Tuesday, November 3, 2009 - 15:00 , Location: Skiles 269 , Sheldon Lin , Department of Statistics, University of Toronto , Organizer: Liang Peng
The discounted penalty function proposed in the seminal paper Gerber and Shiu (1998) has been widely used to analyze the time of ruin, the surplus immediately before ruin and the deficit at ruin of insurance risk models in ruin theory. However, few of its applications can be found beyond, except that Gerber and Landry (1998) explored its use for the pricing of perpetual American put options. In this talk, I will discuss the use of the discounted penalty function and mathematical tools developed for the function for perpetual American catastrophe put options. Assuming that catastrophe losses follow a mixture of Erlang distributions, I will show that an analytical (semi-closed) expression for the price of perpetual American catastrophe put options can be obtained. I will then discuss the fitting of a mixture of Erlang distributions to catastrophe loss data using an EM algorithm.
Testing the stability of the functional autoregressive processwith an application to credit card transaction volume dataTuesday, October 27, 2009 - 15:00 , Location: Skiles 269 , Piotr Kokoszka , Utah State University , Organizer: Liang Peng
The functional autoregressive process has become a useful tool in the analysis of functional time series data. In this model, the observations and the errors are curves, and the role of the autoregressive coefficient is played by an integral operator. To ensure meaningful inference and prediction, it is important to verify that this operator does not change with time. We propose a method for testing its constancy which uses the functional principal component analysis. The test statistic is constructed to have a Kiefer type asymptotic distribution. The asymptotic justification of the procedure is very delicate and touches upon central notions of functional data analysis. The test is implemented using the R package fda. Its finite sample performance is illustrated by an application to credit card transaction data.
Tuesday, October 20, 2009 - 15:00 , Location: Skiles 269 , Daniel Bauer , Georgia State University , Organizer: Liang Peng
In recent literature, different mothods have been proposed on how to define and model stochastic mortality. In most of these approaches, the so-called spot force of mortality is modeled as a stochastic process. In contrast to such spot force models, forward force mortality models infer dynamics on the entire age/term-structure of mortality. This paper considers forward models defined based on best-estimate forecasts of survival probabilities as can be found in so-called best-estimate generation life tables. We provide a detailed analysis of forward mortality models deriven by finite-dimensional Brownian motion. In particular, we address the relationship to other modeling approaches, the consistency problem of parametric forward models, and the existence of finite dimensional realizations for Gaussian forward models. All results are illustrated based on a simple example with an affine specification.
Tuesday, October 13, 2009 - 15:00 , Location: Skiles 269 , Suzanne Lee , College of Management, Georgia Tech , Organizer: Christian Houdre
We propose a new two stage semi-parametric test and estimation procedure to investigate predictability of stochastic jump arrivals in asset prices. It allows us to search for conditional information that affects the likelihood of jump occurrences up to the intra-day levels so that usual factor analysis for jump dynamics can be achieved. Based on the new theory of inference, we find empirical evidence of jump clustering in U.S. individual equity markets during normal trading hours. We also present other intra-day jump predictors such as analysts recommendation updates and stock news releases.
Tuesday, September 22, 2009 - 15:00 , Location: Skiles 269 , Gunter Meyer , School of Mathematics, Georgia Tech , Organizer: Liang Peng
When the asset price follows geometric Brownian motion but allows random Poisson jumps (called jump diffusion) then the standard Black Scholes partial differential for the option price becomes a partial-integro differential equation (PIDE). If, in addition, the volatility of the diffusion is assumed to lie between given upper and lower bounds but otherwise not known then sharp upper and lower bounds on the option price can be found from the Black Scholes Barenblatt equation associated with the jump diffusion PIDE. In this talk I will introduce the model equations and then discuss the computational issues which arise when the Black Scholes Barenblatt PIDE for jump diffusion is to be solved numerically.
Tuesday, February 10, 2009 - 15:00 , Location: Skiles 269 , Rehim Kilic , School of Economics, Georgia Tech , Organizer: Christian Houdre
This paper introduces a new nonlinear long memory volatility process, denoted by Smooth Transition FIGARCH, or ST-FIGARCH, which is designed to account for both long memory and nonlinear dynamics in the conditional variance process. The nonlinearity is introduced via a logistic transition function which is characterized by a transition parameter and a variable. The model can capture smooth jumps in the altitude of the volatility clusters as well as asymmetric response to negative and positive shocks. A Monte Carlo study finds that the ST-FIGARCH model outperforms the standard FIGARCH model when nonlinearity is present, and performs at least as well without nonlinearity. Applications reported in the paper show both nonlinearity and long memory characterize the conditional volatility in exchange rate and stock returns and therefore presence of nonlinearity may not be the source of long memory found in the data.
Tuesday, February 3, 2009 - 15:00 , Location: Skiles 269 , Dmitry Kreslavskiy , Bloomberg , Organizer: Christian Houdre
We will give an overview of the company as it relates to the work of a quant. We will discuss projects of interest, typical lifecycle of a project, and involved areas.
Tuesday, January 27, 2009 - 11:05 , Location: Skiles 269 , Philip Protter , Cornell University , Organizer: Christian Houdre
Wednesday, November 12, 2008 - 14:00 , Location: Skiles 255 , Christian Houdré , School of Mathematics, Georgia Tech , Organizer: Christian Houdre
In connection with the class Stochastic Processes in Finance II, we will have a supplementary lecture where a first, 50 minutes long, movie on Doeblin's life will be shown. This will be followed by a second movie, 30 minutes long, where Yor explains on the blackboard Doeblin's contribution to what Shreeve calls the Ito-Doeblin's lemma.
Wednesday, October 29, 2008 - 15:00 , Location: Skiles 269 , Lily Wang , Department of Statistics, University of Georgia , Organizer: Liang Peng
We analyze a class of semiparametric ARCH models that nests the simple GARCH(1,1) model but has flexible news impact function. A simple estimation method is proposed based on profiled polynomial spline smoothing. Under regular conditions, the proposed estimator of the dynamic coeffcient is shown to be root-n consistent and asymptotically normal. A fast and efficient algorithm based on fast fourier transform (FFT) has been developed to analyze volatility functions with infinitely many lagged variables within seconds. We compare the performance of our method with the commonly used GARCH(1, 1) model, the GJR model and the method in Linton and Mammen (2005) through simulated data and various interesting time series. For the S&P 500 index returns, we find further statistical evidence of the nonlinear and asymmetric news impact functions.