Overview. Financial Section Overview This web space is devoted to a novel approach to the analysis of financial data. The underlying idea is that much of the behavior of financial markets can be described by heavy-tailed statistical distributions. We do not make the assumption that the descriptive distribution is stationary. Stable distributions are used as a tool for modeling data and the scale parameter of a stable distribution is used to estimate volatility of returns.
All of the analysis is based on the distribution of logarithmic returns -- differences in logarithms of prices. The site map below shows suggested pathways through the material. Our research has led to a new set of distributions, the lognormal - stable and lognormal - normal. As the site has grown to more than 70 pages, the thread of a theory of markets that is evolving is hard to follow. New A power tail model for market returns with a double Pareto distribution. Email comments and questions to Bob Rimmer. MathFinance 345. Statistics 390/ Mathematical Finance 345 Fall 2001 Professor Steve Lalley 118 Eckhart Hall Office Hours: Thursday 1:00 - 2:30 Phone: 702-9890 E-mail: lalley "atsign" galton.uchicago.edu Bookmark this page! As the course progresses, I will post Lecture Notes, homework assignments, and other information here. WARNING: Do not reproduce or distribute the lecture notes posted on this web page.
Unauthorized reproduction or distribution of the contents of this page is a copyright violation. The most famous and important paper in mathematical finance may be downloaded at no charge here . EXAMS. WEEKLY REVIEW. Short-rate model. A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written The short rate[edit] Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate.[1] The short rate, , then, is the (continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time .
Specifying the current short rate does not specify the entire yield curve. However no-arbitrage arguments show that, under some fairly relaxed technical conditions, if we model the evolution of as a stochastic process under a risk-neutral measure then the price at time of a zero-coupon bond maturing at time is given by where is the natural filtration for the process. Particular short-rate models[edit] Throughout this section , is assumed to follow an Ornstein–Uhlenbeck process and. A Proposed Fat-Tail Risk Metric: Disclosures, Derivatives, and the Measurement of Financial Risk - Washington University Law Review. The General Theory of Employment, Interest and Money by John Maynard Keynes.