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Nonlinear Valuation and Non-Gaussian Risks in Finance [Hardback]

(University of Maryland, College Park), (Katholieke Universiteit Leuven, Belgium)
  • Formāts: Hardback, 281 pages, height x width x depth: 250x175x20 mm, weight: 700 g, Worked examples or Exercises
  • Izdošanas datums: 03-Feb-2022
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1316518094
  • ISBN-13: 9781316518090
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Nonlinear Valuation and Non-Gaussian Risks in FinancePalielināt
  • Formāts: Hardback, 281 pages, height x width x depth: 250x175x20 mm, weight: 700 g, Worked examples or Exercises
  • Izdošanas datums: 03-Feb-2022
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1316518094
  • ISBN-13: 9781316518090
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781316518090.html
Keywords:
"Risk is often defined by the probabilities of possible future outcomes, be they the tossing of coins, the rolling of dice or the prices of assets at some future date. Uncertainty exists as the possible outcomes are many and the actual outcome that will eventuate is not known. This uncertainty is resolved when at some future time the actual outcome becomes known. The risk may be valued statistically at its expected value or in a market at the current price to be paid or received for acquiring or delivering a unit of currency on the resolution of the risk. The market value is also understood to be a discounted expected value under altered probabilities that reflect prices of events as opposed to their real probabilities. By construction the value of a risk is hence a linear function on the space of risks with the value of a combination being equal to an equivalent combination of values. As a consequence value maximization is not possible as non constant linear functions have no maximal values. Optimization becomes possible only after introducing constraints that limit the set of possibilities"--

Recenzijas

' a nonlinear non-Gaussian valuation account for risk management in finance that will be of use to practitioners and researchers in financial risk.' Hernando Burgos-Soto, zbMATH

