Financial Derivatives and Partial Differential Equations by Robert Almgren (American Mathematical Monthly Vol. 109, Jan. 2002, pp. 1-11)
This well-written article is aimed at mathematically literate readers who want an introduction to finance. The basic theory of pricing and hedging several types of options are introduced. Then Ito’s Lemma, the Black-Scholes equations are derived heuristically. The variables and parameters related to these equations are explained and the notations are “translated” into financial terminology. For examples, the fact that the Black-Scholes equation is linear means that (i) two identical options are worth twice as much as one option and (ii) a portfolio consisting of two different options has a value equalling the sum of the individual options. For those mathematical or financial concepts which the author does not have space to explain, he provides excellent references. This article is recommended for anyone who wants a first glimpse of the modern theory of finance without having to read through one of the other tomes in this review!