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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Main Authors: Nikolai Leonenko, Anqi Liu, Nataliya Schestyuk
Format: Article
Language:English
Published: Austrian Statistical Society 2025-01-01
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
description 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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institution Kabale University
issn 1026-597X
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publishDate 2025-01-01
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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