Pricing and Hedging of Derivative Contracts

In this class we will cover basic ideas and their related methods to price and hedge derivative contracts. The material in this class is most useful if the students have a minimum knowledge of derivative pricing (familiarity with the concepts and main ideas of hedging, as taught in an introduction to Finance class) as well as to be comfortable with using basic calculus and basic statistics. Simple programming will be used too.

The program is divided in two related parts:

Part A: General Valuation of Derivatives

-       Review of Basic Binomial Formula for risk-neutral probability, risk-neutral variation, Delta, and pricing of derivatives. American vs European options.

-       Numerical Implementation of Binomial Formula.

-       Black-Scholes as Limit of Binomial. Lognormal change of probability, risk neutral density.

-       Derivation of Fundamental p.d.e. for the pricing a derivative. Linear vs Non-linear pde’s (ie. European vs American options).

-       (Numerical) Solution methods for p.d.e’s. coming from a derivative contract.

-       Exotic and path dependent derivatives. Monte Carlo valuation. Numerical Techniques.

Part B: Derivatives on Volatility, VIX and others.

-       Derivatives on Volatility: Variance Swaps

-       VIX and Variance Swaps.

-       Stochastic Volatility, and derivatives on VIX.


Fernando Álvarez

I am the Saieh Family Professor of the Kenneth C. Griffin Economics Department of the University of Chicago.

My main area of research interest is macroeconomics, including asset pricing, labor economics, and monetary economics as subareas of specialization. Within these areas I have worked on the effects of monetary policy on the liquidity effect on interest rates, the determination of risk premium on asset prices, household money demand and choice of means of payments, and the effect of nominal rigidities on price setting, among others.

I am an Econometric Society Fellow, an Economic Theory Fellow, a Research Associate of the National Bureau of Economic Research, and a member of the American Academy of Arts & Sciences. I have served as editor of the Journal of Political Economy, associate editor at other journals, and referee for all the top economic journals. I have received grants from the National Science Foundation, the Goldman Sachs Global Market Institute (as fellow), the European Research Council, the Fondation Banque de France, the Alfred P. Sloan Foundation (as fellow), and the Tinker Foundation. I have been a Visiting Scholar at the EIEF (Enaudi Institute of Economics and Finance), and at the Research Department of the European Central Bank (as the Wim Duisenberg Fellow); a consultant at the Research Departments of the Federal Reserve of Minneapolis, the Federal Reserve Bank of Chicago, and the Federal Reserve Bank of Philadelphia; and a Visiting Researcher advising the Board of Directors of the Argentine Central Bank.

My  previous academic position was in the Finance Department of the Wharton School of the University of Pennsylvania. My main teaching responsibilities at the University of Chicago are the first core macroeconomics class at the doctoral level, advance topics on monetary economics at the doctoral level, and Speculative Markets at the undergraduate level. My teaching experience includes short doctoral and post doctoral courses taught at the Toulouse School of Economics, the Cowles's Foundation for Research in Economics at Yale University, the International Monetary Fund, the European Central Bank, the House of Finance at Goethe University, and the Swiss National Doctoral Program.