Economics and Technology of Financial Innovation

GENERAL INFORMATION

  • Stay updated on the business/finance news and check how the markets are doing during the course. (See for exampe Yahoo Finance)
  • Prepare the exam using the slides and the associated material – the slides alone are not enough for a deep understanding of the topics.

Teaching Assistant:
Davi Marim (davi.dealmeidamarim@telecom-paris.fr)

Grading
Problem sets 50%
Exam: 50%

PROBLEM SETS

  • Form groups of 4-3 people to solve the problem sets together.

  • Theory exercises can be handed either in Latex or as pictures of paper documents.
  • Programming and empirical exercises can be done in any language (preferably in Python whenever possible).
  • Business cases can be handed in Word.
  • Groups can manage a private Github to store the solutions to the problem sets.

Exam

3 exercises:
– problem
– case study
– economic modeling

LECTURES

LECTURE 1. The Landscape of Digital Finance
Slides L1

Readings:

  • European Central Bank (2024). Study on the payment attitudes of consumers in the euro area (SPACE). ECB.
  • Bank for International Settlements (2022). Payments and digital money. BIS.
  • European Central Bank (2022). Neobanks: Business models and financial stability implications. ECB.
  • Ahnert, T., Hoffmann, P., & Monnet, C. (2022). The digital economy, privacy, and CBDC. ECB / CEPR seminar paper.
  • Nagel, R. (1995). Unraveling in guessing games: An experimental study. American Economic Review.
  • Frost, J. (2020). The economic forces driving fintech adoption across countries. BIS Working Papers No. 838. Bank for International Settlements.

Sample Balance Sheets

Markets:
https://coinmarketcap.com/
https://polymarket.com/
https://www.justetf.com/

LECTURE 2. Money
Slides L2

Readings:

  • Kiyotaki, N., & Wright, R. (1993). A search-theoretic approach to monetary economics. American Economic Review, 83(1), 63–77.
  • Williamson, S. D., & Wright, R. (2010). New monetarist economics: Methods. Federal Reserve Bank of St. Louis Review.
  • Lagos, R., Rocheteau, G., & Wright, R. (2017). Liquidity: A new monetarist perspective. Journal of Economic Literature.
  • Lagos, R., & Wright, R. (2005). A unified framework for monetary theory and policy analysis. Journal of Political Economy.
  • Kocherlakota, N. R. (1998). Money is memory. Journal of Economic Theory.
  • Fernández-Villaverde, J. (2018). Cryptocurrencies: A crash course. University of Pennsylvania, lecture notes / working paper.
  • McLeay, M., Radia, A., & Thomas, R. (2014). Money creation in the modern economy. Bank of England Quarterly Bulletin, Q1.

Handouts:
Poisson Process in Search Theory
Kiyotaki-Wright Model

Other resources:
Nash Bargaining

LECTURE 3. Blockchain: Cryptography and Nakamoto Consensus
Slides L3

Readings:

  • Nakamoto, S. (2008). Bitcoin: A Peer-to-Peer Electronic Cash System. Self-published whitepaper.
  • Back, A. (2002). Hashcash – A Denial of Service Preventive Measure. Mimeo
  • Biais, B., Bisiere, C., Bouvard, M., & Casamatta, C. (2019). The Blockchain Folk Theorem. The Review of Financial Studies.
  • Guo, D., & Ren, L. (2022). Bitcoin’s Latency–Security Analysis Made Simple. Proceedings of the 4th ACM Conference on Advances in Financial Technologies (AFT ’22).
  • Haber, S., & Stornetta, W. S. (1991). How to time-stamp a digital document. Journal of Cryptology, 3(2), 99–111.
  • Merkle, R. C. (1987). A Digital Signature Based on Conventional Encryption. Advances in Cryptology — CRYPTO ’87
  • Koblitz, N. (1987). Elliptic curve cryptosystems. Mathematics of Computation
  • Miller, V. S. (1985). Use of elliptic curves in cryptography. Advances in Cryptology — CRYPTO ’85, 417–426.

