study of stochastic volatility models for pricing contingent claims on risky assets. In particular, by restricting to domains of bounded volatility, we …
Study shows non-convergence of short-maturity expansion in SABR model.
We discuss modelling of SPX and DAX index option prices using the Shifted Log-Normal (SLN) model, (also known as Displaced Diffusion), and the SABR model. We found out that for SPX options, an example of strongly skewed option prices, SLN can produce a quite accurate fit. Moreover, for both types of index options, the …
RL and DTSOC for final quadratic hedging performance studied.
The paper derives closed-form approximations for mean-reverting SABR models and calibrates them to equity volatilities.
Safe RL with binary feedback using SABRE algorithm.
We study the mass at the origin in the uncorrelated SABR stochastic volatility model, and derive several tractable expressions, in particular when time becomes small or large. As an application--in fact the original motivation for this paper--we derive small-strike expansions for the implied volatility when the maturit…
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 SABR model is a stochastic volatility model not admitting a closed form solution. Hagan, Kumar, Leniewski and Woodward have obtained an approximate solution by means of perturbative techniques. A more precise approximation was found by Henry-Labordère with the heat kernel expansion method. The latter relies on deep…
For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study sho…
We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula by Ito's calculus yields a theoretical replicating strategy for the target volatility option, assuming the accessibilities of all variance swaps and swaptions. The same formula also sugges…
We compute a sharp small-time estimate for the price of a basket call under a bi-variate SABR model with both parameters equal to and three correlation parameters, which extends the work of Bayer,Friz&Laurence [BFL14] for the multivariate Black-Scholes flat vol model. The result follows from the heat kernel on …
Proposes a method to fill in missing swaption volatility data using variational autoencoders.
We compute a sharp small-time estimate for implied volatility under a general uncorrelated local-stochastic volatility model. For this we use the Bellaiche \cite{Bel81} heat kernel expansion combined with Laplace's method to integrate over the volatility variable on a compact set, and (after a gauge transformation) we …
We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its asymptotic properties in the limit of a large number of time steps under a certai…
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of c…
A new method for robust product Markovian quantization overcomes numerical instabilities.
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…