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 (with Thilo Meyer-Brandis)

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.

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 ]

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.

Simon Lee

Discounted penalty at ruin in a jump-diffusion and its application

Chris Rogers,
Cambridge University

Pathwise Stochastic Optimal Control

*Location :
History Conference Room, Sidney Smith Hall, (enter through 2096)

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.

Simon Lee - POSTPONED to April 11

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.

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.

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.

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.

Bill Bobey

Affine and Quadratic Term Structure Models: Model survey and comparisons

Jan. 30, 2006

Sebastian Jaimungal

Stochastic Time Changes and Fourier Transforms

Jan. 23, 2006

Sebastian Jaimungal

Indifference Pricing for Defaultable Securities

Jan. 16, 2006

Xiaoming Liu

Phase Type Models for Mortality

Dec. 13, 2005

Georg Sighloch

Pricing in Incomplete Markets via Duality ( II )

Dec. 6, 2005

Angelo Valov

Hedging Corridor Variance Swaps
( II )

Nov. 29, 2005

Georg Sighloch

Pricing in Incomplete Markets via Duality ( I )

Nov. 22, 2005

Angelo Valov

Hedging Corridor Variance Swaps
( I )

Nov. 15, 2005

Chiu Chu

Reset Features in Dynamic Fund Protection

Nov. 1, 2005

Samuel Hikspoors

Introduction to Stochastic Optimal Control ( II )

Oct. 25, 2005

Tao Wang

Valuing Dynamic Fund Protections
( II )

Oct. 18, 2005

Samuel Hikspoors

Introduction to Stochastic Optimal Control ( I )

Oct. 11, 2005

Tao Wang

Valuing Dynamic Fund Protections
( I )