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Path-dependence properties of levera...

Zhang, Jian.

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Path-dependence properties of leveraged exchange-traded funds: Compounding, volatility and option pricing.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Path-dependence properties of leveraged exchange-traded funds: Compounding, volatility and option pricing./
Author:	Zhang, Jian.
Description:	88 p.
Notes:	Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: .
Contained By:	Dissertation Abstracts International72-01B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3428058
ISBN:	9781124333038

Path-dependence properties of leveraged exchange-traded funds: Compounding, volatility and option pricing.
Zhang, Jian.

Path-dependence properties of leveraged exchange-traded funds: Compounding, volatility and option pricing. - 88 p.

Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: .

Thesis (Ph.D.)--New York University, 2010.

This thesis studies leveraged exchange-traded funds (ETF) and options written on them.

ISBN: 9781124333038Subjects--Topical Terms:

1669109
Applied Mathematics.

Path-dependence properties of leveraged exchange-traded funds: Compounding, volatility and option pricing.
LDR:02614nam 2200313 4500 001 1394291
005 20110506085324.5
008 130515s2010 ||||||||||||||||| ||eng d
020 $a 9781124333038
035 $a (UMI)AAI3428058
035 $a AAI3428058
040 $a UMI $c UMI
100 1 $a Zhang, Jian. $3 1057605
245 1 0 $a Path-dependence properties of leveraged exchange-traded funds: Compounding, volatility and option pricing.
300 $a 88 p.
500 $a Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: .
500 $a Adviser: Marco Avellaneda.
502 $a Thesis (Ph.D.)--New York University, 2010.
520 $a This thesis studies leveraged exchange-traded funds (ETF) and options written on them.
520 $a In the first part, we give an exact formula linking the price evolution of a leveraged ETF (LETF) with the price of its underlying ETF. We test the formula empirically on historical data for 56 leveraged funds (44 double-leveraged, 12 triple-leveraged) using daily closing prices. The results indicate excellent agreement between the formula and the empirical data. The formula shows that the evolution of the price of an LETF is sensitive to the realized volatility of the underlying product. The relationship between an LETF and its underlying asset is "path-dependent."
520 $a The second part of the study focuses on the relations between options on LETFs and options on the underlying ETFs. The main result shows that an option on an LETF can be replicated by a basket of options on the underlying ETF after a suitable choice of strikes and notionals. In particular, we obtain a new, relative-value, model for pricing LETF options. The derivation makes strong use of the path-dependency result of Part I. As a consequence, we derive a simple non-parametric formula which links the volatility skew of an LETF with the volatility skew of the underlying ETF.
520 $a We validate the theory empirically by showing that the model prices for options on LETFs are in excellent agreement with actual mid-market prices observed in markets. The empirical study was carried out on two LETFs linked to the S&P 500 index (one double-leveraged, one reverse-double-leveraged). The issue of vega-hedging options on LETFs with options on the underlying ETFs is also examined from this viewpoint.
590 $a School code: 0146.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Economics, Finance. $3 626650
690 $a 0364
690 $a 0508
710 2 $a New York University. $b Mathematics. $3 1019424
773 0 $t Dissertation Abstracts International $g 72-01B.
790 1 0 $a Avellaneda, Marco, $e advisor
790 $a 0146
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3428058