An analytical approximation for single barrier options under stochastic volatility models
| Autor: | Tomohide Higuchi, Hideharu Funahashi |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematical optimization
050208 finance 021103 operations research Girsanov theorem Stochastic volatility 05 social sciences 0211 other engineering and technologies General Decision Sciences Barrier option 02 engineering and technology Management Science and Operations Research Implied volatility Heston model symbols.namesake Wiener process Local volatility 0502 economics and business symbols Reflection principle (Wiener process) Mathematics |
| Zdroj: | Annals of Operations Research. 266:129-157 |
| ISSN: | 1572-9338 0254-5330 |
| DOI: | 10.1007/s10479-017-2559-3 |
| Popis: | The aim of this paper is to derive an approximation formula for a single barrier option under local volatility models, stochastic volatility models, and their hybrids, which are widely used in practice. The basic idea of our approximation is to mimic a target underlying asset process by a polynomial of the Wiener process. We then translate the problem of solving first hit probability of the asset process into that of a Wiener process whose distribution of passage time is known. Finally, utilizing the Girsanov’s theorem and the reflection principle, we show that single barrier option prices can be approximated in a closed-form. Furthermore, ample numerical examples will show the accuracy of our approximation is high enough for practical applications. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink