ASSET PRICING
Syllabus
EN
IT
Learning Objectives
Knowledge and understanding:
Demonstrate an understanding of the underlying economic concepts and theories of asset pricing models.
Apply theoretical frameworks to explain and analyze financial market phenomena.
Critically evaluate the limitations of asset pricing models in explaining the observed financial data.
Applying knowledge and understanding
Applying knowledge and understanding to solve a dynamic portfolio optimization problem.
Applying knowledge and understanding to compute the prices of European and American calls and puts options
Applying knowledge and understanding to extract information from option prices.
Applying knowledge and understanding to compute abnormal returns using the market model and the FF factors.
Making judgments:
Critically evaluate the performance of asset pricing models and analyze how well they fit with empirical data.
Analyze the impact of market frictions and other real-world factors on asset prices.
Communication:
Communicate financial concepts effectively to various audiences both verbally and in writing.
Collaborate with peers to effectively communicate joint work.
Learning skills:
Develop the ability to self-assess.
Demonstrate the ability to learn independently and actively seek out information and resources to deepen understanding of asset pricing concepts and theories.
Develop effective problem-solving skills through regular assignments and simulations.
Demonstrate an understanding of the underlying economic concepts and theories of asset pricing models.
Apply theoretical frameworks to explain and analyze financial market phenomena.
Critically evaluate the limitations of asset pricing models in explaining the observed financial data.
Applying knowledge and understanding
Applying knowledge and understanding to solve a dynamic portfolio optimization problem.
Applying knowledge and understanding to compute the prices of European and American calls and puts options
Applying knowledge and understanding to extract information from option prices.
Applying knowledge and understanding to compute abnormal returns using the market model and the FF factors.
Making judgments:
Critically evaluate the performance of asset pricing models and analyze how well they fit with empirical data.
Analyze the impact of market frictions and other real-world factors on asset prices.
Communication:
Communicate financial concepts effectively to various audiences both verbally and in writing.
Collaborate with peers to effectively communicate joint work.
Learning skills:
Develop the ability to self-assess.
Demonstrate the ability to learn independently and actively seek out information and resources to deepen understanding of asset pricing concepts and theories.
Develop effective problem-solving skills through regular assignments and simulations.
Prerequisites
Financial mathematics (compound intereset rates, force of interest and annuities).
Probability (Discrete and continuous random variables, expectations, conditional probability)
Probability (Discrete and continuous random variables, expectations, conditional probability)
Program
Introduction to Derivatives and arbitrage pricing: 6 ours
Derivatives, Options, Arbitrage opportunities and Put-Call parity formula, Risk-neutral price
and arbitrage pricing, Risk-neutral price, Risk-neutral probability.
Discrete market models: 10 hours
Discrete markets and arbitrage strategies, Self-financing portfolios, Normalized market,
Equivalent martingale measure, Change of numeraire, European derivatives, Pricing in an
arbitrage-free market , Completeness, Fundamental theorems of asset pricing.
Binomial model: 6 hours
pricing and hedging.
Stochastic analysis: 6 hours
Brownian motion and the stochastic integral. Ito Formula (basics)
Arbitrage pricing in continuous time: 8 hours
The Black and Scholes equation, The Black and Scholes formula, completeness and
absence of arbitrage in the Black and Scholes market.
Derivatives, Options, Arbitrage opportunities and Put-Call parity formula, Risk-neutral price
and arbitrage pricing, Risk-neutral price, Risk-neutral probability.
Discrete market models: 10 hours
Discrete markets and arbitrage strategies, Self-financing portfolios, Normalized market,
Equivalent martingale measure, Change of numeraire, European derivatives, Pricing in an
arbitrage-free market , Completeness, Fundamental theorems of asset pricing.
Binomial model: 6 hours
pricing and hedging.
Stochastic analysis: 6 hours
Brownian motion and the stochastic integral. Ito Formula (basics)
Arbitrage pricing in continuous time: 8 hours
The Black and Scholes equation, The Black and Scholes formula, completeness and
absence of arbitrage in the Black and Scholes market.
