Consistency Problems for Heath-Jarrow-Morton Interest Rate Models Book

1	Introduction	1
1.1	Bond Markets	1
1.2	Forward Curve Fitting Methods and Factor Models	3
1.3	The HJM Methodology	4
1.4	Invariant Manifolds	7
1.5	Outline	9
1.6	Remark on Notation	10
2	Stochastic Equations in Infinite Dimensions	13
2.1	Infinite Dimensional Brownian Motion	13
2.2	The Stochastic Integral	16
2.3	Fundamental Tools	19
2.4	Stochastic Equations	23
3	Consistent State Space Processes	29
3.1	Ito Process Factor Models	29
3.2	Exponential-Polynomial Families	33
3.3	Auxiliary Results	38
3.4	The Case BEP (1,n)	41
3.5	The General Case BEP (K,n)	44
3.6	The Diffusion Case	51
3.7	Applications	54
3.8	Conclusions	56
4	The HJM Methodology Revisited	57
4.1	Term Structure Movements	57
4.2	The Musiela Parametrization	58
4.3	Arbitrage-free Term Structure Movements	60
4.4	Contingent Claim Valuation	66
4.5	What Is a Model?	70
5	The Forward Curve Spaces H[subscript w]	75
5.1	Definition of H[subscript w]	75
5.2	Volatility Specification	81
5.3	The Yield Curve	83
5.4	Local State Dependent Volatility	84
5.5	Functional Dependent Volatility	87
5.6	The BGM Model	89
6	Invariant Manifolds for Stochastic Equations	95
6.1	Finite Dimensional Submanifolds in Banach Spaces	95
6.2	Invariant Manifolds	101
6.3	Proof of Theorems 6.2.1-6.2.4	103
6.4	Consistency Conditions in Local Coordinates	109
7	Consistent HJM Models	113
7.1	Consistency Problems	113
7.2	A Simple Regularity Criterion for G	115
7.3	Regular Exponential-Polynomial Families	117
7.4	Affine Term Structure	122
8	Appendix: A Summary of Conditions	127
8.1	Axioms for the Forward Curve Space	127
8.2	Conditions on the Forward Curve Movements	127
8.3	Conditions for HJM Models	128
8.4	Assumptions for Characterizing Invariant Manifolds	128
	References	129
	Index	133