Student Models for a Risky Asset with Dependence: Option Pricing and Greeks
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Date
2024
Authors
Leonenko, Nikolai
Liu, Anqi
Shchestyuk, Nataliya
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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.
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Keywords
option pricing, fractal activity time, student processes, dependence structure, supOU processes, delta hedging, article
Citation
Leonenko N. N. Student Models for a Risky Asset with Dependence: Option Pricing and Greeks / Leonenko Nikolai N., Liu Anqi, Shchestyuk Nataliya // Austrian journal of statistics. - 2024. - [Article in press]. - https://doi.org/10.17713/ajs.v54i1.1952