Books
1. T. Bjork. Arbitrage theory in continuous time. Oxford University Press.
2. J. Cochrane. Asset pricing. Princeton University Press
2. J. Cochrane. Asset pricing. Princeton University Press
Bibliography
1. T. Bjork. Arbitrage theory in continuous time. Oxford University Press.
2. J. Cochrane. Asset pricing. Princeton University Press
2. J. Cochrane. Asset pricing. Princeton University Press
Teaching methods
Theoretical lectures and exercises
Exam Rules
Learning will be verified through a written exam where you will be asked to solve exercises
and to answer theoretical questions on all topics covered during letures.
The exam is passed if the written test is evaluated 18/30 or more. If the exam is passed
(i.e. the mark in the written test is at least 18/30), you can withdraw and repeat the exam in
one of the next exam calls. This can be done ONE TIME ONLY. The mark obtained at the
next exam date cancels the previous mark and cannot be rejected.
To pass the exam, the student must demonstrate the ability to discuss the condition of
no-arbitrage and market completeness and use these characteristics to determine the
pricing of derivatives and hedging strategies. The student must be able to provide both
economic-financial and mathematical justifications for their statements.
Criteria for Formulating the Grade Out of Thirty:
- Not Sufficient: Significant deficiencies and/or inaccuracies in the knowledge and
understanding of the topics; limited analytical and synthesis skills, frequent generalizations.
- 18-20: Barely sufficient knowledge and understanding of the topics with possible
imperfections; sufficient analytical, synthesis, and judgment autonomy skills.
- 21-23: Routine knowledge and understanding of the topics; correct analytical and
synthesis skills with coherent logical argumentation.
- 24-26: Fair knowledge and understanding of the topics; good analytical and synthesis
skills with arguments expressed with sufficient mathematical and economic/financial rigor.
- 27-29: Complete knowledge and understanding of the topics; considerable analytical and
synthesis skills. Good judgment autonomy and arguments expressed with good
mathematical and economic/financial rigor.
- 30-30L: Excellent level of knowledge and understanding of the topics. Remarkable
analytical, synthesis, and judgment autonomy skills. Arguments expressed with excellent
mathematical and economic/financial mastery.
and to answer theoretical questions on all topics covered during letures.
The exam is passed if the written test is evaluated 18/30 or more. If the exam is passed
(i.e. the mark in the written test is at least 18/30), you can withdraw and repeat the exam in
one of the next exam calls. This can be done ONE TIME ONLY. The mark obtained at the
next exam date cancels the previous mark and cannot be rejected.
To pass the exam, the student must demonstrate the ability to discuss the condition of
no-arbitrage and market completeness and use these characteristics to determine the
pricing of derivatives and hedging strategies. The student must be able to provide both
economic-financial and mathematical justifications for their statements.
Criteria for Formulating the Grade Out of Thirty:
- Not Sufficient: Significant deficiencies and/or inaccuracies in the knowledge and
understanding of the topics; limited analytical and synthesis skills, frequent generalizations.
- 18-20: Barely sufficient knowledge and understanding of the topics with possible
imperfections; sufficient analytical, synthesis, and judgment autonomy skills.
- 21-23: Routine knowledge and understanding of the topics; correct analytical and
synthesis skills with coherent logical argumentation.
- 24-26: Fair knowledge and understanding of the topics; good analytical and synthesis
skills with arguments expressed with sufficient mathematical and economic/financial rigor.
- 27-29: Complete knowledge and understanding of the topics; considerable analytical and
synthesis skills. Good judgment autonomy and arguments expressed with good
mathematical and economic/financial rigor.
- 30-30L: Excellent level of knowledge and understanding of the topics. Remarkable
analytical, synthesis, and judgment autonomy skills. Arguments expressed with excellent
mathematical and economic/financial mastery.