Stochastic Volatility in Financial Markets: Crossing the Bridge to Continuous TimeStochastic Volatility in Financial Markets presents advanced topics in financial econometrics and theoretical finance, and is divided into three main parts. The first part aims at documenting an empirical regularity of financial price changes: the occurrence of sudden and persistent changes of financial markets volatility. This phenomenon, technically termed `stochastic volatility', or `conditional heteroskedasticity', has been well known for at least 20 years; in this part, further, useful theoretical properties of conditionally heteroskedastic models are uncovered. The second part goes beyond the statistical aspects of stochastic volatility models: it constructs and uses new fully articulated, theoretically-sounded financial asset pricing models that allow for the presence of conditional heteroskedasticity. The third part shows how the inclusion of the statistical aspects of stochastic volatility in a rigorous economic scheme can be faced from an empirical standpoint. |
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Contents
INTRODUCTION | 1 |
12 Empirical models in discrete time | 7 |
122 EXTENSIONS | 8 |
RAMIFICATIONS | 11 |
124 DIFFUSIONS AS ARCH APPROXIMATIONS | 14 |
13 Theoretical issues | 16 |
132 THE TERM STRUCTURE OF INTEREST RATES | 20 |
14 Statistical inference | 23 |
331 FEYNMANKAC REPRESENTATION OF THE SOLUTIONS | 71 |
HEDGING COST PROCESSES AND DECOMPOSITION FORMULAE | 74 |
34 On mean selffinancing strategies and the minimal martingale measure | 75 |
relative entropy and the minimal martingale measure | 80 |
MODELS OF THE TERM STRUCTURE WITH STOCHASTIC VOLATILITY | 81 |
42 From the one factor model to the modeling of conditional heteroskedasticity | 83 |
43 Searching for affinity | 87 |
44 Early equilibriumbased models | 90 |
15 Plan | 29 |
CONTINUOUS TIME BEHAVIOR OF NON LINEAR ARCH MODELS | 31 |
23 Interpretation of the moment conditions | 36 |
24 Effectiveness of ARCH as diffusion approximations of theoretical models | 37 |
25 Limiting behavior of the error process | 40 |
26 Continuous time behavior of the volatility switching models | 44 |
262 CONVERGENCE ISSUES | 45 |
263 INVARIANT MEASURES | 46 |
proofs on convergence issues | 48 |
proofs on distributional issues | 52 |
Appendix C | 55 |
CONTINUOUS TIME STOCHASTIC VOLATILITY OPTION PRICING FOUNDATIONAL ISSUES | 57 |
32 The reference model | 59 |
322 INCOMPLETENESS ISSUES | 63 |
323 MODELS COMPLETED BY NONPRODUCTIVE ASSETS | 65 |
A BASIC EXAMPLE | 66 |
33 Applications to stochastic volatility | 70 |
45 A class of equilibrium models of the term structure with stochastic volatility | 91 |
451 PRELIMINARY OPTIMALITY RESULTS | 92 |
taking account of nonlinearities | 96 |
FORMULATING SOLVING AND ESTIMATING MODELS OF THE TERM STRUCTURE USING ARCH MODELS AS DIFFUSION APPROXIMA... | 99 |
52 Specification of the theoretical models | 100 |
53 Econometric strategy | 102 |
54 The pure numerical solution of the theoretical models | 109 |
542 THE GENERAL CASE | 112 |
543 LIMITING AND TRANSVERSALITY CONDITIONS | 113 |
55 An illustrative example | 115 |
a solution method based on the approach of iterated approximations | 119 |
5A2 GENERALITIES | 120 |
5A3 AN ITERATED APPROXIMATION RESULT | 123 |
REFERENCES | 129 |
| 143 | |
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Stochastic Volatility in Financial Markets: Crossing the Bridge to ... Antonio Mele,Fabio Fornari No preview available - 2012 |
Common terms and phrases
agent appendix applied approach approximation ARCH models asset assumption Brownian motion changes chapter claim complete concerning consider consists continuous convergence correspondence cost defined denote density derive diffusion discrete distribution drift dynamics economic empirical equilibrium error estimates et al example existence expected fact factor filtering Finally Financial formula Fornari and Mele function given hedging hold implied incomplete instance instantaneous interest interest rate interpretation introduced issues lemma limit linear martingale means measure methods minimal natural Nelson normal notice observed obtained option pricing parameters partial differential equation positive preceding presented primitive problem proof properties referred representative restrictions risk sampled satisfies shocks short simulated solution specification standard stationary stochastic differential equations stochastic volatility strategy techniques term structure theorem values variables variance
Bibliographic information
| Title | Stochastic Volatility in Financial Markets: Crossing the Bridge to Continuous Time Volume 3 of Dynamic Modeling and Econometrics in Economics and Finance, ISSN 1566-0419 |
| Authors | Fabio Fornari, Antonio Mele |
| Edition | illustrated |
| Publisher | Springer Science & Business Media, 2000 |
| ISBN | 0792378423, 9780792378426 |
| Length | 145 pages |
| Subjects | › › Business & Economics / Econometrics Business & Economics / Economics / General Business & Economics / Economics / Theory Business & Economics / Finance / General Business & Economics / General Business & Economics / Investments & Securities / General |
| Export Citation | BiBTeX EndNote RefMan |