Dynamic Asset Pricing

FIN-615 / 3 crédits

Enseignant: Andrei Daniel

Langue: Anglais

Remark: To register, please contact edfi@epfl.ch. The timetable and location is available on the Google doc below under "Websites" (1 tab per term).

Frequency

Every year

Summary

This course provides an advanced, research-oriented introduction to the methods and results of continuous-time (dynamic) asset pricing.

Content

This course develops the main tools of continuous-time finance stochastic control and the martingale approach and uses them to study optimal portfolio and consumption choice, general-equilibrium asset pricing, the major asset-pricing puzzles, and richer environments featuring recursive utility, habit formation, learning under incomplete information, and heterogeneous beliefs.

It is not a course in applied mathematics: it is a course on how to do economics using a particular kind of applied mathematics as a tool. Its aim is to build the economic intuition and technical fluency needed to begin original research in theoretical asset pricing.

The course is compressed into eight sessions. Some material is developed in lectures; the remainder is assigned as required reading that students are expected to master independently. A tentative outline is as follows:

 

Session 1: Mathematical foundations and continuous-time tools

- Dynamic programming: the Bellman and Hamilton-Jacobi-Bellman (HJB) equations; the Euler equation

- Stochastic processes, Brownian motion, and Itô's lemma

- Reviewed quickly - assumed through FIN-415; see readings

Session 2: No-arbitrage and the Black-Scholes paradigm

- Hedging-, replicating-, and martingale-pricing arguments

- The stochastic discount factor and the change of measure (risk-neutral pricing)

- The Feynman-Kac formula

Session 3: Individual optimality I - portfolio and consumption choice

- The intertemporal budget constraint and Merton's problem

- Optimal portfolio choice with constant investment opportunities (CRRA and CARA utility)

- The dynamic-programming (HJB) approach

Session 4: Individual optimality II - hedging demands and the martingale approach

- Random investment opportunities and intertemporal hedging demands

- Myopic versus strategic portfolios; the (M+2)-fund theorem

- The martingale / static-budget approach to portfolio choice

Session 5: Equilibrium in continuous time

- The representative agent and the consumption CAPM (CCAPM)

- The intertemporal CAPM (ICAPM) and the role of state variables

- Global optimization and the stochastic discount factor in equilibrium

Session 6: Asset-pricing puzzles

- The equity-premium, risk-free-rate, and excess-volatility puzzles

- Hansen-Jagannathan bounds

- Equilibrium in affine settings; the term structure of risk

Session 7: Recursive utility and habit formation

- Non-time-additive (Epstein-Zin) preferences and the timing of the resolution of uncertainty

- Equilibrium in affine settings with recursive utility

- Internal and external habit formation

Session 8: Incomplete information, learning, and heterogeneous beliefs

- Filtering in continuous time (the Kalman-Bucy filter) and learning

- The impact of learning on asset prices

- Heterogeneous beliefs and disagreement: noisy rational expectations versus differences of opinion

Time permitting, the final sessions also connect the material to current research questions in the field.

Keywords

Dynamic asset pricing; general equilibrium; optimal portfolio choice; stochastic control; recursive utility; habit formation; learning; heterogeneous beliefs; asset-pricing puzzles.

 

Learning Prerequisites

Required courses

-  FIN-415 Probability and Stochastic Calculus
-  FIN-701 Asset Pricing

 

Important concepts to start the course

-  Foundations in probability theory and statistics
-  Working knowledge of stochastic calculus
-  Working knowledge of discrete-time asset pricing

 

Learning Outcomes

By the end of the course, the student must be able to:

  • Solve a dynamic portfolio and consumption-choice problem using both the dynamic-programming and the martingale methods
  • Construct and solve a continuous-time general-equilibrium asset-pricing model
  • Characterize the main asset-pricing puzzles and the mechanisms proposed to address them
  • Analyze models featuring recursive utility, habit formation, learning, and heterogeneous beliefs

Transversal skills

  • Demonstrate the capacity for critical thinking
  • Plan and carry out activities in a way which makes optimal use of available time and other resources.

Teaching methods

Lectures, with problem sets assigned regularly and discussed in class.

Expected student activities

  • Class attendance
  • Weekly readings
  • Weekly problem sets

Assessment methods

- Final written exam - 60%
- Problem sets (in class) - 25%
- Referee report - 15%

Each student is assigned a research paper at the start of the course and submits a written referee report on it by the final session.

Resources

Bibliography

The course draws on research papers and on the following texts:

-  Dumas and Luciano, The Economics of Continuous-Time Finance, MIT Press, 2017

-  Munk, Financial Asset Pricing Theory, Oxford University Press, 2013

-  Duffie, Dynamic Asset Pricing Theory, Princeton University Press, 2001

-  Ziegler, Incomplete Information and Heterogeneous Beliefs in Continuous-Time Finance, Springer, 2003

A complete list of references will be distributed in the first session.

 

Ressources en bibliothèque

Websites

Dans les plans d'études

  • Forme de l'examen: Ecrit (session libre)
  • Matière examinée: Dynamic Asset Pricing
  • Cours: 28 Heure(s)
  • Type: obligatoire

Semaine de référence

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