Asset Pricing and Derivatives
Prof. Rasa Karapandza, Ph.D.
This module presents classical and modern ideas of finance with an applied focus. Students will master the analytic tools and the financial theory for making smart investments but also to hedge risks by using stocks, bonds, and financial derivatives.
The asset pricing course covers recent developments in investments, bridging the gap from the basic finance courses to the current research and practice. Asset pricing has gone through a lot of change over the last decades. We have realized that expected returns do vary across time, and across assets in ways that the CAPM does not recognize. The course starts with an overview of important methods from mathematics and statistics, software tools, and financial data. It continues with the pricing of bonds and other fixed-income instruments, discusses the risks associated with fixed-income investments, demonstrates the methods to derive zero-coupon yield curves, and shows how to hedge interest rate risk. The course then deals with stocks and covers the following topics: Predictability of stock returns, The cross-section of stock returns, Asset pricing theory (utility, discount factors, expected returns, CAPM, ICAPM, APT), Empirical asset pricing methods (time-series, cross-sectional and Fama-MacBeth regressions). We also study the performance of Mutual funds and Hedge funds.
The derivatives course aims to give an overview of derivatives markets and to illustrate basic methods of derivatives pricing. The course starts with the mechanics of derivatives markets, and introduces forwards and futures, and the application of these instruments in hedging. The no-arbitrage argument is used to derive prices of the most important types of forwards and futures. The course continues with options, their properties, trading strategies involving options, and a brief overview of exotic options. These topics are followed by interest-rate derivatives, CDSs, commodity, energy, and weather derivatives.
The second part of the course introduces stochastic processes used for asset price modeling, Itô’s lemma, and general principles of risk-neutral pricing in continuous time and its relationship with the no-arbitrage principle. Partial differential equations and risk-neutral expected values are used as two equivalent ways to price derivatives and other contingent claims. Here, the Black-Scholes-Merton model is introduced as an illustration of these principles in option pricing. Some related topics, such as option “Greeks” and volatility smiles, are presented. The course concludes with the most important numerical methods used in derivatives pricing, with an emphasis on Monte Carlo simulations.