STAT 598F. Modeling with Jump Processes and Applications to Mathematical Finance.

• Office: Math 542
• Office hours: TTH 2:30 - 3:20, or by appointment
• Phone: (765) 494 6036
• E-mail: figueroa@stat.purdue.edu (best way to contact me)

• Assignment 4. Due: Tuesday April 6.
• Assignment 3. Due: Tuesday March 9.
• Assignment 2. Due: Tuesday Feb. 9.
• Assignment 1. Due: Tuesday Jan. 26.
• Syllabus.

• Topics on stochastic control and portfolio optimization of processes under jumps.
Reference: Applied Stochastic Control of Jump Diffusions by Sulem and Oksendal.
• Topics on inverse problems and model calibration.
Possible References:
• (Group 1) Chapter 13 in Cont and Tankov. See also Non-parametric calibration of jump-diffusion option pricing models, and Retriving Levy processes from option prices: Regularization of an ill-posed inverse problem.
• (Group 2) Spectral calibration of exponential Levy models by Belomestny and Reiss (Original paper was published in Finance Stoch.). See also Spectral estimation of the fractional order of a Levy process.
• Some option data. Note: I would like to suggest the GS and SPY data for your implementation.
• Topics related to Malliavin Calculus with jumps
Some references: Estimating Greeks in Simulating Levy-Driven Models by P. Glasserman and Z. Liu; Absolute continuous laws of jump-diffussions in finite and infinite dimensions with applications to mathematical finance by Forster et. al.

• The Variance Gamma Process and Option Pricing by Madan, Carr, and Chang.
• A MATLAB program for approximating the marginal density of a Normal distribution.
• A MATLAB program for approximating the marginal density in a CGMY Levy model via FFT.
• A recent paper on MLE estimation for certain Levy processes.
• Pitfalls in estimating jump-diffusion models by Honore.
• Approximation of small jumps of Levy processes with a view towards simulation by Asmussen and Rosinski.
• Nonparametric adaptive estimation for pure jump Levy processes.
by Comte and Genon-Catalot.
• A review paper on financial models based on Levy processes.
• An interesting motivational paper: Empirical properties of asset returns: stylized facts and statistical issues by Rama Cont.
• Levy processes and Poisson random measures.

• Levy processes and stochastic calculus, Applebaum.
• Levy processes and infinitely divisible distributions, Sato.
• Poisson processes, Kingman.
• Financial modelling with jump processes, Cont and Tankov.
• Limit theorems for stochastic processes, Jacod and Shiryaev.

The content of this page and any opinions expressed therein are solely those of Jose E. Figueroa-Lopez.