Sumários
Levy processes simulation
28 Novembro 2017, 10:00 • João Guerra
Simulation of the variance-gamma process.
Discussion of some simulation problems in the group assignments.
Lévy processes simulation
23 Novembro 2017, 10:00 • João Guerra
How to simulate a Lévy process?
1) Numerical Simulation of a Brownian motion
2) Numerical Simulation of a Standard Poisson Process
3) Approximate the big jumps by a sum of independent Poisson processes (Commpound Poisson process)
4) Approximate the small jumps by a Brownian jump, under a technical assumption
5) Simulation of a Gamma process
Application of the AACSB AOL Learning Goal Technical Skills survey.
Parameter Estimation in Levy models and exotic option pricing
21 Novembro 2017, 10:00 • João Guerra
The Problem of parameter estimation in Lévy market models.
The parameters in the risk neutral measure (using the mean correcting term martingale measure) and how to estimate them from option data. The root mean square error measure for the quality of the fit of the model to data.
An example of parameter estimation using the Variance Gamma process.
The Black-Scholes model as a Benchmark.
An example of pricing an exotic option - the up and in Barrier call option. Pricing this option using the Monte Carlo method.
The Fourier transform method for option pricing and the problem of parameter estimation from data
16 Novembro 2017, 10:00 • João Guerra
The Fourier transform method for pricing options in Lévy Market models. The Fast Fourier Transform algorithm for calculating call option prices in a computational fast way.
Application of these methods to the Variance-Gamma and other models in order to estimate the parameter from real market data.
Equivalent martingale measures and incomplete markets
14 Novembro 2017, 10:00 • João Guerra
Equivalent martingale measures: complete versus incomplete markets.
Examples and exercises.
The mean-correcting method for choosing an equivalent martingale measure.