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Valuation of Multi-Period Barrier Options and Extensions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Valuation of Multi-Period Barrier Options and Extensions.
Author:	Zhexembay, Abylay.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2021
Description:	200 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Notes:	Advisor: Shiu, Elias S.W.
Contained By:	Dissertations Abstracts International83-02B.
Subject:	Statistics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28491409
ISBN:	9798534667066

Valuation of Multi-Period Barrier Options and Extensions.
Zhexembay, Abylay.

Valuation of Multi-Period Barrier Options and Extensions. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 200 p.

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--The University of Iowa, 2021.

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

Barrier options are widely used financial instruments with a long history. Because their payoff depends on whether or not the underlying asset has reached a predetermined barrier level, these options are cheaper than the corresponding standard options. This distinctive feature makes them a popular investment tool traded on various markets, including over-the-counter and foreign exchange. In addition, barrier options are used in pricing and modeling problems in both finance and insurance, including construction of more accurate pricing and hedging models of variable annuity products that reflect dynamic policyholder lapsations, and pricing of popular auto-callable, or auto-trigger, derivatives.Importance of these applications motivated this thesis which focuses on valuation of multi-period barrier options and extensions under the Black-Scholes framework. These options are characterized by having different barrier levels at distinct time intervals as well as vertical barriers, called icicles, appended to the horizontal ones at certain time points. The static hedging theorem developed in this thesis for the purpose of pricing barrier option extensions does not rely on traditional tools, such as integration or solving the Black-Scholes partial differential equation, and instead makes use of the technique of Esscher transform and the reflection principle.In the first part of the thesis, we review the technique of Esscher transform and its extension from random variables to Levy processes and, in particular, to Brownian motions. Application of the Esscher transform in determining the distribution properties of Brownian motion characteristics such as the running maximum and the first passage time plays a key role in barrier option valuation.In the second part, we inform the reader of the static hedging formula which is a powerful tool that allows pricing ordinary barrier options. We extend this result to develop the static hedging theorem that permits the payoff function to depend on the underlying asset prices beyond the barrier monitoring interval, hence can be applied in valuation of multi-period options. Use of this instrument is particularly beneficial in pricing options with large number of periods where the use of traditional tools can prove extremely laborious.Lastly, we apply the obtained pricing tool in valuation of barrier option extensions, including compound, sequential, and double barrier options. When possible, we demonstrate that the results coincide with those from the existing literature. However, for quite a few derivatives, pricing formulas have not been derived in earlier literature, to the best of the author’s knowledge. Furthermore, we develop the versions of the static hedging theorem that allow pricing options with exponential barriers and outside barrier options written on multiple assets. For options with exponential barriers, the closed-form pricing formulas for compound, sequential, and double barrier options are also derived.

ISBN: 9798534667066Subjects--Topical Terms:

182057
Statistics.
Subjects--Index Terms:

Barrier options

Valuation of Multi-Period Barrier Options and Extensions.
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245 1 0 $a Valuation of Multi-Period Barrier Options and Extensions.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 200 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
500 $a Advisor: Shiu, Elias S.W.
502 $a Thesis (Ph.D.)--The University of Iowa, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Barrier options are widely used financial instruments with a long history. Because their payoff depends on whether or not the underlying asset has reached a predetermined barrier level, these options are cheaper than the corresponding standard options. This distinctive feature makes them a popular investment tool traded on various markets, including over-the-counter and foreign exchange. In addition, barrier options are used in pricing and modeling problems in both finance and insurance, including construction of more accurate pricing and hedging models of variable annuity products that reflect dynamic policyholder lapsations, and pricing of popular auto-callable, or auto-trigger, derivatives.Importance of these applications motivated this thesis which focuses on valuation of multi-period barrier options and extensions under the Black-Scholes framework. These options are characterized by having different barrier levels at distinct time intervals as well as vertical barriers, called icicles, appended to the horizontal ones at certain time points. The static hedging theorem developed in this thesis for the purpose of pricing barrier option extensions does not rely on traditional tools, such as integration or solving the Black-Scholes partial differential equation, and instead makes use of the technique of Esscher transform and the reflection principle.In the first part of the thesis, we review the technique of Esscher transform and its extension from random variables to Levy processes and, in particular, to Brownian motions. Application of the Esscher transform in determining the distribution properties of Brownian motion characteristics such as the running maximum and the first passage time plays a key role in barrier option valuation.In the second part, we inform the reader of the static hedging formula which is a powerful tool that allows pricing ordinary barrier options. We extend this result to develop the static hedging theorem that permits the payoff function to depend on the underlying asset prices beyond the barrier monitoring interval, hence can be applied in valuation of multi-period options. Use of this instrument is particularly beneficial in pricing options with large number of periods where the use of traditional tools can prove extremely laborious.Lastly, we apply the obtained pricing tool in valuation of barrier option extensions, including compound, sequential, and double barrier options. When possible, we demonstrate that the results coincide with those from the existing literature. However, for quite a few derivatives, pricing formulas have not been derived in earlier literature, to the best of the author’s knowledge. Furthermore, we develop the versions of the static hedging theorem that allow pricing options with exponential barriers and outside barrier options written on multiple assets. For options with exponential barriers, the closed-form pricing formulas for compound, sequential, and double barrier options are also derived.
590 $a School code: 0096.
650 4 $a Statistics. $3 182057
650 4 $a Finance. $3 183252
650 4 $a Motivation. $3 252310
650 4 $a Random variables. $3 199057
650 4 $a Payoffs. $3 915660
650 4 $a Hypotheses. $3 915661
650 4 $a Binomial distribution. $3 915662
650 4 $a Prices. $3 182958
650 4 $a Stochastic models. $3 242915
653 $a Barrier options
653 $a Esscher transform
653 $a Exotic barrier options
653 $a Icicled barrier options
653 $a Reflection principle
653 $a Static hedging
690 $a 0463
690 $a 0508
710 2 $a The University of Iowa. $b Statistics. $3 915659
773 0 $t Dissertations Abstracts International $g 83-02B.
790 $a 0096
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28491409