Pricing of Bond Options (eBook)

Foreword 5
Acknowledgements 6
Contents 7
Introduction 9
The option pricing framework 14
2.1 Zero-coupon bond options 15
2.2 Coupon bond options 17
The Edgeworth Expansion 21
3.1 The generalized EE scheme 22
3.2 The approximation of a .2v -pdf 27
3.3 The approximation of a lognormal-pdf 30
The Integrated Edgeworth Expansion 35
4.1 The generalized IEE scheme 36
4.2 An approximation of the .2v -cdf 38
4.3 An approximation of the lognormal-cdf 40
Multi-Factor HJM models 45
5.1 The change of measure 49
5.2 Pricing of zero-coupon bond options 50
5.3 Pricing of coupon bond options 59
Multiple-Random Fields term structure models 76
6.1 Random Fields 76
6.2 Multiple-Random Field HJM-framework 80
6.3 Change of measure 85
6.4 Pricing of zero bond options 86
6.5 Pricing of coupon bond options 91
Multi-factor USV term structure model 98
7.1 The change of measure 102
7.2 Pricing of zero-coupon bond options 103
7.3 Pricing of coupon bond options 111
Conclusions 118
Appendix 122
9.1 Independent Brownian motions 122
9.2 Dependent Brownian motions 124
Matlab codes for the EE and IEE 129
10.1 Integer equation 129
10.2 Computation of the cumulants given the moments 130
10.3 Computation of the Hermite polynomial 131
10.4 The EE 132
10.5 The IEE 133
References 135
List of figures 139
List of tables 141