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:
https://lup.lub.lu.se/record/3008464
- author
- Lindström, Erik
LU
- organization
- publishing date
- 2012
- 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)
- 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
- 2016-04-01 14:12:38
- date last changed
- 2022-01-27 23:23:25
@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 & P 500 and VIX, all with satisfactory<br/><br>
results.}},
author = {{Lindström, Erik}},
issn = {{1998-0140}},
keywords = {{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)}},
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}},
url = {{http://naun.org/multimedia/NAUN/m3as/16-261.pdf}},
volume = {{6}},
year = {{2012}},
}