20.500.12556/RUL-169517 Esscherjeva transformacija in njena uporaba delo diplomskega seminarja Esscher transform and its application V diplomski nalogi definiramo Esscherjevo transformacijo tako za slučajne procese v diskretnem času kot tudi za slučajne procese v zveznem času. Najprej transformiramo nekaj znanih diskretnih in zveznih porazdelitev, kot so Poissonova, binomska in normalna. Potem razširimo definicijo na slučajne procese in pokažemo, kako Esscherjevo transformacijo preidemo do za tveganje nevtralne mere, glede na katero so diskontirani cenovni procesi martingali. Posebej se osredotočimo na vrednotenje evropskih nakupnih oz. prodajnih opcij v Var-Gama in Black-Scholesovem modelu. This thesis explores the theoretical foundation and practical applications of the Esscher transform in both discrete and continuous-time stochastic processes. We begin by introducing the transform for random variables and apply it to well-known probability distributions such as the Poisson, Binomial, and Normal distributions. We then extend the concept to stochastic processes, demonstrating how the Esscher transform leads to construction of an equivalent risk-neutral measure, ensuring that the discounted price process is a martingale. A key focus is its application in the Var-Gama and Black-Scholes models, where the use of Esscher transformation enables effective option pricing. Esscherjeva transformacija martingalska mera Var-Gama model evropske opcije slučajni proces vrednotenje opcij Black-Scholesov model Esscher transform martingale measure Variance Gamma model European options stochastic process option pricing Black-Scholes model true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2025-06-01 08:15:06 2025-06-01 08:15:11 2025-07-10 13:58:14 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 150249 237924611 16804.pdf 16804.pdf 1 4FCEE571477F19028FD7692A16D2CB83 75f36daf8badd8cf20c21435531a388a091674ab76c17d1016795c541311a5aa 77c6cb4c-3eae-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=210947 Fakulteta za matematiko in fiziko 0 0 0