| Description |
1 online resource |
| Series |
Cambridge elements. Elements in quantitative finance |
|
Cambridge elements. Elements in quantitative finance.
|
| Contents |
Cover -- Title Page -- Copyright Page -- Girsanov, Numeraires, and All That -- Contents -- 1 Introduction -- 2 Girsanov's Theorem -- 2.1 Radon-Nikodym Derivative -- 2.2 Girsanov's Theorem in One Dimension -- 2.3 Girsanov's Theorem in Many Dimensions -- 3 Arbitrage Asset Pricing in a Nutshell -- 3.1 Frictionless Market Models -- 3.2 Self-Financing Portfolios and No Arbitrage -- 3.3 Complete Markets -- 3.4 The Fundamental Theorems of Arbitrage Pricing -- 3.5 Changing Numeraire -- 3.6 Drift Transformation under Change of Numeraire -- 4 Riskless Bond Numeraires and Associated EMMs |
|
4.1 Bank Account Numeraire -- 4.2 Forward Numeraire -- 4.3 Annuity Numeraire -- 5 Change of Numeraire in Interest Rate and FX Models -- 5.1 CMS and Change from Forward Measure to Swap Measure -- 5.2 FMM Term Structure Model -- 5.3 Foreign Exchange Markets and Quanto Adjustment -- 6 Incomplete Markets -- 6.1 Stochastic Volatility -- 6.2 SABR-FMM Term Structure Model -- 6.3 Event Risk and Event Intensity -- 6.4 Credit Risk and Defaultable Numeraire -- 6.5 Cross Currency CDS and Quanto Spreads -- 6.6 Mortgage-Backed Securities and Prepayable Numeraire -- References -- Acknowledgment |
| Summary |
In this Element the authors review the technique of the change of numeraire in the martingale approach to option pricing. Their intention is to present a reader friendly explanation of the technique itself, and illustrate how it is applied in various fields of quantitative finance as the basis for building option valuation models. They start with an informal review of Girsanov's theorem, followed by a brief summary of the basic concepts of the arbitrage free pricing, and the technique of change of numeraire. This is followed by a number of applications of the change of numeraire technique including interest rate models, FX quanto adjustments, credit risk modeling, mortgage backed securities, and CMS rates |
| Notes |
Description based on online resource; title from digital title page (viewed on November 01, 2022) |
| Subject |
Options (Finance) -- Prices -- Mathematical models
|
|
Options (Finance) -- Prices -- Mathematical models.
|
| Form |
Electronic book
|
| Author |
Lesniewski, Andrew, author
|
| ISBN |
9781009339278 |
|
1009339273 |
|
