Student models for a risky asset with dependence: Option pricing and Greeks

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091, Liu, Anqi ORCID: https://orcid.org/0000-0002-9224-084X and Shchestyuk, Nataliya 2024. Student models for a risky asset with dependence: Option pricing and Greeks. Austrian Journal of Statistics 54 (1) , 138–165..

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Abstract

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.

Item Type:	Article
Status:	In Press
Schools:	Mathematics
Publisher:	Austrian Society for Statistics
ISSN:	1026-597X
Date of First Compliant Deposit:	26 September 2024
Date of Acceptance:	17 September 2024
Last Modified:	07 Nov 2024 05:00
URI:	https://orca.cardiff.ac.uk/id/eprint/172395

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