Buch, Englisch, 288 Seiten
Buch, Englisch, 288 Seiten
ISBN: 978-1-394-37007-8
Verlag: John Wiley & Sons Inc
Master the quantitative foundations you need to successfully invest in and trade digital assets
Financial Mathematics for Cryptocurrencies by Tom J. Espel combines two of today's most dynamic fields – quantitative finance and cryptocurrencies – in a comprehensive guide that addresses the unique mathematical challenges faced by everyone involved in the crypto markets. Espel draws on his extensive experience in frontier assets to explain the analytical frameworks you’ll need to make informed investment decisions, identify pricing opportunities, and manage risk in this volatile asset class.
The book adapts relevant quantitative finance methodologies specifically for digital assets, bridging the gap between traditional financial mathematics and the distinctive characteristics of blockchain-based instruments. Espel introduces three essential constructs for DeFi pricing theory: network time, the validator account as a new numéraire, and wrapped token frameworks for cross-chain valuation. Its modular structure allows readers to navigate directly to relevant sections, covering everything from blockchain fundamentals to advanced valuation models, staking contract mathematics, and liquidity cost analysis in cryptocurrency markets.
You’ll find: - Mathematical frameworks for staking contracts, liquid staking derivatives, and yield farming strategies with rigorous ex-ante and ex-post valuations
- Comprehensive coverage of network valuation methods including Metcalfe's Law, Reed's Law, and the ZBOT framework specifically applied to digital assets
- Pricing theory extending arbitrage-free pricing to blockchain assets through the validator account and blockchain measure (B-measure)
- Expert insights from an author specializing in quantitative strategies for electronic and illiquid assets, with expertise in market microstructure and volatility modeling
- Accessible mathematical solutions designed for practitioners in applied mathematics and quantitative finance, with clear and rigorous explanations
Perfect for quantitative analysts, traders, portfolio managers, cryptocurrency researchers, and finance students, Financial Mathematics for Cryptocurrencies is an indispensable resource for applying established financial mathematics to the digital asset ecosystem. It’s a must-read for everyone developing trading algorithms and pricing models, conducting digital asset analysis, or researching cryptocurrency markets.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preface xvii
Acknowledgments xix
Acronyms xxi
Notations xxiii
Introduction xxv
PART ONE
Fundamentals of Digital Assets
CHAPTER 1
Overview of Digital Assets 3
1.1 Semantics 3
1.1.1 Digital Assets 3
1.1.2 Blockchain 4
1.1.3 Cryptocurrencies and Tokens 4
1.2 Brief History 5
1.2.1 Background 5
1.2.2 Bitcoin 6
1.2.3 Ethereum 7
1.2.4 Tokens and Layer 2 7
1.2.5 dApps and Layer 3 7
1.2.6 Meme Coins 8
1.2.7 NFTs 8
1.2.8 ETFs 9
1.3 Major Coins 10
CHAPTER 2
Topology of Networks 11
2.1 Blockchain Networks 11
2.1.1 Ledger 11
2.1.2 Three Pillars of Blockchains 12
2.1.3 Forks 13
2.2 Sidechains 14
2.3 Technical Characteristics 15
2.3.1 Protocol Layer 15
2.3.2 Consensus Mechanism 17
2.3.3 Anonymity 19
2.4 Network Indicators 19
2.5 Staking 20
2.5.1 Direct Staking 20
2.5.2 Liquid Staking 21
2.5.3 Yield Farming 22
CHAPTER 3
Asset Characteristics 23
3.1 Network Versus Asset 23
3.2 Conventional Asset Classification 24
3.2.1 Financial Instruments and Assets 24
3.2.2 Asset Classes 25
3.2.3 Cash Products 26
3.2.4 Derivatives 26
3.2.5 Options 33
3.2.6 Hybrids 41
3.2.7 Claims and Cash Flows 42
Open Problems 44
PART TWO
Network Valuation
CHAPTER 4
Digital Asset Classification 47
4.1 Prudential Classification 48
4.2 Sector Classification 48
4.2.1 HHR’s Classification 48
4.2.2 Other Sectoral Classifications 49
4.2.3 Limitations 49
4.3 WWS Market Cap Characterization 50
4.4 Ecosystem Classification 51
4.4.1 Schär’s Classification 51
4.4.2 Linnaean Classification 52
4.5 Functional Classification 53
4.5.1 FINMA Classification 53
4.5.2 Enhanced Functional Classification 54
CHAPTER 5
Network Valuation 57
5.1 Market Capitalization Multiple 58
5.2 Business Valuations 59
5.2.1 Peer Comparison 59
5.2.2 Book Valuation 60
5.2.3 Dividend Valuation 60
5.2.4 Cash Flow Valuation 61
