20.500.12556/RUL-126499 Tree methods for option pricing master's thesis Drevesne metode za vrednotenje opcij magistrsko delo The first tree model for option pricing was introduced by Cox, Ross and Rubinstein a few years after the revolutionary Black-Scholes formula. It provides a simple and intuitive pricing method, and it can also be used for decision making about early exerciseof options. We show how to construct this tree model and derive the pricing formula. When the number of time steps n increases, the price obtained by the tree method converges to the Black-Scholes price. We prove this convergence and investigate further its behaviour. The convergence rate is slow and oscillatory, and thus we discuss how to accelerate this convergence. Many other tree models have been constructed through the years in order to improve efficiency. We present both binomial and trinomial tree models and various choices of their parameters. Our focus is on European and American put and call options. However, it remains a challenge to decide on the optimal parametrization of the tree. Prvi drevesni model določanja cen opcij so Cox, Ross in Rubinstein predstavili nekaj let kasneje po revolucionarni formuli Blacka in Scholesa. Ponuja preprosto in intuitivno metodo določanja cen, uporablja pa se lahko tudi za odločanje o zgodnji izvršitvi opcij. V tem delu je prikazano, kako zgraditi ta drevesni model in izpeljati cenovno formulo. Ko se število časovnih korakov n poveča, se cena, dobljena z drevesno metodo, približa ceni iz Black- Scholesovega modela. Ta konvergenca je dokazana in raziskovana v tem delu. Stopnja konvergence je počasna in nihajna, zato razpravljamo o tem, kako to konvergenco pospešiti. Številni drugi drevesni modeli so bili skozi leta izdelani za izboljšanje učinkovitosti. Predstavljamo tako binomski kot trinomski drevesni model in različno izbiro njihovih parametrov. Naš poudarek je na evropskih in ameriških prodajnih in nakupnih opcijah. Vendar ostaja izziv, kako določiti optimalno parametrizacijo drevesa. option pricing Cox-Ross-Rubinstein model tree methods vrednotenje opcij Cox-Ross-Rubinstein model drevesne metode true false false Angleški jezik Slovenski jezik Magistrsko delo/naloga 2021-04-24 08:15:02 2021-04-24 08:15:07 2024-05-29 14:16:33 0000-00-00 00:00:00 2021 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 117995 60769539 2641.pdf 2641.pdf 1 034298229F2FA14988F747AF3F4C3BF6 c6a598cc9ab2824df8ce6f8643984f721ab17f2809b3589b8074b34fda02c858 68650073-a4c4-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=142485 Fakulteta za matematiko in fiziko 0 0 0