American-Style Derivatives: Valuation and Computation

by Detemple; Jerome

• ISBN13: 9781584885672
• ISBN10: 158488567X
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-12-09
• Publisher: Chapman & Hall/

Summary

While the valuation of standard American option contracts has now achieved a fair degree of maturity, much work remains to be done regarding the new contractual forms that are constantly emerging in response to evolving economic conditions and regulations. Focusing on recent developments in the field, American-Style Derivatives provides an extensive treatment of option pricing with an emphasis on the valuation of American options on dividend-paying assets.The book begins with a review of valuation principles for European contingent claims in a financial market in which the underlying asset price follows an Ito process and the interest rate is stochastic and then extends the analysis to American contingent claims. In this context the author lays out the basic valuation principles for American claims and describes instructive representation formulas for their prices. The results are applied to standard American options in the Black-Scholes market setting as well as to a variety of exotic contracts such as barrier, capped, and multi-asset options. He also reviews numerical methods for option pricing and compares their relative performance.The author explains all the concepts using standard financial terms and intuitions and relegates proofs to appendices that can be found at the end of each chapter. The book is written so that the material is easily accessible not only to those with a background in stochastic processes and/or derivative securities, but also to those with a more limited exposure to those areas.

Table of Contents

Introduction	1	(6)
European Contingent Claims	7	(30)
Definitions	7	(1)
The Economy	8	(2)
Attainable Contingent Claims	10	(4)
Valuation of Attainable Claims	14	(2)
Claims Involving Negative Payoffs	16	(2)
The Structure of Contingent Claims' Prices	18	(1)
Changes of Numeraire and Valuation	19	(2)
Option and Forward Contracts	21	(3)
Markets with Deterministic Coefficients	24	(4)
Markets with Multiple Assets	28	(1)
Appendix: Proofs	29	(8)
American Contingent Claims	37	(18)
Contingent Claims with Random Maturity	37	(2)
American Contingent Claims	39	(2)
Exercise Premium Representations	41	(3)
A Duality Formula: Upper Price Bounds	44	(1)
American Options and Forward Contracts	45	(2)
Multiple Underlying Assets	47	(1)
Appendix: Proofs	48	(7)
Standard American Options	55	(30)
The Immediate Exercise Region	55	(2)
The Call Price Function	57	(2)
Early Exercise Premium Representation	59	(2)
A One-Dimensional Integral Equation	61	(1)
Hedging	62	(1)
Diffusion Processes	63	(4)
Floating Strike Asian Options	67	(2)
American Forward Contracts	69	(2)
Appendix: Proofs	71	(14)
Barrier and Capped Options	85	(22)
Barrier Options	85	(4)
Definitions and Literature	85	(1)
Valuation	86	(3)
Capped Options	89	(8)
Definitions, Examples and Literature	89	(1)
Constant Cap	89	(4)
Capped Options with Growing Caps	93	(3)
Stochastic Cap, Interest Rate and Volatility	96	(1)
Diffusion Processes	97	(1)
Appendix: Proofs	98	(9)
Options on Multiple Assets	107	(48)
Definitions, Examples and Literature	107	(2)
The Financial Market	109	(1)
Call Options on the Maximum of 2 Prices	109	(12)
Exercise Region of a Max-Call Option	110	(4)
Valuation of Max-Call Options	114	(5)
Dual Strike Max-Options	119	(1)
Put Options on the Minimum of 2 Prices	120	(1)
Economic Implications	120	(1)
American Spread Options	121	(4)
Exercise Region and Valuation	121	(2)
Options to Exchange One Asset for Another	123	(1)
Exchange Options with Proportional Caps	124	(1)
Options on an Average of 2 Prices	125	(4)
Geometric Averaging	125	(1)
Arithmetic Averaging	126	(3)
Call Options on the Minimum of 2 Prices	129	(6)
Exercise Region of a Min-Call Option	129	(3)
The EEP Representation	132	(3)
Integral Equations for the Boundary Components	135	(1)
Appendix A: Derivatives on Multiple Assets	135	(8)
Appendix B: Proofs	143	(12)
Occupation Time Derivatives	155	(40)
Background and Literature	155	(1)
Definitions	156	(1)
Symmetry Properties	157	(1)
Quantile Options	158	(5)
Contractual Specification	158	(1)
The Distribution of an α-Quantile	159	(1)
Pricing Quantile Options	159	(3)
A Reduction in Dimensionality	162	(1)
Quantile Contingent Claims	163	(1)
Parisian Options	163	(7)
Contractual Specification	164	(1)
Parity and Symmetry Relations	165	(1)
Pricing Parisian Options	166	(3)
Parisian Contingent Claims	169	(1)
Cumulative Parisian Contingent Claims	170	(3)
Definitions and Parity/Symmetry Relations	170	(1)
Pricing Cumulative Barrier Claims	171	(1)
Standard and Exotic Cumulative Barrier Options	172	(1)
Step Options	173	(2)
Contractual Specification	173	(1)
Pricing European-style Step Options	174	(1)
American Occupation Time Derivatives	175	(4)
Early Exercise Premium Representation	175	(1)
Valuation in the Standard Model	176	(3)
Multiasset Claims	179	(2)
Symmetry Properties	179	(2)
Valuation	181	(1)
Appendix: Proofs	181	(14)
Numerical Methods	195	(22)
Numerical Methods for American Options	195	(2)
Integral Equation Methods	197	(2)
Exercise Time Approximations: LBA-LUBA	199	(3)
A Lower Bound for the Option Price	199	(1)
A Lower Bound for the Exercise Boundary	200	(1)
An Upper Bound for the Option Price	201	(1)
Price Approximations	202	(1)
Diffusion Processes	202	(2)
Integral Equation Methods	203	(1)
Stopping Time Approximations: LBA and LUBA	203	(1)
Other Recent Approaches	204	(1)
Lattice Methods: Binomial Black-Scholes Algorithm	204	(1)
Integral Equation: Non-linear Approximations	204	(1)
Monte Carlo Simulation	205	(1)
Performance Evaluation	205	(2)
Experiment Design	206	(1)
Results and Discussion	206	(1)
Methods for Multiasset Options	207	(5)
Lattice Methods	207	(2)
Monte Carlo Simulation	209	(2)
Monte Carlo Simulation and Duality	211	(1)
Methods for Occupation Time Derivatives	212	(3)
Laplace Transforms	212	(1)
PDE-based Methods	212	(1)
Binomial/Trinomial Lattices	213	(2)
Appendix: Proofs	215	(2)
Bibliography	217	(12)
Index	229