Quantitative Finance and Insurance

1. Intermediate knowledge of microeconomics, econometrics-statistics, finance is very useful, as we cover advanced material.
2. Erasmus students without such background may not want to chose this course, because time for catching up is very short.
3. Institutional arrangements of financial markets are taken for granted. They are covered in ch. 1-4 of the Bodie Kane Marcus textbook.
4. Professor Alberto Plazzi, visiting from USI Lugano, will teach a module in Empirical Asset Pricing showing Matlab codes. It is straightforward to turn from Matlab to Python in case you do not master Matlab.

 asset pricing and investments.

This enables to make informed choices about portfolio management on the one side and stock market outcomes on the other.

This course presents methods for portfolio choice and asset pricing.

FIRST PART: Portfolio Choice and Asset Pricing  (Elisa Luciano).

1. CAPM review and discussion

see Bodie, Kane and Marcus (Investments,
McGrawHill, any edition) or
Copeland and Weston (Corporate Finance, any edition) or Cvitanic and Zapatero (Intro to
the Econ and Math of Financial Markets, MIT press, ch. 4, 5.1, 13).

2. Pricing of redundant securities in a single period model

a motivating example.
definition of redundant versus basic securities
arbitrage
fundamental theorem of asset pricing
complete versus incomplete markets: necessary and sufficient conditions for
the market to be complete.
state prices, stochastic discount factor and risk-neutral probabilities.
complete markets characterization.
replication and hedging
example revisited

see ch 2 in Dumas, Luciano, The Economics of Continuous-time Finance, 2nd ed., MIT press, 2017 + its exercises

3. Pricing of redundant securities in a multiperiod model
Information arrival over time and dynamic models
dynamic budget constraints
self financing strategies
arbitrage
complete vs incomplete markets
martingale pricing
replication
hedging
the binomial model as an example

See ch 2 in Dumas, Luciano, The Economics of Continuous-time Finance, 2nd ed., MIT press, 2017 + its exercises

4.  Optimality and non-redundant asset pricing
Single period
Optimality
Fisher
Arrow Debreu and simple claims
Complex claims
The stochastic discount factor

See ch 3 in Dumas, Luciano, The Economics of Continuous-time Finance, 2nd ed., MIT press, 2017 + its exercises

5. Optimality and non-redundant asset pricing
Multi period
Recursive optimality
Global optimality
The stochastic discount factor

See ch 3 in Dumas, Luciano, The Economics of Continuous-time Finance, 2nd ed., MIT press, 2017 + its exercises

6.  Equilibria
In one-period economies:
risk sharing
CAPM
isoelastic utility
incomplete market equilibrium
In multiperiod economies:
Radner vs Arrow Debreu equilibria
risk sharing

See ch 4 in Dumas, Luciano, The Economics of Continuous-time Finance, 2nd ed., MIT press, 2017 + its exercises

7. Continuous-time portfolio optimality

See ch 9 in Dumas, Luciano, The Economics of Continuous-time Finance, 2nd ed., MIT press, 2017 + its exercises

8. From static to dynamic equilibria in continuous time & CAPM extensions
Lifetime budget constraint
Static vs dynamic optimization and equilibria characterization

See ch 10-11 in Dumas, Luciano, The Economics of Continuous-time Finance, 2nd ed., MIT press, 2017 + their exercises

9. Asset pricing puzzles
Anomalies
Markets with restricted participation as a solution for the puzzles
Basak and Cuoco
Panageas

See ch 15 in Dumas, Luciano, The Economics of Continuous-time Finance, 2nd ed., MIT press, 2017 + its exercises;

Basak, S. and Cuoco,D., An Equilibrium Model with Restricted Stock Market Participation, The Review of Financial Studies, 1998, 11 (2), pp. 309-341;

Panageas, S., The Implications of Heterogeneity and Inequality for Asset Pricing”, Foundations and Trends in Finance: Vol. 12, No. 3, pp. 199–275. DOI: 10.1561/0500000057

SECOND PART:

Return Predictability (Alberto Plazzi)

The final program for the 2nd part will be available on Moodle in mid-February.

Written exam:

there will be three composite questions or exercises, each on a different topic, with limited space for precise answers to the questions and explanations/proofs.

Questions will concern all parts of the program, including the part taught by Professor Plazzi.

20'-30' per question. 10 points each.

Questions may refer to discussion in the classroom that may not be reflected in the material.   

The maximum number of tests (3) that each student can sit for during the
academic year is established by Article 21, Comma 7 of the ESOMAS Department's
teaching regulations. Withdrawals (ritiri) count towards the limit.

Oral optional (if written >= 18)