This course is an introduction to the modern approach to the pricing of financial assets based on the stochastic discount factor (SDF) methodology. This methodology gives the representation of the price of any financial asset as the expectation of its stochastically discounted final payoff. It allows to treat in a unified way the pricing problem of financial assets under general market conditions, including settings with, for instance, stochastic interest rates and volatilities.
In the theory part of the course, we fist introduce the SDF approach to the representation and the computation of asset prices in a discrete-time setting. Benchmark applications to the pricing problem under stochastic volatilities or stochastic interest rates will then be highlighted. In the applied part of the course, we make usef of the SDF approach to understand and empirically implement recent proposals for the model-free modelling and trading of volatility and other risks like skewness using suitable option portfolios. While this part provides the foundations for well-known volatility and skew indeces used in the practice, such as the CBOE VIX and SKEW indeces, it offers more generally a powerful unifying methodology for defining tradable model-independent notions of nonlinear risks that are easily implemenable in practice.
Empirical and numerical analysis will be conducted in programming language Python. Empirical analyses are based on option market data available from the Optionmetrics database.