Derivatives Demystified: A Step-by-Step Guide to Forwards, Futures, Swaps and Options, Second Edition

14

Option Valuation Concepts (2)

INTRODUCTION

Chapter 13 explained the basics of option pricing. It discussed the binomial pricing approach and the industry-standard Black-Scholes model for valuing European stock options. It described the inputs to the model and the importance of volatility. This chapter introduces the concept of implied volatility and explains its applications. It uses Black-Scholes to show how the values of calls and puts are affected by changes in the spot price of the underlying. Finally, the chapter explores issues relating to pricing index, currency and interest rate options.

PROBLEMS WITH HISTORICAL VOLATILITY

The advantage of using historical volatility to price an option is that (normally) the sample data are readily available and the calculation is quite straightforward. In fact all the necessary functions required to work out the mean and the standard deviation for a set of data are included in spreadsheet packages such as Excel. However, there are serious practical and theoretical problems when using historical volatility to price options.

• The Sample Data. What is the correct historical time period on which to base the sample of price data? Perhaps it is best to use data from the last few months, since this is likely to be most representative of the current behaviour of the underlying. However, this risks not capturing the more extreme price movements that happen infrequently. This could underestimate volatility. Equally, including data that ...