##### Department of Mathematics,

University of California San Diego

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### Math 196 - Student Colloquium

## Amber Puha

#### California State University, San Marcos, Department of Mathematics

## The Mathematics of Options Pricing

##### Abstract:

Consider the question of how a derivatives security (e.g., a call option) should be priced. Due to their potential utility for hedging and speculation, economists started becoming interested in this question in the early 1900s. In the late 1960s, this emerged as an important concern for finance markets as well, due to a relaxation in regulations that allowed insurance companies and banks to invest in derivatives. After decades of growing interest and research efforts, Fisher Black and Myron Scholes developed a mathematically based pricing strategy in the early 1970s that was later simplified and expanded on by Robert Merton. The resulting formulas revolutionized trading practices worldwide. In 1997, Merton and Scholes received the Nobel prize for this body of work (Black had passed away and therefore was ineligible). In the talk, we will examine an extremely simplified version of this body of work. In particular, we will analyze the single-period Cox-Ross-Rubenstein (CRR) model using some of the key principles and methodologies that Black, Scholes, and Merton developed to construct their derivatives pricing theory. Despite the fact that this model is very simple, the analysis will illustrate certain essential aspects of their Nobel prize winning work such as dynamic hedging and the risk neutral probability measure. This will give a flavor of the mathematical content of Math 194, being offered in the winter quarter.

Host: Glenn Tesler

### November 12, 2013

### 11:00 AM

### AP&M B402A

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