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.
A new model prices Bermudan swaptions without calibration.
New SL algorithms improve Bermudan Swaption pricing efficiency.
We study American swaptions in the linear-rational (LR) term structure model introduced in [5]. The American swaption pricing problem boils down to an optimal stopping problem that is analytically tractable. It reduces to a free-boundary problem that we tackle by the local time-space calculus of [7]. We characterize th…
Tensor Neural Networks improve pricing accuracy for interest rate derivatives.
We derive measure change formulae required to price midcurve swaptions in the forward swap annuity measure with stochastic annuities' ratios. We construct the corresponding linear and exponential terminal swap rate pricing models and show how they capture the midcurve swaption correlation skew.
The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives with Libor market models is mainly carried out with Monte Carlo simulation. The PDE…
We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consist…
Pricing Bermudan swaptions with few exercise dates using analytic methods.
The Hull-White one factor model is used to price interest rate options. The parameters of the model are often calibrated to simple liquid instruments, in particular European swaptions. It is therefore very important to have very efficient pricing formula for simple instruments. Such a formula is proposed here for Europ…
The paper uses deep learning to efficiently price Bermudan swaptions.
Closed form formulas for swaption prices in HJM model are derived. These formulas are used for nonparametric fit of deterministic forward volatility. It is demonstrated that this formula and non-parametric fit works very well and can be used to identify arbitrage opportunities
We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasiński interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Loève expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them useful for nu…
Proposes a new model for negative interest rates that fits market data closely.
Paper presents a fast algorithm for pricing Bermudan swaptions under the two-factor Hull-White model.
We present a new model for credit index derivatives, in the top-down approach. This model has a dynamic loss intensity process with volatility and jumps and can include counterparty risk. It handles CDS, CDO tranches, Nth-to-default and index swaptions. Using properties of affine models, we derive closed formulas for t…
We introduce a multiple curve framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. Negatives rates and positive spreads can also be accommodated in this framework. The dynamics of OIS and LIBOR rates are specified following the methodology of the …
A semi-static approach efficiently replicates and prices callable interest rate derivatives.
Efficiently calibrates SABR/LIBOR models to real market caplets and swaptions data.
We propose an elementary model to price European physical delivery swaptions in multicurve setting with a simple exact closed formula. The proposed model is very parsimonious: it is a three-parameter multicurve extension of the two-parameter Hull-White (1990) model. The model allows also to obtain simple formulas for a…
We propose a fast and accurate numerical method for pricing European swaptions in multi-factor Gaussian term structure models. Our method can be used to accelerate the calibration of such models to the volatility surface. The pricing of an interest rate option in such a model involves evaluating a multi-dimensional int…
Improved LV model for interest rate swaptions and caplets.
We study a Markov-Functional (MF) interest-rate model with Uncertain Volatility Displaced Diffusion (UVDD) digital mapping, which is consistent with the volatility-smile phenomenon observed in the option market. We first check the impact of pricing Bermudan swaptions by the model. Next, we also investigate the future s…
The study models mortgage prepayment risk using stochastic housing market activity.
In this article, we apply the forward variance modeling approach by L.Bergomi to the co-terminal swap market model. We build an interest rate model for which all the market price changes of hedging instruments, interest rate swaps and European swaptions, are interpreted as the state variable variations, and no diffusio…
Paper proposes a deep hedging method for Bermudan swaptions to manage residual profit and loss.
A new model uses a Levy-driven process to value credit index swaptions.
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic numerical method. Then, we apply the latter to some specific financial problems. In…
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 develop a multi-factor stochastic volatility Libor model with displacement, where each individual forward Libor is driven by its own square-root stochastic volatility process. The main advantage of this approach is that, maturity-wise, each square-root process can be calibrated to the corresponding cap(let)vola-stri…
The atomic swap protocol allows for the exchange of cryptocurrencies on different blockchains without the need to trust a third-party. However, market participants who desire to hold derivative assets such as options or futures would also benefit from trustless exchange. In this paper I propose the atomic swaption, whi…
Proposes efficient calibration method for LIBOR Market Model with stochastic volatility.
Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump-diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stoc…
We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. I…
Hedging strategies in bond markets are computed by martingale representation and the Clark-Ocone formula under the choice of a suitable of numeraire, in a model driven by the dynamics of bond prices. Applications are given to the hedging of swaptions and other interest rate derivatives, and our approach is compared to …
Paper uses RL for dynamic swaption hedging, outperforming traditional methods.
The study models mortgage prepayment risk, accounting for behavioral uncertainty, and provides replication strategies.
We introduce Dirac processes, using Dirac delta functions, for short-rate-type pricing of financial derivatives. Dirac processes add spikes to the existing building blocks of diffusions and jumps. Dirac processes are Generalized Processes, which have not been used directly before because the dollar value of non-Real nu…
We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear payoffs written on the consumer price index have prices that are rational functions of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that …
We present a flexible approach for the valuation of interest rate derivatives based on Affine Processes. We extend the methodology proposed in Keller-Ressel et al. (2009) by changing the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. We then show that it is possible…
Enhances swaption modeling with rough stochastic volatility.
Proposes a method to fill in missing swaption volatility data using variational autoencoders.
Option pricing is the most elemental challenge of mathematical finance. Knowledge of the prices of options at every strike is equivalent to knowing the entire pricing distribution for a security, as derivatives contingent on the security can be replicated using options. The available data may be insufficient to determi…
Proposes a new model to handle negative interest rates using CIR framework.
In this paper we consider the pricing of options on interest rates such as caplets and swaptions in the Lévy Libor model developed by Eberlein and Özkan (2005). This model is an extension to Lévy driving processes of the classical log-normal Libor market model (LMM) driven by a Brownian motion. Option pricing is signif…
The aim of this paper is to present a dual-term structure model of interest rate derivatives in order to solve the two hardest problems in financial modeling: the exact volatility calibration of the entire swaption matrix, and the calculation of bucket vegas for structured products. The model takes a series of long-ter…
Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FBSDEs. In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives, including options and swaptions, with XVA under the flexible dynamics of a local…
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…
The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative and caplet and swaption prices can be calculated analytically. In order to guarantee nonnegative interest rates affine LIBOR models are driven by no…