Arbitrage-free Nelson–Siegel model for multiple yield curves

From arbitrage to arbitrage-free implied volatilities

We propose a method for determining an arbitrage-free density implied by the Hagan formula. (We use the wording “Hagan formula” as an abbreviation of the Hagan– Kumar–Leśniewski–Woodward model.) Our method is based on the stochastic collocation method. The principle is to determine a few collocation points on the implied survival distribution function and project them onto the polynomial of an ...

A model-free no-arbitrage price bound for variance options

In the framework of Galichon, Henry-Labordère and Touzi [9], we consider the model-free no-arbitrage bound of variance option given the marginal distributions of the underlying asset. We first make some approximations which restrict the computation on a bounded domain. Then we propose a gradient projection algorithm together with a finite difference scheme to approximate the bound. The general ...

An arbitrage-free method for smile extrapolation

A robust method for pricing options at strikes where there is not an observed price is a vital tool for the pricing, hedging, and risk management of derivatives. All institutions that trade derivatives will have an approach to this task. Typical examples might be a simple interpolation scheme across implied volatilities, or the use of a modelbased formula optimized to fit observed prices. It is...

Arbitrage-free pricing of XVA

Arbitrage-free valuation of interest rate securities under forward curves with stochastic speed and acceleration

Arbitrage-free models for valuing interest rate securities posit that stochastic changes in spot or forward interest rates (forward rate " speed ") follow a diffusion process. This paper extends the Heath, Jarrow and Morton (1992, HJM) framework by allowing diffusive shocks to both the " speed " and " acceleration " of forward rates. The arbitrage-free restriction on forward rates is identified...