PDE Valuation of Interest Rate Derivatives: From Theory to ImplementationBoD – Books on Demand, 2007 - 222 Seiten The Libor Market Model and its several extensions can be seen as state of the art in interest rate modeling. However, due to the ever increasing complexity of interest rate products, the high dimensionality of this approach starts to reach its limits from the computational side. This book is mainly concerned with a class of Markovian Yield Curve Models which try to overcome that disadvantage as they enable a low-dimensional deterministic and fast PDE valuation. The objective of this book is thereby threefold: - To illuminate in a compact way the connection between stochastic processes and partial differential equations as well as review the key features of arbitrage-free pricing. - To embed the here analyzed Markovian model class into the entire framework of interest rate models. - To present and implement robust numerical schemes, which enable an efficient computational treatment of risk-neutral product valuation by using PDE methods. |
Inhalt
Foundations | 3 |
List of Figures | 12 |
Fixed Income Markets | 37 |
Models of the Yield Curve | 60 |
Markovian Representations of the Yield Curve | 77 |
Numerical Solution | 99 |
Practical Considerations | 149 |
Design Issues and C++ Implementation | 167 |
A Additional Calculations iii | iii |
B Probability Essentials | ix |
Häufige Begriffe und Wortgruppen
able according additional Algorithm analytical applied approximation assume becomes bond price boundary Brownian Motion calculated called Chapter chosen combination conditional consider consistency corresponding define Definition depend derivative diffusion direction directly discretization discussed distributed domain drift dynamics equation expectation factor Figure finite first formula forward rate function future given grid implies integral interest rate introduced Libor linear lognormal Markov Markovian maturity measure method Model numerical obtain operator options parameter particular points problem Proof Proposition quantities random variable Remark resulting risk-neutral scheme scheme equation securities sense setting short short-rate solution solve space specific step stochastic structure swap Swaption tenor term rate Theorem tion usually valuation valuation PDE vector volatility weighted writes yield curve yields zero-coupon