R Programming for Actuarial Science

33 Financial Options: Pricing, Characteristics, and Strategies

Peter McQuire

library(matrixcalc)
library(derivmkts)

33.1 Introduction

The purpose of this chapter is to develop an understanding of the fundamental concepts of financial options, and to write code to tackle various problems involving such options.

The chapter starts with a brief discussion of the key components of a financial option contract, and applies the famous Black-Scholes-Merton (“B-S-M”) formula to analyse the dependence of the option price on a number of factors. We proceed to discuss how options may be used in the market, that is, speculation, leveraging, and risk management. In particular, we look at a technique used by options traders known as delta hedging.

Please note that only a brief description of financial options is included below; it is assumed that the reader will have alternative sources of learning material in this respect. In particular, we will not formally derive the B-S-M equation, although a sketch is provided in Section 33.11; the full derivation can be found in countless textbooks and its duplication here is unwarranted. Apart from a discussion on the riskless portfolio in Section 33.11, we will cover little theory in this chapter.

33.2 What is a Financial Option?

A financial option is a contract which gives the buyer of the option contract the right (or “option”) to either buy or sell an agreed asset at an agreed time (or times) for an agreed price. If the option is to buy the underlying ...