Financial Economics — lecture notes

Lec 04 #

Arbitrage opportunity

Pice bounds for options

Put-call parity

Binomial model

Blackscholes

Lec 05 #

Pricing by arbitrage

We have multiple linear independent assets (think of polymarket contracts)

Arbitrage portfolio

Lec 06 #

Economic analysis of asset markets

• Pareto-optimal allocations

• Contract curve

• Market clearing condition: everything sold by one is bought by another

• Comotinicity

• Price responce to risk changes

Lec 07 #

Uncertain environments:

• compound lottery $λL+(1−λ)L′$

• Preference relation

  • Complete $for any L and L′∈L(Z ) we have L ⪰L′or L′⪰L$

  • Transitive $(L1 ⪰L2 and L2 ⪰L3) ⇒L1 ⪰L3$

• VNM (Von Neumann and Morgenstern) Expected Utility Theory

  • Independence

  • Continuity

Risk Averse

• Utility Index u

• Expected utility function v

• VNM preferences is risk averse if and only if her utility index is concave

Risk increase

• SOSD: Second-order stochastic dominance: if dominant then less risky than other

  • $EL[x] ≥EL′[x]$

  • $\int_{-\infty}^{y} F_L(x)dx \leq \int_{-\infty}^{y} F_{L'}(x)dx$ less weight on smaller returns

• Mean preserving spread -> more risk

• White noise: mean 0, can be seen as risk

Quantifying Risk Aversion

• Certainty Equivalant: uncertain lottery utility compared to a certain lottery

• Risk Premium: Expectation - certainty equivalant $\pi_L = E_L[x] - e_L$

• Risk Aversion coefficient

Lec 10 #

CAPM: combination of risk free asset and tangent portfolio

Sharpe Ratio: Slope of riskfree + risky of efficient frontier = sharpe ratio

Tangent Portfolio has the highest sharpe ratio among risky assets