Recent papers in Mathematical Finance

This page contains recent research publications in the field of Mathematical Finance. My interest is in the general area of derivatives, with emphasis on modeling financial risk.

Some of the questions studied so far with my collaborators include the issue of incorporating transaction costs into dynamic hedging and the management of uncertainty of future market volatility. Recently, with Yingzi Zhu, we have made some econometric modeling of the implied volatility of foreign-exchange options (see below).

Our main objective is to develop models and numerical algorithms that are mathematically sound and have practical application (with the understanding that we will usually fall short of this objective!).

The papers are in .ps files that can be dowloaded and printed/viewed if you have a postcript reader. All comments and suggestions are greatly appreciated and can be sent to avellane@cims.nyu.edu .

Note (10/1999): Most of these papers have been in print for at least 2 years. For more recent papers, go to the Courant Finance Server.


An introduction to option pricing and the mathematical theory of risk


To appear in Proceedings of AMS Winter meeting, San Diego Jan 1997.


A risk-neutral stochastic volatility model


Authors:

Y. Zhu and M. Avellaneda

Submitted to:

International Journal of Theoretical and Applied Finance, August 1997.


E-ARCH Model for the Term-Structure of Implied Volatility of FX Options


Authors:

Y. Zhu and M. Avellaneda

Submitted to:

Applied Mathematical Finance, January 1997


Calibrating volatility surfaces via relative-entropy minimization


Authors:

M. Avellaneda, C. Friedman, R. Holmes, D. Samperi

Appeared in:

Applied Mathematical Finance, March 1997


Pricing Interest Rate Contingent Claims in Markets with Uncertain Volatilities


Authors:

P. Lewicki and M. Avellaneda

Appeared in:

CIMS Preprint version, Fall 1996


Pricing and hedging derivative securities in markets with uncertain volatilities


Authors:

M. Avellaneda, A. Levy and A. Paras

Appeared in:

Applied Mathematical Finance 2, 73-88 (1995)


Managing the volatility risk of portfolios of derivative securities: the Lagrangian Uncertain Volatility Model


Authors:

M. Avellaneda and A. Paras

Appeared in:

Applied Mathematical Finance , 3, 21-52 (1996)


Dynamic hedging with transaction costs: from lattice models to nonlinear volatility and free-boundary problems


Authors:

M. Avellaneda and A. Paras

Submitted to:

Communications in Pure and Applied Math, Preprint version: August 1995.


Dynamic hedging portfolios for derivative securities in the presence of large transaction costs


Authors:

M. Avellaneda and A. Paras

Appeared in:

Applied Mathematical Finance, 1, 165-193 (1994)