|
VIGRE Advanced Seminar: Computational Finance |
Fall 2003: Upcoming Speakers
October 1: Chad Bhatti “Some Notes on Brownian Motion and Its Relationship to
Black-Scholes”
November 5: Gretchen Fix “A Brief Overview of *Really* Current Research on Dividends”
November 26: Donald C.
Williams “On the Formulation of an Optimization Framework for Pricing
American-style Options”
December
3: Matthias Mathaes “Nonparametric Option Pricing”
Matthias Mathaes
STAT
Nonparametric Option
Pricing
I will present a paper
that can be found in the journal of econometrics 116.
The title is: Nonparametric option pricing under shape restrictions
by Yacine
Ait-Sahalia, Jefferson Duarte.
A summary of their
abstract:
In agreement with the economic theory, the authors placed shape restrictions on
the values of the first and second derivative of nonparametric locally density
estimators. With this technique they are able to estimate the state price
density (SPD), also known as risk-neutral density, implicit in the market price
of options. The restriction on the option pricing function are: 1)
function is monotone, and 2) function is convex.
The authors' simulations show that nonparametric estimates can do well in small
samples, which is important for day to day option pricing, once the restrictions
are imposed on the first two derivatives. The authors find that the
unconstrained estimators violate the constraints half of the trading days
during 1999 for S&P 500 options, as opposed to the constrained estimator,
which always satisfy the constraints.
Wednesday, December 03, 2003
2:00 –3:00pm
DH 3092
Donald C. Williams
CAAM
On the
Formulation of an Optimization Framework for Pricing American-style Options
Fundamental to many complex
derivative financial products is the valuation and optimal exercise of options
with American-style exercise features. In this talk, we review some fundamental
notions regarding option contract specifications. We then examine the PDE
approach to modeling American-style option contracts. We discuss the
variational inequality formulation of the problem, the resulting linear
complementarity problem (LCP), and a typical technique for approximating
numerical solutions. A more general optimization framework will be motivated
and discussed from the perspective of incorporating additional economic
constraints into the pricing model.
Wednesday, November 26, 2003
2:00 –3:00pm
DH 2014
Gretchen Fix
Graduate Student
STAT
A Brief
Overview of *Really* Current Research on Dividends
As outlined in my first talk, Fama and French present evidence that shows that the proportion of firms paying dividends dropped from 66.5% in 1978 to 20.8% in 1999. They attribute much of this decline to the surge of new lists that hit the market in 1979 and continued through the 1990s. In our research, we compare the dividend initiation behavior of new lists from two time periods--1965-1975 and 1985-1995. Viewing the data from a survival analysis standpoint, we explore dividend initiation using Kaplan-Meier estimates for the survival curves and implement our hypothesized "lifecycle model for dividend initiation" using the Cox regression framework.
Wednesday, November 5, 2003
2:00 –3:00pm
DH 3092
Chad Bhatti
Graduate Student
STAT
Some Notes on Brownian Motion and Its Relationship to
Black-Scholes
This talk will begin in the first
seminar and conclude in the second seminar. We will develop the Brownian
motion process as the limit of a Random Walk and define the properties of
Brownian motion. We will examine the return process of the S&P 500
over several time spans with monthly and daily sampling frequency and compare
our empirical findings with the Brownian motion hypothesis. We will discuss how
defining the price process as a geometric Brownian motion builds implicit
assumptions into the Black-Scholes model and how the Black-Scholes differential
equation is derived from a no arbitrage replicating portfolio.
This talk is titled "Notes" because we will offer no definitive
statements nor claim any original presentation or ideas. The purpose of
this talk is to introduce the student to a popular continuous time model and to
better develop a understanding of a popular and tractable but not the most pliable
option pricing model.
Wednesday, October 1, 2003
2:00 –3:00pm
DH 2014