Nonlinear Economic Dynamics and Financial Modelling [recurso electrónico] Essays in Honour of Carl Chiarella

This book reflects the state of the art on nonlinear economic dynamics, financial market modelling and quantitative finance. It contains eighteen papers with topics ranging from disequilibrium macroeconomics, monetary dynamics, monopoly, financial market and limit order market models with boundedly rational heterogeneous agents to estimation, time series modelling and empirical analysis, and from risk management of interest-rate products, futures price volatility and American option pricing with stochastic volatility to evaluation of risk and derivatives of electricity market. The book illustrates some of the most recent research tools in these areas and will be of interest to economists working in economic dynamics and financial market modelling, to mathematicians who are interested in applying complexity theory to economics and finance, and to market practitioners and researchers in quantitative finance interested in limit order, futures and electricity market modelling, derivative pricing and risk management Preface 5 Contents 8 Contributors 11 1 Introduction 14 References 19 Part ICarl Chiarella: An Interviewand Some Perspectives 21 2 An Interview to Carl Chiarella, an Italo-Australian Globe Trotter Who Studies Dynamic Models for Economics and Finance 22 3 What's Beyond? Some Perspectives on the Future of Mathematical Economics 29 References 33 Part IINonlinear Economic Dynamics 34 4 Expectations, Firms' Indebtedness and Business Fluctuations in a Structural Keynesian Monetary Growth Framework 35 1 Introduction 35 2 A Medium-Scale Keynes-Metzler Macroeconomic Framework of Firms' Indebtedness and Business Fluctuations 36 3 The Model in Intensive Form 43 4 Numerical Analysis 44 5 Concluding Remarks 46 References 47 5 Mathematical Modelling of Financial Instability and Macroeconomic Stabilisation Policies 48 1 Introduction 48 2 Basic Model: Two-dimensional Model with Fixed Prices 49 3 An Extension: Four-Dimensional Model of Monetary Stabilisation Policy with Flexible Prices 53 4 A Further Extension: Six-Dimensional Model of Monetary and Fiscal Stabilisation Policy Mix with Flexible Prices 59 5 Concluding Remarks: Economic Interpretation of the Analytical Results 65 References 68 6 Bifurcation Structure in a Model of Monetary Dynamics with Two Kink Points 71 1 Introduction 71 2 The Monetary Dynamics Model 72 3 Bifurcation Structure of the Parameter Space 74 3.1 Preliminaries 75 3.2 Region D1: Skew Tent Map Bifurcation Structure 78 3.3 Bifurcation Structure of the Region D3 82 4 Conclusion 86 References 87 7 Boundedly Rational Monopoly with Single Continuously Distributed Time Delay 88 1 Introduction 88 2 Delay Monopoly 90 3 Dynamics with Continuous Delay 92 4 Delay Dynamics with Adaptive Expectation 100 5 Concluding Remarks 111 References 112 8 Learning and Macro-Economic Dynamics 113 1 Introduction 113 2 Few Ontological Notes 114 3 The Micro-Model 116 4 Behavioural Rules and Species in the Economy 120 5 Simulation Results 122 6 Macro-Dynamics 124 6.1 The Financial Soundness State Master Equation 125 6.2 The Learning Master Equation 129 7 Concluding Remarks 136 References 137 9 How Non-normal Is US Output? 139 1 Introduction 139 2 Test Statistics to Detect Non-normality 141 3 Asymptotic Results for the Empirical Data 147 4 Small-sample Results for the Empirical Data 149 5 A Two-regime Monte Carlo Experiment 151 6 The Laplacian as an Alternative Hypothesis 153 7 On the Precision of the Estimates of the Shape Parameter 155 8 Conclusion 159 References 162 Part IIIFinancial Market Modelling 164 10 Heterogeneous Beliefs and Quote Transparency in an Order-Driven Market 165 1 Introduction 165 2 The Model 166 3 Order Book Simulations 168 4 Stylised Facts 169 4.1 Abnormal Returns 171 4.2 Order Placement Patterns 172 4.3 Memory Properties 178 5 Conclusion 182 References 183 11 The Simplicity of Optimal Trading in Order Book Markets 184 1 Introduction 184 2 Set-up 187 3 The Models 189 3.1 Linear Strategies 189 3.2 Markov Perfect Equilibrium Strategies 191 3.3 Further Comments 192 4 Results 193 5 Conclusion 199 References 199 12 Regime Switching Models in the Foreign Exchange Market 201 1 Introduction 201 2 Model Specifications 204 2.1 Benchmark Model 204 2.2 Strategy Switching Based on Past Performance 207 2.3 Strategy Switching Based on Macro Fundamentals 208 2.4 Markov-Switching Beliefs 208 3 Methodology and Data Description 209 3.1 Data 209 3.2 Linearity Tests 211 4 Estimation Results 212 4.1 BHM Estimation Results 212 4.2 LSTR Estimation Results 213 4.3 MS Estimation Results 215 5 Efficiency Tests 218 6 Predictive Power 219 7 Conclusion 221 References 222 13 Time-Varying Cross-Speculation in Currency Futures Markets: An Empirical Analysis 224 1 Introduction 224 2 Data and Model Description 227 3 Time-Varying Responses to a Shock to CHF Speculative Activity 228 4 Conclusion 230 References 230 14 Computational Issues in the Stochastic Discount Factor