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Derivatives Pricing and Hedging for Affine GARCH Models.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Derivatives Pricing and Hedging for Affine GARCH Models./
Author:	Cao, Hongkai .
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	185 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-09, Section: B.
Contained By:	Dissertations Abstracts International81-09B.
Subject:	Finance. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27670046
ISBN:	9781392584996

Derivatives Pricing and Hedging for Affine GARCH Models.
Cao, Hongkai .

Derivatives Pricing and Hedging for Affine GARCH Models. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 185 p.

Source: Dissertations Abstracts International, Volume: 81-09, Section: B.

Thesis (Ph.D.)--Stevens Institute of Technology, 2019.

This item must not be sold to any third party vendors.

Over the past few years, along with the rapid development in the financial market, many newly developed financial instruments are introduced and have become increasingly popular. Leveraged exchange-traded funds (LETFs) closely track the value of an underlying index while allowing for additional leverage. VIX futures and VIX options make it possible to directly invest in volatility as a tradable asset. Target volatility options (TVOs) emerged as a second generation of volatility derivatives, which allow investors to take a joint position in the underlying asset and its realized volatility. The purpose of this thesis is to apply affine GARCH models to price and hedge those new derivative products. Chapter 2 of the thesis considers the valuation of options written on LETFs under two popular affine GARCH models, the Heston-Nandi GARCH model and the Inverse Gaussian GARCH model. We also calibrate the two models using market data, and demonstrate the superior pricing performance. Chapter 3 of the thesis derives semi-closed-form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and TVOs under affine GARCH models based on Gaussian and Inverse Gaussian distributions. We illustrate the advantage of the proposed analytic expressions by comparing them with those obtained from benchmark Monte-Carlo simulations. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on observed market quotes on VIX and SPX options. Variance-optimal hedging in discrete-time framework is a practical options strategy that aims to reduce the residual risk. Therefore, in Chapter 4 of the thesis, we consider variance-optimal hedging for affine GARCH models. Applying the Laplace transform method, we explore semi-explicit formulas for the variance-optimal hedging strategy and initial endowment. We also apply the Long Short-Term Memory (LSTM) recurrent neural network (RNN) architectures to model hedging strategies under mean square error loss function. Numerical examples are investigated to illustrate the hedging performance for different approaches, option styles, and hedging frequencies.

ISBN: 9781392584996Subjects--Topical Terms:

559073
Finance.
Subjects--Index Terms:

Affine GARCH Models

Derivatives Pricing and Hedging for Affine GARCH Models.
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300 $a 185 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-09, Section: B.
500 $a Advisor: Cui, Zhenyu.
502 $a Thesis (Ph.D.)--Stevens Institute of Technology, 2019.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a Over the past few years, along with the rapid development in the financial market, many newly developed financial instruments are introduced and have become increasingly popular. Leveraged exchange-traded funds (LETFs) closely track the value of an underlying index while allowing for additional leverage. VIX futures and VIX options make it possible to directly invest in volatility as a tradable asset. Target volatility options (TVOs) emerged as a second generation of volatility derivatives, which allow investors to take a joint position in the underlying asset and its realized volatility. The purpose of this thesis is to apply affine GARCH models to price and hedge those new derivative products. Chapter 2 of the thesis considers the valuation of options written on LETFs under two popular affine GARCH models, the Heston-Nandi GARCH model and the Inverse Gaussian GARCH model. We also calibrate the two models using market data, and demonstrate the superior pricing performance. Chapter 3 of the thesis derives semi-closed-form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and TVOs under affine GARCH models based on Gaussian and Inverse Gaussian distributions. We illustrate the advantage of the proposed analytic expressions by comparing them with those obtained from benchmark Monte-Carlo simulations. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on observed market quotes on VIX and SPX options. Variance-optimal hedging in discrete-time framework is a practical options strategy that aims to reduce the residual risk. Therefore, in Chapter 4 of the thesis, we consider variance-optimal hedging for affine GARCH models. Applying the Laplace transform method, we explore semi-explicit formulas for the variance-optimal hedging strategy and initial endowment. We also apply the Long Short-Term Memory (LSTM) recurrent neural network (RNN) architectures to model hedging strategies under mean square error loss function. Numerical examples are investigated to illustrate the hedging performance for different approaches, option styles, and hedging frequencies.
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650 4 $a Statistics. $3 556824
650 4 $a Mathematics. $3 527692
653 $a Affine GARCH Models
653 $a Calibration
653 $a Deep learning
653 $a LETF options
653 $a TVOs
653 $a VIX options
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690 $a 0463
690 $a 0405
710 2 $a Stevens Institute of Technology. $b Financial Engineering. $3 1189394
773 0 $t Dissertations Abstracts International $g 81-09B.
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793 $a English
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