國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Modern SABR analyticsformulas and in...

Antonov, Alexandre.

Modern SABR analyticsformulas and insights for quants, former physicists and mathematicians /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Modern SABR analyticsby Alexandre Antonov, Michael Konikov, Michael Spector.
其他題名:	formulas and insights for quants, former physicists and mathematicians /
作者:	Antonov, Alexandre.
其他作者:	Konikov, Michael.
出版者:	Cham :Springer International Publishing :2019.
面頁冊數:	ix, 127 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	FinanceMathematical models.
電子資源:	https://doi.org/10.1007/978-3-030-10656-0
ISBN:	9783030106560$q(electronic bk.)

Modern SABR analyticsformulas and insights for quants, former physicists and mathematicians /
Antonov, Alexandre.

Modern SABR analyticsformulas and insights for quants, former physicists and mathematicians /[electronic resource] :by Alexandre Antonov, Michael Konikov, Michael Spector. - Cham :Springer International Publishing :2019. - ix, 127 p. :ill., digital ;24 cm. - SpringerBriefs in quantitative finance,2192-7006. - SpringerBriefs in quantitative finance..

1 Introduction -- 1.1 Introduction -- 1.2 Wide popularity of the SABR -- 1.3 Simple derivation -- 1.4 Modifications and extensions of the SABR -- 1.5 CMS and the SABR -- 1.6 Approximation accuracy and its improvements -- 1.7 About this book -- 2 Exact Solutions to CEV Model with Stochastic Volatility -- 2.1 Introduction -- 2.2 Transforming CEV Process into the Bessel One -- 2.3 Solution behavior near singular point x = 0, integrability, flux -- 2.4 Laplace Transform -- 2.5 Probability distributions -- 2.6 Back to CEV model -- 2.6.1 Option pricing through Chi Square distributions -- 2.7 Alternative expressions for CEV option values -- 2.8 CEV Model with Stochastic Volatility -- 2.9 Conclusion -- 3 Classic SABR Model: Exactly Solvable Cases -- 3.1 Introduction -- 3.2 Probability Density Functions for the Free Normal and Log-Normal SABR, Probabilistic Approach -- 3.3 Deriving PDFs using Kolmogorov equations -- 3.4 Option Value for the Free Normal SABR -- 3.5 Option Value for the Lognormal SABR -- 3.6 The Zero Correlation case -- 4 Classic SABR Model: Heat Kernel Expansion and Projection on Solvable Models -- 4.1 Introduction -- 4.2 Invariant forms of Diffusion Equations -- 4.3 Heat Kernel Expansion -- 4.4 Non-Zero Correlation General Case -- 4.5 Conclusion -- References.

Focusing on recent advances in option pricing under the SABR model, this book shows how to price options under this model in an arbitrage-free, theoretically consistent manner. It extends SABR to a negative rates environment, and shows how to generalize it to a similar model with additional degrees of freedom, allowing simultaneous model calibration to swaptions and CMSs. Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia. Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.

ISBN: 9783030106560$q(electronic bk.)

Standard No.: 10.1007/978-3-030-10656-0doiSubjects--Topical Terms:

183782
Finance
--Mathematical models.

LC Class. No.: HG106 / .A58 2019

Dewey Class. No.: 332.0151

Modern SABR analyticsformulas and insights for quants, former physicists and mathematicians /
LDR:03280nam a2200337 a 4500 001 556876
003 DE-He213
005 20190423155656.0
006 m d
007 cr nn 008maaau
008 191127s2019 gw s 0 eng d
020 $a 9783030106560$q(electronic bk.)
020 $a 9783030106553$q(paper)
024 7 $a 10.1007/978-3-030-10656-0 $2 doi
035 $a 978-3-030-10656-0
040 $a GP $c GP
041 0 $a eng
050 4 $a HG106 $b .A58 2019
072 7 $a KF $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a KF $2 thema
082 0 4 $a 332.0151 $2 23
090 $a HG106 $b .A635 2019
100 1 $a Antonov, Alexandre. $3 839227
245 1 0 $a Modern SABR analytics $h [electronic resource] : $b formulas and insights for quants, former physicists and mathematicians / $c by Alexandre Antonov, Michael Konikov, Michael Spector.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a ix, 127 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in quantitative finance, $x 2192-7006
505 0 $a 1 Introduction -- 1.1 Introduction -- 1.2 Wide popularity of the SABR -- 1.3 Simple derivation -- 1.4 Modifications and extensions of the SABR -- 1.5 CMS and the SABR -- 1.6 Approximation accuracy and its improvements -- 1.7 About this book -- 2 Exact Solutions to CEV Model with Stochastic Volatility -- 2.1 Introduction -- 2.2 Transforming CEV Process into the Bessel One -- 2.3 Solution behavior near singular point x = 0, integrability, flux -- 2.4 Laplace Transform -- 2.5 Probability distributions -- 2.6 Back to CEV model -- 2.6.1 Option pricing through Chi Square distributions -- 2.7 Alternative expressions for CEV option values -- 2.8 CEV Model with Stochastic Volatility -- 2.9 Conclusion -- 3 Classic SABR Model: Exactly Solvable Cases -- 3.1 Introduction -- 3.2 Probability Density Functions for the Free Normal and Log-Normal SABR, Probabilistic Approach -- 3.3 Deriving PDFs using Kolmogorov equations -- 3.4 Option Value for the Free Normal SABR -- 3.5 Option Value for the Lognormal SABR -- 3.6 The Zero Correlation case -- 4 Classic SABR Model: Heat Kernel Expansion and Projection on Solvable Models -- 4.1 Introduction -- 4.2 Invariant forms of Diffusion Equations -- 4.3 Heat Kernel Expansion -- 4.4 Non-Zero Correlation General Case -- 4.5 Conclusion -- References.
520 $a Focusing on recent advances in option pricing under the SABR model, this book shows how to price options under this model in an arbitrage-free, theoretically consistent manner. It extends SABR to a negative rates environment, and shows how to generalize it to a similar model with additional degrees of freedom, allowing simultaneous model calibration to swaptions and CMSs. Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia. Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.
650 0 $a Finance $x Mathematical models. $3 183782
650 1 4 $a Quantitative Finance. $3 274071
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Game Theory, Economics, Social and Behav. Sciences. $3 274083
700 1 $a Konikov, Michael. $3 839228
700 1 $a Spector, Michael. $3 802230
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in quantitative finance. $3 683267
856 4 0 $u https://doi.org/10.1007/978-3-030-10656-0
950 $a Mathematics and Statistics (Springer-11649)