Papildus informācija

Explore how market valuation must abandon linearity to deliver efficient resource allocation.
Preface xi
Acknowledgments xiii
1 Introduction
1(4)
2 Univariate Risk Representation Using Arrival Rates
5(25)
2.1 Pure Jump Finite Variation Probability Models
7(4)
2.2 Probability Densities and Arrival Rates
11(5)
2.3 The Complex Exponential Variation
16(4)
2.4 Evaluating Event Arrival Rates
20(2)
2.5 Variation Outcomes
22(4)
2.6 Drift, Volatility, Risk Dimensions, and Their Compensation
26(4)
3 Estimation of Univariate Arrival Rates from Time Series Data
30(9)
3.1 Complex Exponential Variations and Data
30(1)
3.2 Digital Moment Estimation
31(2)
3.3 Variance Gamma, Bilateral Gamma, and Bilateral Double Gamma Estimation Results
33(2)
3.4 Assessing Parameter Contributions
35(4)
4 Estimation of Univariate Arrival Rates from Option Surface Data
39(9)
4.1 Depreferencing Option Prices
39(4)
4.2 Estimation Results
43(5)
5 Multivariate Arrival Rates Associated with Prespecified Univariate Arrival Rates
48(11)
5.1 Multivariate Model for Bilateral Gamma Marginals
49(3)
5.2 The Role of Dependency Parameters in the Multivariate Bilateral Gamma Model
52(1)
5.3 Multivariate Bilateral Gamma Levy Copulas
53(2)
5.4 Multivariate Model for Bilateral Double Gamma Marginals
55(1)
5.5 Simulated Count of Multivariate Event Arrival Rates
56(3)
6 The Measure-Distorted Valuation As a Financial Objective
59(26)
6.1 Linear Valuation Issues
61(2)
6.2 Modeling Risk Acceptability
63(2)
6.3 Nonlinear Conservative Valuation
65(1)
6.4 Risk Reward Decompositions of Value
66(1)
6.5 Remarks on Modigliani-Miller Considerations
67(1)
6.6 Probability Distortions
67(6)
6.7 Measure Distortions Proper
73(5)
6.8 Dual Formulation of Measure Distortions
78(4)
6.9 Explicit Representation of Dual Distortions Φ, Φ
82(2)
6.10 Generic Considerations in the Maximization of Market Valuations
84(1)
7 Representing Market Realities
85(13)
7.1 Risk Charges and the Measure Distortion Parameters
86(1)
7.2 Measure Distortions and Option Prices
87(3)
7.3 Measure-Distorted Value-Maximizing Hedges for a Short Gamma Target
90(5)
7.4 Measure Distortions Implied by Hedges for a Long Gamma Target
95(3)
8 Measure-Distorted Value-Maximizing Hedges in Practice
98(12)
8.1 Hedging Overview
99(1)
8.2 The Hedge-Implementing Enterprise
100(1)
8.3 Summarizing Option Surfaces Using Gaussian Process Regression
101(3)
8.4 Selecting the Hedging Arrival Rates
104(1)
8.5 Approximating Variation Exposures
105(1)
8.6 Measure Distortion Parameters
106(2)
8.7 Backtest Hedging Results for Multiple Strangles on SPX
108(2)
9 Conic Hedging Contributions and Comparisons
110(16)
9.1 Univariate Exposure Hedging Study
112(1)
9.2 Distorted Least Squares
113(3)
9.3 Example Illustrating Distorted Least-Squares Hedges
116(2)
9.4 Incorporating Weightings
118(1)
9.5 Measure-Distorted Value Maximization
119(1)
9.6 Greek Hedging
120(1)
9.7 Theta Issues in Exposure Design
120(2)
9.8 Incorporating Spreads
122(2)
9.9 No Spread Access and Theta Considerations
124(2)
10 Designing Optimal Univariate Exposures
126(9)
10.1 Exposure Design Objectives
127(1)
10.2 Exposure Design Constraints
128(1)
10.3 Exposure Design Problem
128(1)
10.4 Lagrangean Analysis of the Design Problem
129(1)
10.5 Discretization and Solution
130(1)
10.6 Details Related to Levy Measure Singularities at Zero
131(1)
10.7 Sample Optimal Exposure Designs
131(1)
10.8 Further Details about Some Particular Cases
132(3)
11 Multivariate Static Hedge Designs Using Measure-Distorted Valuations
135(15)
11.1 A Two-Dimensional Example
136(6)
11.2 A 10-Dimensional Example
142(8)
12 Static Portfolio Allocation Theory for Measure-Distorted Valuations
150(21)
12.1 Measure Integrals by Simulation
152(1)
12.2 Dual Formulation of Portfolio Problem
152(2)
12.3 Approximation by Probability Distortion
154(1)
12.4 Implementation of Portfolio Allocation Problems
154(2)
12.5 Mean Risk Charge Efficient Frontiers
156(7)
12.6 Sensitivity of Required Returns to Choice of Points on Frontiers
163(1)
12.7 Conic Alpha Construction Based on Arrival Rates
164(1)
12.8 Fixed Income Asset Efficient Exposure Frontiers
165(6)
13 Dynamic Valuation via Nonlinear Martingales and Associated Backward Stochastic Partial Integro-Differential Equations
171(13)
13.1 Backward Stochastic Partial Integro-Differential Equations and Valuations
173(2)
13.2 Nonlinear Valuations and BSPIDE
175(1)
13.3 Spatially Inhomogeneous Bilateral Gamma
176(3)
13.4 Dynamic Implementation of Hedging Problems
179(5)
14 Dynamic Portfolio Theory
184(11)
14.1 The Dynamic Law of Motion
185(2)
14.2 Relativity Dynamics
187(1)
14.3 The Full Sample
188(1)
14.4 Portfolio Construction
188(3)
14.5 Stationary Exposure Valuation
191(1)
14.6 Stationary Value and Policy Results
192(1)
14.7 Building Neural Net Policy Functions and Simulating Trades
192(3)
15 Enterprise Valuation Using Infinite and Finite Horizon Valuation of Terminal Liquidation
195(28)
15.1 Bilateral Gamma Enterprise Returns
197(4)
15.2 Prudential Capital for Bilateral Gamma Returns
201(8)
15.3 Regulatory Risk Capital for Enterprises with Bilateral Gamma Returns
209(1)
15.4 Calibration of Measure-Distortion Parameters
210(6)
15.5 Results for Equity Enterprises
216(1)
15.6 Results for Treasury Bond Investments
216(1)
15.7 Results for Hedge Fund Enterprises
217(3)
15.8 Short Position Capital Requirements
220(1)
15.9 Equity versus Leveraged Equity
220(3)
16 Economic Acceptability
223(12)
16.1 Interplay between Equity Markets and Regulators
224(1)
16.2 Candidate Physical Laws of Motion
225(1)
16.3 Adapted Measure Distortions
226(2)
16.4 Equity and Regulatory Capital Constructions
228(2)
16.5 Financial Sector Capital during and after the Financial Crisis
230(5)
17 Trading Markovian Models
235(10)
17.1 Return Dependence on States
237(2)
17.2 Markovian State Dynamics
239(1)
17.3 Formulation and Solution of Market Value Maximization
240(2)
17.4 Results on Policy Functions for 10 Stocks
242(1)
17.5 Results for Sector ETFs and SPY
243(2)
18 Market-Implied Measure-Distortion Parameters
245(12)
18.1 Designing the Time Series Estimation of Measure-Distortion Parameters
245(2)
18.2 Estimation Results
247(1)
18.3 Distribution of Measure-Distorted Valuations for Equity Underliers
247(2)
18.4 Structure of Measure-Distorted Valuation-Level Curves
249(1)
18.5 Valuation Frontiers
250(1)
18.6 Acceptability Indices
251(1)
18.7 Acceptability-Level Curves
252(1)
18.8 Equilibrium Return Distributions
253(1)
18.9 Empirical Construction of Return Distribution Equilibria and Their Properties
254(3)
References 257(8)
Index 265
Dilip B. Madan is Professor Emeritus at the Robert H. Smith School of Business. He has been Consultant to Morgan Stanley since 1996 and Consultant to Norges Bank Investment Management since 2012. He is a founding member and past President of the Bachelier Finance Society. He was a Humboldt Awardee in 2006, was named Quant of the Year in 2008, and was inducted into the University of Maryland's Circle of Discovery in 2014. He is the co-creator of the Variance Gamma Model (1990, 1998) and of Conic Finance. He co-authored, with Wim Schoutens, Applied Conic Finance (Cambridge, 2016). Wim Schoutens is Professor at the Katholieke Universiteit Leuven, Belgium. He has extensive practical experience of model implementation and is well known for his consulting work to the banking industry and other institutions. He served as expert witness for the General Court of the European Union, Luxembourg and has worked as an expert for the IMF and for the European Commission. In 2012, he was awarded the John von Neumann Visiting Professorship of the Technical University of Munich. He has authored several books on financial mathematics and is a regular lecturer to the financial industry. Finally, he is a member of the Belgium CPI commission.