| Title | A Monte Carlo EM algorithm for discretely observed Diffusions, Jump-diffusions and Lévy-driven Stochastic Differential Equations |
| Authors | Erik Lindström |
| Alternative Location | http://naun.org/multimedia/... |
| Publication | International journal of mathematical models and methods in applied sciences |
| Year | 2012 |
| Volume | 6 |
| Issue | 5 |
| Pages | 643 - 651 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | The North Atlantic University Union (NAUN) / World Scientific and Engineering Academy and Society (WSEAS) |
| Abstract English | Stochastic differential equations driven by standard<br> Brownian motion(s) or Lévy processes are by far the most popular<br> models in mathematical finance, but are also frequently used in<br> engineering and science. A key feature of the class of models is<br> that the parameters are easy to interpret for anyone working with<br> ordinary differential equations, making connections between statistics<br> and other scientific fields far smoother.<br> We present an algorithm for computing the (historical probability<br> measure) maximum likelihood estimate for parameters in diffusions,<br> jump-diffusions and Lévy processes. This is done by introducing<br> a simple, yet computationally efficient, Monte Carlo Expectation<br> Maximization algorithm. The smoothing distribution is computed<br> using resampling, making the framework very general.<br> The algorithm is evaluated on diffusions (CIR, Heston), jump-diffusion<br> (Bates) and Lévy processes (NIG, NIG-CIR) on simulated<br> data and market data from S & P 500 and VIX, all with satisfactory<br> results. |
| Keywords | Bates model, Heston model, Jump-Diffusion, Lévy process, parameter estimation, Monte Carlo Expectation Maximization, NIG, Stochastic differential equation, |
| ISBN/ISSN/Other | ISSN: 1998-0140 |
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