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A Monte Carlo EM algorithm for discretely observed Diffusions, Jump-diffusions and Lévy-driven Stochastic Differential Equations

Lindström, Erik LU (2012) In International Journal of Mathematical Models and Methods in Applied Sciences 6(5). p.643-651
Abstract
Stochastic differential equations driven by standard

Brownian motion(s) or Lévy processes are by far the most popular

models in mathematical finance, but are also frequently used in

engineering and science. A key feature of the class of models is

that the parameters are easy to interpret for anyone working with

ordinary differential equations, making connections between statistics

and other scientific fields far smoother.

We present an algorithm for computing the (historical probability

measure) maximum likelihood estimate for parameters in diffusions,

jump-diffusions and Lévy processes. This is done by introducing

a simple, yet computationally... (More)
Stochastic differential equations driven by standard

Brownian motion(s) or Lévy processes are by far the most popular

models in mathematical finance, but are also frequently used in

engineering and science. A key feature of the class of models is

that the parameters are easy to interpret for anyone working with

ordinary differential equations, making connections between statistics

and other scientific fields far smoother.

We present an algorithm for computing the (historical probability

measure) maximum likelihood estimate for parameters in diffusions,

jump-diffusions and Lévy processes. This is done by introducing

a simple, yet computationally efficient, Monte Carlo Expectation

Maximization algorithm. The smoothing distribution is computed

using resampling, making the framework very general.

The algorithm is evaluated on diffusions (CIR, Heston), jump-diffusion

(Bates) and Lévy processes (NIG, NIG-CIR) on simulated

data and market data from S & P 500 and VIX, all with satisfactory

results. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bates model, Heston model, Jump-Diffusion, Lévy process, parameter estimation, Monte Carlo Expectation Maximization, NIG, Stochastic differential equation
in
International Journal of Mathematical Models and Methods in Applied Sciences
volume
6
issue
5
pages
643 - 651
publisher
The North Atlantic University Union (NAUN) / World Scientific and Engineering Academy and Society (WSEAS)
external identifiers
  • scopus:84871073470
ISSN
1998-0140
language
English
LU publication?
yes
id
56d4483b-7f73-430e-8478-7aaca196270c (old id 3008464)
alternative location
http://naun.org/multimedia/NAUN/m3as/16-261.pdf
date added to LUP
2012-09-21 19:31:35
date last changed
2017-02-08 13:39:14
@article{56d4483b-7f73-430e-8478-7aaca196270c,
  abstract     = {Stochastic differential equations driven by standard<br/><br>
Brownian motion(s) or Lévy processes are by far the most popular<br/><br>
models in mathematical finance, but are also frequently used in<br/><br>
engineering and science. A key feature of the class of models is<br/><br>
that the parameters are easy to interpret for anyone working with<br/><br>
ordinary differential equations, making connections between statistics<br/><br>
and other scientific fields far smoother.<br/><br>
We present an algorithm for computing the (historical probability<br/><br>
measure) maximum likelihood estimate for parameters in diffusions,<br/><br>
jump-diffusions and Lévy processes. This is done by introducing<br/><br>
a simple, yet computationally efficient, Monte Carlo Expectation<br/><br>
Maximization algorithm. The smoothing distribution is computed<br/><br>
using resampling, making the framework very general.<br/><br>
The algorithm is evaluated on diffusions (CIR, Heston), jump-diffusion<br/><br>
(Bates) and Lévy processes (NIG, NIG-CIR) on simulated<br/><br>
data and market data from S &amp; P 500 and VIX, all with satisfactory<br/><br>
results.},
  author       = {Lindström, Erik},
  issn         = {1998-0140},
  keyword      = {Bates model,Heston model,Jump-Diffusion,Lévy process,parameter estimation,Monte Carlo Expectation Maximization,NIG,Stochastic differential equation},
  language     = {eng},
  number       = {5},
  pages        = {643--651},
  publisher    = {The North Atlantic University Union (NAUN) / World Scientific and Engineering Academy and Society (WSEAS)},
  series       = {International Journal of Mathematical Models and Methods in Applied Sciences},
  title        = {A Monte Carlo EM algorithm for discretely observed Diffusions, Jump-diffusions and Lévy-driven Stochastic Differential Equations},
  volume       = {6},
  year         = {2012},
}