DEPARTMENT OF COMPUTER SCIENCE

DOCTORAL DISSERTATION DEFENSE

Candidate: Juan C. Porras

Advisor: Marco Avellaneda

DOCTORAL DISSERTATION DEFENSE

Candidate: Juan C. Porras

Advisor: Marco Avellaneda

**Pricing and hedging volatility risk in interest-rate
derivatives **

10:00 a.m., Wednesday, September 10

12th floor conference room, 719 Broadway

Abstract

This work addresses the problem of pricing interest-rate derivative
securities
and the use of quoted prices of traded instruments to calibrate the
corresponding interest-rate dynamics.
To this end, an arbitrage-free model of interest
rate evolution is adopted, for which the local drift will depend on the
history of volatility, thus leading to path-dependent pricing.
This model is based on the Heath-Jarrow-Morton formulation but, in
addition, presupposes that the volatility process is not defined
*a-priori*. This leads to a path-dependent model that can be formulated
in a Markovian framework by considering additional state-variables and hence
increasing the dimensionality of the computation. Instead of
solving the resulting 3-dimensional partial differential equation, an
alternative approach, based on conditional expectations of the history
of volatility, is taken. This pricing method is applied to a non-linear
(adverse volatility) setting, and used as the core of a non-parametric
model calibration technique. The algorithm,
by performing an optimization over volatility surfaces,
finds a volatility surface that matches the market prices of a given set
of securities. This method also finds a hedge for volatility
risk, using derivative securities as hedging instruments. In particular,
we present results obtained for the problem of hedging
American swaptions (options on interest-rate swaps) using European
swaptions.

The conditional expectation approach is explored further, and found to be of interest in its own right for the pricing of several kinds of path-dependent instruments, providing an alternative to increasing state-space dimension in order to satisfy a Markov property. In particular, we show how this method speeds up the computation of prices for some types of exotic options, while being general enough to apply to both linear and non-linear pricing of portfolios.