Books:

  • Shi, E. (2020). Foundations of Distributed Consensus and Blockchains – Chapter 14. (online)
  • Narayanan, A., Bonneau, J., Felten, E., Miller, A., & Goldfeder, S. (2016). Bitcoin and Cryptocurrency Technologies: A Comprehensive Introduction. Princeton University Press.

Other resources:

Julien Prat’s course on blockchain:
https://sites.google.com/site/julienpratecon/teaching/blockchain?authuser=0

Example of ECC:
– elliptic curve over the reals
– elliptic curve over prime field
– attempt to guess the private key from public key and generator

LECTURE 4. BFT-Blockchains, DAG-Blockchains, and Scaling Solutions
Slides L4
Presentation on Ethereum

LECTURE 5. Trading, Hedging, and Market-Making

Slides L5

Readings:

  • Cochrane, J. H. (2005). Asset pricing (Rev. ed.). Princeton University Press.
  • Milgrom, P., & Stokey, N. (1982). Information, trade and common knowledge. Journal of Economic Theory.
  • Glosten, L. R., & Milgrom, P. R. (1985). Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of Financial Economics.
  • Kyle, A. S. (1985). Continuous auctions and insider trading. Econometrica.
  • Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy.
  • Avellaneda, M., & Stoikov, S. (2008). High-frequency trading in a limit order book. Quantitative Finance.

LECTURE 6. Digital Currencies in International Finance
Slides L6


Readings:

  • Benigno, P., Schilling, L. M., & Uhlig, H. (2022). Cryptocurrencies, currency competition, and the impossible trinity. Journal of International Economics.
  • Fernández-Villaverde, J., & Sanches, D. (2023). A model of the gold standard. Journal of Economic Theory.
  • Fernández-Villaverde, J., & Sanches, D. (2024). Price-level determination under the gold standard. Federal Reserve Bank of Philadelphia Working Paper.
  • Clayton, C., Maggiori, M., & Schreger, J. (2026). A framework for geoeconomics. Econometrica.
  • Clayton, C., Maggiori, M., & Schreger, J. (2025). Putting economics back into geoeconomics. NBER Macroeconomics Annual.
  • Clayton, C., Dos Santos, A., Maggiori, M., & Schreger, J. (2025). Internationalizing like China. American Economic Review.
  • Mundell, R. A. (1963). Capital mobility and stabilization policy under fixed and flexible exchange rates. Canadian Journal of Economics and Political Science.
  • Fleming, J. M. (1962). Domestic financial policies under fixed and under floating exchange rates. IMF Staff Papers.

Handouts:
Handout on Lagos-Wright model

DIARY:


Day 1

The digitalization of finance:
– shifts in payment methods, market volumes, business models
– new actors in the financial economy (bigtech, fintech, wealthtech)
– financial innovation and financial inclusion
– business model and balance sheet  
– attention markets: meme stocks, meme coins
– information markets: polymarket

Asset values and coordination games:
– the Keynesian Beauty Contest game (experiment guess 2/3 of average)
– Nash Equilibrium of the Keynesian Beauty Contest

Basic economic notions:
– equity, debt, stock, bond, asset, liability
– long position, short position, strike price, spot price
– inflation, nominal value, real value
– discount factor, discount rate

Money:
– historical examples of monies
– money as unit of account, medium of exchange, and store of value

Money as a Network Good:
– first encounter with the Kiyotaki Wright model
– conditions for sustaining money exchanges
– coordination failure and multiplicity of equilibria

Day 2

– Recap on definition of money

– Kiyotaki Wright (KW) model basics (2 periods)

– WK with single coincidence meetings in discrete time:
— model definition: agents, payoffs, states, distributions, value functions
— From discrete time to continuous time
— Equilibria of the KW model (non-monetary, monetary, and mix)
— Welfare calculation in the KW model

