Publication

Functional Vašiček Model

2025

Abstract

We propose a new formulation of the Vašičekmodel within the framework of functional data analysis. We treat observations (continuous‐time rates) within a suitably defined trading day as a single statistical object. We then consider a sequence of such objects, indexed by day. In addition to the common long‐term rate, the objects are parametrized by two functional parameters, the volatility curve and the reversion curve, which replace analogous scalar parameters in the classical Vašičekmodel. Such a modeling paradigm allows us to estimate instantaneous reversion and volatility parameters within a trading day, thus allowing them to evolve with the time of day. The model is estimated within a new framework that combines techniques of functional data analysis with those of SDEs. In particular, large sample properties are derived as the number of days and the number of discrete time points at which the rate curves are observed tend to infinity.

Official source

https://infoscience.epfl.ch/entities/publication/825e70ea-dbd8-4c2f-9372-4f544daee7a1

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/825e70ea-dbd8-4c2f-9372-4f544daee7a1

About this result

Related concepts (32)

Volatility smile

Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices (and thus implied volatilities) than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money.

Local volatility

A local volatility model, in mathematical finance and financial engineering, is an option pricing model that treats volatility as a function of both the current asset level and of time . As such, it is a generalisation of the Black–Scholes model, where the volatility is a constant (i.e. a trivial function of and ). Local volatility models are often compared with stochastic volatility models, where the instantaneous volatility is not just a function of the asset level but depends also on a new "global" randomness coming from an additional random component.

Lattice model (finance)

In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date.

Related publications (2)

Functional Vašiček Model

Chat with Graph Search

Simulation of Pedestrian Behaviour using a Discrete Choice Model Calibrated on Actual Motion Data

Sampling signals with finite rate of innovation