Framework for Equity Risk Premium 233 1 Introduction 233 2 Bibliographical Review 234 3 Equity Risk Premium in Stochastic Discount Factor Framework 236 4 Observable Determinants for SDF 238 5 Empirical Setup and Econometric Issues 240 6 Alternative Empirical Setup for SDF 243 7 Concluding Remarks 243 References 246 Part IVQuantitative Finance 248 15 On the Risk Evaluation Method Based on the Market Model 249 1 Introduction 249 2 Yield-Curve Modelling under the Observed Measure 251 2.1 Principal Component Analysis 252 2.2 Estimation of Parameters 255 3 The Change of Measure 255 3.1 Forward-Rate Dynamics 256 3.2 The Log-Forward Rate Model 259 3.3 The QG Model 261 4 Monte Carlo Simulation 264 4.1 Generation of Scenarios 265 4.2 Valuation of Derivative Prices 265 5 Concluding Remarks 267 References 268 16 On Multicurve Models for the Term Structure 270 1 Introduction 270 2 The Model 272 2.1 Preliminary Considerations 272 2.2 Description of the Model Itself 274 3 Main Result (FRAs) 275 3.1 Preliminary Notions and Results 275 3.2 The Result Itself 277 3.3 Comments on the Main Result 278 3.4 Proof of the Main Result 280 4 Aspects of CAP Pricing 283 4.1 Preliminary Comments 283 4.2 A Possible Pricing Methodology 283 References 285 17 Pricing an American Call Under Stochastic Volatility and Interest Rates 286 1 Introduction 286 2 Problem Statement-American Call Option with Stochastic Volatility and Stochastic Interest Rates 287 2.1 Model Description 287 2.2 Boundary Conditions 289 3 Method of Lines Implementation 294 4 Sparse Grid Implementation 298 4.1 The Sparse Grid Combination Technique 299 4.2 Finite Difference Method with PSOR 302 5 Numerical Examples 305 6 Conclusion 308 References 309 18 On the Volatility of Commodity Futures Prices 310 1 Introduction 310 2 A Markovian Commodity Futures Price Model 311 3 Data and the Estimation Method 315 3.1 Data 315 3.2 Estimation Method 318 4 Empirical Results 320 4.1 Parameter Estimation 320 4.2 Gold Volatility 320 4.3 Crude Oil Volatility 322 4.4 Natural Gas Volatility 324 4.5 Soybean Volatility 325 4.6 Sugar Volatility 325 4.7 Corn Volatility 325 4.8 Model Fit 326 5 Conclusion 327 References 328 19 A Multi-factor Structural Model for Australian Electricity Market Risk 330 1 Introduction 330 2 The Model 331 2.1 The Temperature Model 332 2.2 The Regional Load Model 335 2.3 The Regional Reference Price Model 338 3 Numerical Results 340 3.1 The Data 340 3.2 Estimation 340 3.3 Simulation Results 345 4 Summary and Conclusions 348 References 348 20 On an Integral Arising in Mathematical Finance 350 1 Introduction 350 2 The Asian Option Pricing PDE 351 3 The Yakubovich Heat Kernel 353 4 Alternative Forms for ht(x,w) 358 5 Some Applications 360 5.1 Asian Options 360 5.2 Yor's Integral 361 5.3 Bond Pricing in the Dothan Model 362 5.4 Numerical Implementation 362 References 364 21 Change of Numéraire and a Jump-Diffusion Option Pricing Formula 366 1 Introduction 366 2 The Extended Model of Black-Scholes-Merton 367 3 Transformation of Measures 371 4 The Forward Measure 373 5 The Reciprocal Forward Measure 375 6 Pricing a European Call Option 378 7 Conclusion 383 References 384 Front Matter....Pages i-xv Introduction....Pages 1-7 Front Matter....Pages 9-9 An Interview to Carl Chiarella, an Italo-Australian Globe Trotter Who Studies Dynamic Models for Economics and Finance....Pages 11-17 What’s Beyond? Some Perspectives on the Future of Mathematical Economics....Pages 19-23 Front Matter....Pages 25-25 Expectations, Firms’ Indebtedness and Business Fluctuations in a Structural Keynesian Monetary Growth Framework....Pages 27-39 Mathematical Modelling of Financial Instability and Macroeconomic Stabilisation Policies....Pages 41-63 Bifurcation Structure in a Model of Monetary Dynamics with Two Kink Points....Pages 65-81 Boundedly Rational Monopoly with Single Continuously Distributed Time Delay....Pages 83-107 Learning and Macro-Economic Dynamics....Pages 109-134 How Non-normal Is US Output?....Pages 135-159 Front Matter....Pages 161-161 Heterogeneous Beliefs and Quote Transparency in an Order-Driven Market....Pages 163-181 The Simplicity of Optimal Trading in Order Book Markets....Pages 183-199 Regime Switching Models in the Foreign Exchange Market....Pages 201-223 Time-Varying Cross-Speculation in Currency Futures Markets: An Empirical Analysis....Pages 225-233 Computational Issues in the Stochastic Discount Factor Framework for Equity Risk Premium....Pages 235-249 Front Matter....Pages 251-251 On the Risk Evaluation Method Based on the Market Model....Pages 253-273 On Multicurve Models for the Term Structure....Pages 275-290 Pricing an American Call Under Stochastic Volatility and Interest Rates....Pages 291-314 On the Volatility of Commodity Futures Prices....Pages 315-334 A Multi-factor Structural Model for Australian Electricity Market Risk....Pages 335-354 On an Integral Arising in Mathematical Finance....Pages 355-370 Front Matter....Pages 251-251 Change of Numéraire and a Jump-Diffusion Option Pricing Formula....Pages 371-389