Abstract
We are interested in the approximation of the law of a real diffusion killed as it goes out of D (interval of ℝ), when the diffusion is approximated by its continuous Euler scheme, with discretization step N-1 T. We show that the error on script capital E signx[script capital I signT<r f(XT)] (where τ = inf{t > 0 : Xt ∉ D}) can be developed to the first order in N-1, under some conditions on f near the boundary of D. We also compare the transition densities of the two killed processes. These results enable us to give approached price for barrier options.
| Translated title of the contribution | Schéma d'Euler continu pour des diffusions tuées et options barrière |
|---|---|
| Original language | English |
| Pages (from-to) | 1411-1414 |
| Number of pages | 4 |
| Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |
| Volume | 326 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 1 Jan 1998 |
| Externally published | Yes |