Student Models for a Risky Asset with Dependence: Option Pricing and Greeks
We propose several new models in finance known as the Fractal Activity Time Geometric Brownian Motion (FATGBM) models with Student marginals. We summarize four models that construct stochastic processes of underlying prices with short-range and long-range dependencies. We derive solutions of option...
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Format: | Article |
Language: | English |
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Austrian Statistical Society
2025-01-01
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Series: | Austrian Journal of Statistics |
Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1952 |
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author | Nikolai Leonenko Anqi Liu Nataliya Schestyuk |
author_facet | Nikolai Leonenko Anqi Liu Nataliya Schestyuk |
author_sort | Nikolai Leonenko |
collection | DOAJ |
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We propose several new models in finance known as the Fractal Activity Time Geometric Brownian Motion (FATGBM) models with Student marginals. We summarize four models that construct stochastic processes of underlying prices with short-range and long-range dependencies. We derive solutions of option Greeks and compare with those in the Black-Scholes model. We analyse performance of delta hedging strategy using simulated time series data and verify that hedging errors are biased particularly for long-range dependence cases. We also apply underlying model calibration on S&P 500 index (SPX) and the U.S./Euro rate, and implement delta hedging on SPX options.
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format | Article |
id | doaj-art-4ae1a64bb3c64baf8dfc4b47e9cb34e6 |
institution | Kabale University |
issn | 1026-597X |
language | English |
publishDate | 2025-01-01 |
publisher | Austrian Statistical Society |
record_format | Article |
series | Austrian Journal of Statistics |
spelling | doaj-art-4ae1a64bb3c64baf8dfc4b47e9cb34e62025-01-13T07:12:23ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2025-01-0154110.17713/ajs.v54i1.1952Student Models for a Risky Asset with Dependence: Option Pricing and GreeksNikolai Leonenko0Anqi LiuNataliya SchestyukCardiff University We propose several new models in finance known as the Fractal Activity Time Geometric Brownian Motion (FATGBM) models with Student marginals. We summarize four models that construct stochastic processes of underlying prices with short-range and long-range dependencies. We derive solutions of option Greeks and compare with those in the Black-Scholes model. We analyse performance of delta hedging strategy using simulated time series data and verify that hedging errors are biased particularly for long-range dependence cases. We also apply underlying model calibration on S&P 500 index (SPX) and the U.S./Euro rate, and implement delta hedging on SPX options. https://www.ajs.or.at/index.php/ajs/article/view/1952 |
spellingShingle | Nikolai Leonenko Anqi Liu Nataliya Schestyuk Student Models for a Risky Asset with Dependence: Option Pricing and Greeks Austrian Journal of Statistics |
title | Student Models for a Risky Asset with Dependence: Option Pricing and Greeks |
title_full | Student Models for a Risky Asset with Dependence: Option Pricing and Greeks |
title_fullStr | Student Models for a Risky Asset with Dependence: Option Pricing and Greeks |
title_full_unstemmed | Student Models for a Risky Asset with Dependence: Option Pricing and Greeks |
title_short | Student Models for a Risky Asset with Dependence: Option Pricing and Greeks |
title_sort | student models for a risky asset with dependence option pricing and greeks |
url | https://www.ajs.or.at/index.php/ajs/article/view/1952 |
work_keys_str_mv | AT nikolaileonenko studentmodelsforariskyassetwithdependenceoptionpricingandgreeks AT anqiliu studentmodelsforariskyassetwithdependenceoptionpricingandgreeks AT nataliyaschestyuk studentmodelsforariskyassetwithdependenceoptionpricingandgreeks |