– Poisson process in continuous-time search and matching models
— Poisson distribution
— Exponential random variable
— Minima of exponential RVs
— Probability of state arrivals
— Derivation of the Bellman equation (Value function in recursive form)

– KW with double coincidence meetings and barater
— model definition,
— equilibrium,
— welfare

– KW with idle producer state (V0, Vg, Vm)
— value function
— steady state balance equation
— equilibrium system


Day 3

Money creation (modern system)
— narrow vs broad money (cash/reserves vs deposits)
— “loans create deposits” (bank balance sheet expansion)
— constraints on lending: reserves/settlement, funding cost, regulation, default risk

Policy rates and the role of the central bank
— central bank sets the price of money (policy rate), not a money quantity
— ECB rate vs Euribor (interbank)
— nominal vs real: r≈i−πr \approx i-\pi
— quantity-theory rule of thumb: MV=PYMV = PY

QE and “whatever it takes”
— zero lower bound
— quantitative easing: central bank buys assets to inject liquidity
— Draghi “whatever it takes” as commitment moment

Private money / crypto motivation
— distrust in discretionary money + account control (freeze/censorship)
— “digital gold” idea (scarcity narrative)
— policy debate on crypto

From toy coins to blockchain
— GoofyCoin: signatures work, but double spending is possible
— ScroogeCoin: central ledger fixes double spending, but centralizes power
— distributed consensus problem

Bitcoin / Nakamoto consensus (3 rules)
— proof-of-work: find nonce s.t. H(⋅)<DH(\cdot) < D
— longest-chain rule (resolve forks)
— confirmations: wait k blocks for finality

Crypto tools used
— hash functions (tamper-evident chaining)
— Merkle trees (logn verification)
— public-key signatures (ECC)

Incentives + security preview
— miner income: block reward + fees (later: MEV)
— security intuition: honest vs attacker “Poisson race”; deeper blocks harder to rewrite

Day 4

– Recap on blockchain as decentralized money and record-keeping
-– Blockchain infrastructure
–— public-key infrastructure: public key, private key, signing, verification
–— double spending problem
–— hash chaining of transactions
–— SHA-256 and immutability

– Economics of blockchain
— why miners / validators participate
— block rewards and transaction fees
— Bitcoin as deflationary “digital gold”
— Ethereum and alternative tokenomics

– Recap of Nakamoto consensus
— proof of work
— longest-chain rule
— confirmation rule

– Blockchain security
— Poisson race model (honest chain vs adversarial chain)
— notion of probabilistic security
— 50% threshold intuition
— Probability tools
–— Moment generating function
–— Markov inequality
–— Chernoff bounds
–— exponential tail bounds
–— Random walk
-– Formal security properties
–— liveness
–—– chain growth
–—– chain quality
–— consistency / safety

– Financial markets recap
— asset classes: stocks, bonds, currencies, commodities
— indices and ETFs
— yield curve

Day 5

– Recap on financial markets
— asset classes: stocks, bonds, currencies, commodities
— yield curve: yield as a function of maturity
— normal, inverted, and hump-shaped yield curves
— link between bond yields, macro expectations, and central-bank rates

– Futures and forwards
— futures as standardized contracts for future delivery
— forwards as less regulated bilateral contracts
— spot price vs futures price
— commodity examples: oil, Brent benchmark, delivery month conventions
— interpreting the oil futures curve under geopolitical risk

– No-arbitrage pricing of forwards
— payoff of a long forward: ST−F0S_T – F_0
— replication with spot asset + borrowing/lending
— cost-of-carry formula
— arbitrage intuition when forward price differs from replicated value

– Bond pricing and the yield curve
— zero-coupon bonds and discounting
— relation between bond prices and yields
— rolling over short-term bonds vs holding a long-term bond
— forward rates and no-arbitrage restrictions across maturities

– Derivatives
— distinction between forwards/futures and options
— call option: right to buy at strike price at maturity T
— put option: right to sell at strike price at maturity T
— option payoffs

