Diskretni HJM model za vrednotenje obrestnih opcij
magistrsko delo
Abstract
Heath-Jarrow-Mortonov model služi kot orodje za modeliranje terminskih obrestnih mer in določitev cen obrestno občutljivih vrednostnih papirjev. Uporabljajo ga tako razne finančne ustanove za vrednotenje in ščitenje obrestnih izvedenih finančnih instrumentov kot investitorji, ki iščejo arbitražne priložnosti. V magistrskem delu je predstavljen enoobdobni diskretni HJM model, njegova razširitev na večobdobni model in HJM LIBOR model. Podane so predpostavke modelov, pogoji za neobstoj arbitraže, ki določijo psevdo verjetnosti, primerjava psevdo in dejanskih verjetnosti, razvoj cen brezkuponskih obveznic ter do tveganja nevtralno vrednotenje obrestnih izvedenih finančnih instrumentov. Poudarek je na vrednotenju obrestnih kapic in obrestnih dnov, ki vlagateljem služijo kot zaščita pred obrestnim tveganjem. Prikazana je razširitev enofaktorskega modela na več faktorjev. Večobdobni diskretni HJM model se lahko uporabi kot aproksimacija zveznemu HJM modelu. Pri tem je potrebno zmanjšati velikost časovnih korakov in izbrati ustrezne parametre za diskretni model, da bo slednji čim boljša aproksimacija HJM LIBOR modelu.
Keywords
finančna matematika;obrestna kapica;obrestno dno;obrestni izvedeni finančni instrumenti;do tveganja nevtralno vrednotenje;terminska obrestna mera;
Data
| Language: | Slovenian |
|---|---|
| Year of publishing: | 2022 |
| Typology: | 2.09 - Master's Thesis |
| Organization: | UL FMF - Faculty of Mathematics and Physics |
| Publisher: | [M. Sirk] |
| UDC: | 519.8 |
| COBISS: |
113697795
|
| Views: | 722 |
| Downloads: | 77 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | English |
|---|---|
| Secondary title: | Discrete HJM model for valuing interest rate options |
| Secondary abstract: | Heath-Jarrow-Morton model serves as a tool for modeling forward rates and valuation of interest rate sensitive securities. It is used by various financial institutions for the valuation and hedging of interest rate derivatives, as well as arbitrageurs seeking arbitrage opportunities. The master's thesis presents single-period discrete HJM model, its extension to multiperiod model and HJM LIBOR model. Model assumptions, conditions for no arbitrage that determine pseudo probabilities, comparison of pseudo and actual probabilities, evolution of zero-coupon bond prices and risk-neutral valuation of interest rate financial instruments are given. The emphasis is on valuing interest rate caps and floors, which serve as a hedge against interest rate risk. The extension of the one-factor model to several factors is shown. The multi-period discrete HJM model can be used as an approximation to the continuous HJM model. It is necessary to reduce the size of the time steps and select the appropriate parameters for the discrete model, so that the latter will be the best possible approximation for the HJM LIBOR model. |
| Secondary keywords: | caplet;floorlet;interest rate derivatives;risk-neutral valuation;forward rate; |
| Type (COBISS): | Master's thesis/paper |
| Study programme: | 0 |
| Embargo end date (OpenAIRE): | 1970-01-01 |
| Thesis comment: | Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 2. stopnja |
| Pages: | IX, 52 str. |
| ID: | 15795553 |
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