5.3 User-based Network Valuations 62
5.3.1 Sarnoff’s Law 62
5.3.2 Metcalfe’s Law 62
5.3.3 Reed’s Law 63
5.3.4 ZBOT Law 63
5.4 Discussion on Network Valuations 65
5.4.1 Comparison of Network Valuations 65
5.4.2 Limitations 65
5.4.3 Beyond User-based Network Valuations 66
5.5 Transaction Volume Pricing 66
5.5.1 Volume Multiple Valuation 66
5.5.2 Block Time Valuations 67
5.5.3 Cost Accounting 67
5.6 Factor Analysis 70
5.6.1 Fundamental Factor Analysis 70
5.6.2 Regressions 71
5.6.3 Principal Component Analysis 72
5.6.4 Limitations 72
5.7 Relative Value Pricing and Interchain Basis 73
5.7.1 Credit Default Swap Basics 73
5.7.2 Interchain Basis 74
5.7.3 Network Default Swaps 74
Open Problems 76
PART THREE
Market Structure
CHAPTER 6
Carry and Storage 79
6.1 Lending and Margin 79
6.2 Carry and Forward Pricing 81
6.2.1 Forward Pricing Framework 81
6.2.2 Foreign Exchange Forward Pricing 82
6.3 Cost of Carry and Convenience Yield 83
6.4 Digital Asset Custody 86
6.4.1 Wallet Types 86
6.4.2 Custodial Models and Exchange Custody 86
6.4.3 Storage Risk and Asset Pricing 88
CHAPTER 7
Liquidity Interface 89
7.1 Traditional Finance Pathways 89
7.2 Stablecoins 90
7.2.1 Definition and Classification 90
7.2.2 Market Development and Regulation 91
7.2.3 Economic Characteristics and Pricing 91
7.3 Tokenized Assets 91
7.3.1 Tokenized Bonds 92
7.3.2 CBDCs and Tokenized Deposits 93
7.3.3 RWA Tokens 93
7.4 Defi Liquidity Interface 94
CHAPTER 8
Cost of Liquidity 97
8.1 Price Decomposition Framework 97
8.1.1 Order Books and Market Structure 97
8.1.2 Economic Surplus and Market Making 99
8.1.3 Mathematical Framework 99
8.2 Components of the Spread 100
8.2.1 Settlement and Counterparty Risk 100
8.2.2 Peg Risk 100
8.2.3 Network and Technical Risk 101
8.2.4 Liquidity Risk 102
8.3 The Blockchain Paradox 103
CHAPTER 9
Fee Models 107
9.1 Fees 107
9.2 Oscillating Fees Model 108
9.3 Extended Fee Models 112
Open Problems 114
PART FOUR
Price Returns
CHAPTER 10
Price Process 117
10.1 Mathematical Framework for Price Processes 117
10.2 Price Returns 118
10.3 Empirical Properties of Financial Time Series 119
10.3.1 Stylized Facts 119
10.3.2 Long-range Dependence Analysis 121
CHAPTER 11
Price Return Models 125
11.1 AR Models 125
11.1.1 ARMA 126
11.1.2 ARIMA 129
11.1.3 Calibration 130
11.2 Constant Volatility Models 131
11.2.1 Geometric Brownian Motion 131
11.2.2 Ornstein-Uhlenbeck Process 134
11.2.3 Lévy Process 135
11.3 Stochastic Volatility Models 136
11.3.1 GARCH Model 136
11.3.2 Heston Model 137
11.3.3 Rough Volatility Models 140
Open Problems 142
PART FIVE
Pricing Theory
CHAPTER 12
Discounting and Staking 145
12.1 Clocks 145
12.1.1 Network Time 145
12.1.2 Market Time 148
12.2 Pricing Assumptions 149
12.2.1 Axioms 149
12.2.2 Terminology 149
12.2.3 Risk-free Rate 149
12.2.4 Compounding 154
12.2.5 Time Value of Money 155
CHAPTER 13
Forward Rate Curve 159
13.1 Rates and Curves 159
13.2 Zero-coupon Bond (ZCB) 161
13.3 Interest Rate Curve 163
13.4 Interest Rate Swap (IRS) 166
CHAPTER 14
Arbitrage Pricing Theory 171
14.1 Numéraire 171
14.2 Martingales 172
14.3 Risk-neutral Measure 173
14.4 Money Market Account 176
14.5 Validator Account 177
14.6 Stablecoins 182
CHAPTER 15
Cross-chain Asset Pricing 183
15.1 On-off-chain Pricing 183
15.1.1 Ex Post Valuation 184
15.1.2 Ex Ante Valuation 185
15.2 Siegel Paradox 186
15.3 Interchain Valuation 188
CHAPTER 16
Overview of Interest Rate Models 191
16.1 CIR Model 191
16.2 SABR Model 192
16.3 SVJC Model 193
16.4 HJM Model 194
Open Problems 196
PART SIX
Staking Contract
CHAPTER 17
Direct Staking Contracts 199
17.1 Direct Staking 199
17.2 With Accrual 202
17.2.1 Ex Post Valuation 202
17.2.2 Ex Ante Valuation 203
17.3 Non-accrual 204
17.3.1 Ex Posts Valuation 204
17.3.2 Ex Ante Valuation 206
17.4 Non-accrual with Queue Mechanisms 207
17.4.1 Ex Post Valuation 209
17.4.2 Ex Ante Valuation 211
17.4.3 Queue Overrun Risk 212
CHAPTER 18
Other Staking Contracts 215
18.1 Liquid Staking 215
18.1.1 Liquid Staking Rewards 215
18.1.2 Pricing in LST Units 216
18.1.3 Protocol Value 217
18.1.4 Pricing Under Blockchain Measure 218
18.1.5 Pricing Only with Peg Risk 219
18.1.6 Pricing with Both LST Rate and Peg Risk 221
18.2 Liquid Restaking 222
18.3 Yield Farming 224
18.3.1 Reward Paid in Native Coin 225
18.3.2 Reward Paid-in-kind 225
Open Problems 227
Afterword 229
Glossary 231
References 235
Disclaimer 253
About the Author 255
Index 257
