Pricing and Hedging Financial Derivatives: A Guide for Practitioners

5

The Fundamentals of Option Pricing

In this chapter, we discuss the basics of option pricing. There is some mathematics but we have kept it to a minimum. We will discuss the basic terminology in options and options pricing and we will explain why volatility of asset prices is important but the direction of movement is not. We will look at the nature of the time value of options, i.e., the price of optionality. We will discuss the Black–Scholes framework for pricing options and begin looking at the idea of the delta of an option and how it is relevant to the construction of portfolios that have no directional exposure. Finally, we will move on to option replication and risk-neutral valuation.

5.1 INTRINSIC VALUE AND TIME VALUE OF AN OPTION

5.1.1 Introduction and definitions

The essential feature to consider when building a framework for option pricing is related to the idea of intrinsic value and the time value of an option. We will use IVO_t to denote the intrinsic value of the option at time t and TVO_t to denote the time value of the option at time t.

For a call option, the intrinsic value at time t is the difference, if positive, between the actual price of the underlying at time t (S_t) and the strike price (K); if this difference is negative, the intrinsic value is equal to zero since the option has no intrinsic value.

For a call option: IVO_t = max(S_t − K, 0)

For a put option, the intrinsic value at time t is the difference, if positive, between the strike price (K) and the ...