Course Description:
Financial models have come to be used extensively in the
securities industry. In this course we will study models for pricing and hedging equity,
fixed income and credit derivative securities. The course begins by developing a
standard tool for hedging and risk management known as regression hedging. Models
and theoretical underpinnings for pricing equity options are covered next. In addition to
standard European and American equity options on a single underlying asset, we will
investigate the pricing and hedging of path-dependent options, such as barriers,
lookbacks, and Asian options, and multi-asset options, including spread,
outperformance, and basket options. We will study the standard Black-Scholes model
and its multi-asset extension, and will also cover jump-diffusion and stochastic volatility
models which are capable of explaining some observed deviations of option prices from
the Black-Scholes model, e.g., the implied volatility smile. Since derivative securities are
typically held as part of larger portfolios, we will briefly cover the topics of asset
allocation and portfolio optimization.
Investments over long time horizons can have very
different characteristics than short-term investments, so we will also study multiperiod
investment planning. The pricing of fixed income derivatives requires a model of the
evolution of the entire yield curve. After investigating the statistical properties of yield
curve movements, we will study the Ho-Lee and Black-Derman-Toy single-factor interest
rate models and then proceed to the general multi-factor Heath-Jarrow-Morton interest
rate model. These models will be used to price caps, floors, swaptions, callable bonds,
and other interest-rate sensitive securities. The course will conclude with a brief
introduction to the pricing and hedging of credit sensitive securities, e.g., credit default
swaps.
Faculty/Manager:
Ciamac Moallemi
Contact Information:
Ciamac Moallemi
email: ciamac@gsb.columbia.eduCredits for Course: 3 Viewing Schedule: 2 lectures per week Notes: Syllabus
* The information contained in this syllabus is subject to change at any time.