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Unformatted text preview: Economics 141A: Mathematical Finance A Introduction Fall 2010 ( last update: 9/26/10) Goals. The goal of the course is to study asset pricing on financial markets in continuous time. More specifically, our goal is to consider pricing for a class of financial instruments called derivatives. A derivative is a financial security whose price depends on some other security, asset, or benchmark (e.g. an interest rate or a financial index) at a specified future time. The asset on which the derivative depends is called the underlying asset of the derivative security. Examples of underlying assets include stocks, bonds, currency exchange rates, commodities, stock indices, and (yes) other derivatives. Note that the non-derivative securities are based directly on real assets or on payments from the issuer. Purposes for derivatives are hedging (insurance against certain kinds of risk), speculation (via cheap entry and leverage), and arbitrage (taking advantage of mispricing). We will study the mathematical models which are at the heart of pricing financial derivatives, but we will ignore many real-world complications in the modeling and we will not directly address the institutional issues of how existing markets work. (Some of this will sneak in by osmosis.) Some Terminology for Financial Markets. Financial instruments are the objects that are traded in financial markets. A financial contract links two specific parties, e.g. buyer-seller, borrower-lender, etc. A security is a document that confers on its owner a financial claim. Two types of real securities will be particularly emphasized in this course. 1. Stocks a security that gives its holder a specific share of ownership in the issuing company. This gives the holder a corresponding portion of (a) dividends the profits distributed to the stockholders rather than being rein- vested; (b) equity share the value of the firm if it were to close and liquidate. The price of a stock reects what investors (for whatever reason) think its worth. Nobody knows for sure what the price of a stock will be in the future, but there are tools that allow probabilistic estimates. Also, there is uncertainty about the amount of future dividends. The presence of such uncertainties makes a stock a risky asset. 2. Bonds a security that gives its holder the right to a fixed, predetermined payment at a future, pre-set date ( maturity ). There is no uncertainty 1 in the bonds payoff at maturity. Thus, we call a bond a risk-free asset. Although there are at last count well over 1,000 kinds of derivatives, the most common derivative securities are: 1 Actually, this means that there is no uncertainty in the terms of the bond. There are other uncertainties outside this model in the real world such as default risk, inflation risk, and liquidity risk....
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