Portale di Ateneo - En.Unibs.it

1. The financial market

(a) The financial market in discrete time

i. One period market: model with n assets and s states of the world

ii. The asset portfolio: present and future financial wealth

iii. The arbitrage on the market: strong and weak arbitrage, Farkas-Stiemke lemma

iv. Redundant assets (replication)

v. Riskless assets: uniqueness and interest rate

vi. Asset pricing: the fundamental theorem of asset pricing

vii. Compounding and discounting

viii. A new probability: «risk neutral» or «martingale equivalent»

ix. Uniqueness of non-arbitrage price

x. Market completeness

xi. Future price estimation: historical simulation

(b) A multi-period model

i. The stochastic riskless asset

ii. Multi-period compounding

iii. Backward pricing for a cash flow paying asset

iv. The fundamental theorem of asset pricing

v. Infra-period analysis (bond pricing)

vi. A stock price model

(c) Continuous time and space market

i. The riskless asset and the continuous compounding

ii. A stochastic process representing a risky asset

iii. Derivatives and Itô's lemma

iv. Stochastic processes simulation (Euler discretization)

v. Geometric Brownian motion: theoretical properties and parameter estimation

vi. A multi-asset market: variances, covariances, and correlations

vii. Pricing of derivatives written on many underlying assets (multi-dimensional Itô's lemma)

viii. Portfolio dynamics in continuous time

ix. Arbitrage

x. Market price of risk

xi. The risk neutral (or martingale equivalent) probability

xii. The fundamental theorem of asset pricing

xiii. Market completeness

xiv. Switching between probabilities (Girsanov's theorem)

xv. The numéraire and the change in probability

(d) Assets with jumps

i. Poisson jumps

ii. Jump-diffusion stochastic processes for asset prices

iii. Simulation of jump-diffusion processes

iv. Itô's lemma for Poisson jumps

(e) Financial markets and utility

i. Utility and preferences (HARA, CARA, CRRA...)

ii. Critiques to the expected utility

iii. Risk aversion: the Arrow-Pratt index

iv. Inter-temporal utility maximization and asset pricing

2. Interest rate risk

(a) The interest rate

i. Spot and forward interest rates

ii. Relationship between spot and forward rates

iii. Instantaneous interest rates

iv. Interest rate dynamics

v. Historical interest rate

(b) Bond pricing

i. Zero-coupon bonds

ii. Fixed coupon bonds

iii. Floating coupon bonds

iv. Yield to maturity

v. Par yield

(c) Stochastic models for interest rates and bonds

i. Instantaneous interest rate and bond pricing

ii. Forward probability

iii. Duration

iv. Immunization

v. Affine processes for interest rate

vi. Affine jump-diffusion processes

vii. Merton model: theoretical properties and parameter estimation

viii. Vasiček model: theoretical properties and parameter estimation

ix. Cox-Ingersoll-Ross model: theoretical properties and parameter estimation

(d) Yield curve interpolation

i. Nelson-Siegel and Svensson models

3. Measuring risk

(a) The risk

i. Properties of a coherent risk measure (ADEH)

ii. The variance is not a coherent risk measure

iii. (ADEH) Representation theorem

iv. Coherent risk measures

v. Expected Shortfall: theoretical properties and historical simulation

vi. Spectral risk measures

vii. The portfolio optimizing spectral risk measures

(b) Value at Risk

i. The case of the Gaussian distribution

ii. What's wrong with VaR

iii. A comparison between Expected Shortfall and VaR about diversification

iv. CVaR

v. Relationship between Expected Shortfall and VaR

(c) Back-testing

i. Basel proposals

ii. Bask-test thresholds