– Economic intuition of option pricing
— hedging vs speculation
— replication principle
— derivative pricing under complete markets and no arbitrage
— one-period binomial model
— replicating portfolio with stock and bond

– Stochastic calculus (intuition)
— random walk as building block
— Brownian motion as continuous-time limit of random walk
— mean, variance, and normal increments
— Brownian motion as model of continuous asset-price shocks
— quadratic variation and why dW^2 = dt (a.s.)
— Itô multiplication table
— Itô’s lemma as the chain rule for stochastic processes

– Black–Scholes pricing
— stock price as geometric Brownian motion
— self-financing replicating portfolio
— dynamic hedging and delta hedging
— Black–Scholes partial differential equation
— interpretation of Δ\Delta as sensitivity of option value to the stock price

– Risk-neutral pricing
— pricing by replication vs pricing by expectation
— idea of changing from the physical to the risk-neutral measure
— discounted expected payoff under the risk-neutral measure
— preview of applications to later topics in international finance

Day 6

– Recap on Option Pricing and Complete Markets
— the Black-Scholes formula requires two main assumptions: no arbitrage and complete markets
— no arbitrage guarantees the existence of a replicating portfolio and thus a price
— complete markets guarantee the uniqueness of the replicating portfolio and price
— a market is “complete” if the traded assets span the entire payoff space, allowing any state-contingent payoff to be replicated
— state prices allow the price of an asset today to be expressed as a weighted sum of its state-dependent payoffs in the future

– Risk-Neutral Pricing
— the price of an option does not depend on the asset’s drift ( $\mu$ ) because dynamic hedging neutralizes the trend
— under complete markets and no arbitrage, probabilities can be mathematically rescaled to a “risk-neutral measure”
— under this measure, the expected return of all assets is simply the deterministic risk-free rate ( $r$ )
— derivation of the Black-Scholes partial differential equation using risk-neutral expectations and Itô’s lemma

– The Lagos-Wright Model (Continuous Money)
— moves beyond the Kiyotaki-Wright model by treating money as a continuous variable rather than a binary 0 or 1 state
— solves the complex problem of tracking wealth distribution by splitting each period into a centralized market and a decentralized market
— Centralized Market (CM): perfectly liquid market where agents work, consume, and rebalance their money holdings to the exact same optimal amount for the next day
— Decentralized Market (DM): features liquidity friction and Poisson matching, where agents must carry money to trade “special goods”
— value function linearity: the value function in the centralized market is linear with respect to an agent’s current money holdings
— purchasing power ( $\phi$ ) and the opportunity cost of holding money
— the nominal interest rate on bonds is pinned down by the must reflect the liquidity services provided by money
— welfare discussions: the Friedman rule advocates for zero nominal interest rates (deflation) to eliminate the opportunity cost of holding money

– International Finance and Open Economies
— transition from closed economy models to open economies with imports, exports, and exchange rates
— using the IS-LM model for policy: central bank interest rate hikes to prevent overheating cause capital inflows, which appreciate the home currency and hurt net exports
— Uncovered Interest Parity links foreign interest rates, domestic interest rates, and exchange rates

– The Impossible Trinity (Trilemma)
— an open economy cannot simultaneously achieve fixed exchange rates, monetary independence, and free capital mobility
— a country can choose at most two of these three goals
— example: if a country wants fixed exchange rates and free capital mobility, it loses independent monetary policy and must synchronize interest rates

– Global Digital Currencies
— extending the Mundell-Fleming model to include a globally adopted third currency (e.g., a widespread stablecoin or CBDC)
— crypto-enforced monetary policy synchronization: the widespread use of a global digital currency forces countries to synchronize both their interest rates and exchange rates, weakening national monetary sovereignty
— distinctions between native crypto (volatile, speculative), stablecoins (pegged to fiat), and CBDCs (digital fiat backed by the state)