SCIENTIFIC PROGRAMS AND ACTIVITIES

November 26, 2014

Actuarial Science and Mathematical Finance Group Meetings
2006-07

My research group meets on a regular basis to discuss various problems and methods that arise in Finance and Actuarial Science. These informal meetings are held at the Fields Institute for Mathematical Sciences and are open to the public. Typically intendees come from Rotman Business School of Management, Dept. Mathematics, Statistics, Computer Science and Engineering.
Sebastian Jaimungal, Department of Statistics and Associate Director, Mathematical Finance Program, University of Toronto

Meetings are held from 2pm to 3:30pm room 210 at The Fields Institute for Mathematical Sciences.

May 23, 2007

Alvaro Cartea, Co-Director Commodities Finance Centre,
Birkbeck College, University of London
How Do Waiting Times or Duration Between Trades of Underlying Securities Affect Option Prices

We propose a model for stock price dynamics that explicitly incorporates (random) waiting times, also known as duration, and show how option prices are calculated. We use ultra-high frequency data for blue-chip companies to justify a particular choice of waiting time or duration distribution and then calibrate risk-neutral parameters from options data. We also show that implied volatilities may be explained by the presence of duration between trades.

Apr 25, 2007

Yan Bai

Forward PIDE for European options with fixed fractional jumps
We consider the model of European stock with jumps. A partial integro differential equation, which related the price of a calendar spread to the prices of butterfly spreads, is derived. The functions describing the evolution of the process are also given. The evolution functions are the forward local variance rate and forward local default arrival rate. We specialize the case where the only jump which can occur reduces the underlying stock price by a fixed fraction of its pre-default value. In particular using a few calendar dates, we derive closed form expressions for both the local variance and the local default arrival rate.

[ This is a review of the article by Peter Carr and Alireza Javaheri ]

Apr. 18, 2007

Alex Badescu

Option valuation, GARCH models and risk-neutral measures

Option pricing based on GARCH models is typically obtained under the assumption that the random innovations are standard normal (normal GARCH models). However, these models fail to capture the skewness and the leptokurtosis observed in financial data, so a number of various other distributions have been proposed. Since under GARCH models the markets are incomplete, there are an infinite number of risk neutral measures for pricing contingent claims. The impact of the choice of an appropriate martingale measure on option pricing has yet to be addressed in these setups. The present work investigates the applicability of some well-known risk neutral measures for various GARCH models.

Since only a few papers have studied the pricing performance of non-normal driving noise, we propose a new semiparametric GARCH option pricing model. Our approach is to compute option prices based on a non-parametric density estimator for the unknown distribution of the innovations based on standardized residuals. An empirical study regarding European Call option valuation on S&P500 Index shows our semiparametric model outperforms the normal GARCH option pricing models.

Apr 11, 2007

Simon Lee
Discounted penalty at ruin in a jump-diffusion and its application
We consider the jump-diffusion that is obtained if an independent Wiener process is added to the surplus process of classical ruin theory. In this model, we examine the expected discounted value of a penalty at ruin. It can be shown that the solution satisfies a defective renewal equation which has probabilistic interpretation. As an application, we determine the optimal exercise boundary for a perpetual put option.

Mar 28, 2007 Quantitative Finance Seminar Series instead
Mar 23, 2007 *Location :
History Conference Room, Sidney Smith Hall, (enter through 2096)

Chris Rogers, Cambridge University
Pathwise Stochastic Optimal Control
This talk approaches optimal control problems for discrete-time controlled Markov processes by representing the value of the problem in a dual Lagrangian form. This approach is a completely novel way to look any stochastic optimal control problem, independent of (but complementing) the classical dynamic-programming/value-function approach. The representation obtained opens up the possibility of numerical methods based on Monte Carlo simulation which may be advantageous in high-dimensional problems, or in problems with complicated constraints.

 

Mar 21, 2007

Simon Lee - POSTPONED to April 11

Mar 14 , 2007

Hamidreza Arian
Stochastic Correlation Models

The data from financial markets show that the correlation, which is typically assumed to be constant, is a stationary stochastic process. Very little has been published on stochastic correlation models so far. In this talk, I will discuss the obstacles for considering correlation as a stochastic process and illustrate how to price options with stochastic correlations.

Feb 28, 2007 Quantitative Finance Seminar Series instead
Feb 21, 2007

Eddie Ng

Stochastic Volatlity Models: Overview, Model Calibration, and all that...
This talk will provide an overview for the GARCH and Heston Model, including their mathematical formulation, stylized facts, and methods for model calibration.

Feb 14, 2007

Benjamin Verschuere
A MCMC-MLE Algorithm for Hidden Markov Process in Financial Time Series

Many time series are affected by a hidden process. An interesting example can be found in the financial markets which experience in alternance periods of stress and calm; and accordingly period of high and low volatility. When modelling the volatility of stock returns it is sensible to take into consideration the above mentioned hidden process. The goal of this presentation is to explain how we can identify the hidden process which is responsible for the fluctuation of volatility between two states (high and low) by adopting a Bayesian approach. We then use simulation to asses the efficiency of our method.

Dec 6, 2006

Sheldon X. Lin

Analytical Methods for Insurance Risk Models
In this talk, I will discuss some analytical methods developed in the past few years for insurance risk models. One of the advantages for using such analytical methods is that they require little probabilistic argument and hence can easily be understood by non-probabilists. These methods also allow us to utilize results in analysis and differential equations. Another is that it can some time handle more complex risk models, especially the risk models with dividend policies, for which probabilistic reasoning might be difficult. I will also briefly discuss some potential applications in option pricing.

 

Nov 22, 2006

Bill Bobey
Affine and Quadratic Term Structure Models: Model survey and comparisons
The discussion will present and contrast affine and quadratic risk-free rate term structure models. It will highlight the key differences in the models both in terms of financial interpretation and mathematical representation. Specific attention will be paid to the representative Riccati equations. Issues related to parameter estimation and numerical modelling will be discussed. Comments regarding extensions to corporate bond modelling will also be provided. This presentation will draw from two primary references, (Dai and Singleton, 2000) and (Ahn et al, 2002), and results related to research requiring the use of the key results of these papers.

Nov 8, 2006 Wanhe Zhang
Forward starting Collaterized Debt Obligations