Fixed Income Markets: Management, Trading and Hedging, 2nd Edition

CHAPTER 17 Options II

We continue with options in this chapter with a look at how options behave in response to changes in market conditions. To start, we consider the main issues that a market maker in options must consider when writing options. We then review “the Greeks”, the measures by which the sensitivity of an option book is calculated. We conclude with a discussion on an important set of interest-rate options in the market, caps and floors. Options may seem complex at first sight, but there are many analogies in the behaviour of option price sensitivity to bond sensitivity measures.

BEHAVIOUR OF OPTION PRICES

As we noted in the previous chapter, the value of an option is a function of five factors:

1. The price of the underlying asset; Notation: S
2. The strike price of the option; Notation: K
3. The time to expiry of the option; Notation: T
4. The volatility level of the underlying asset price returns; Notation: σ
5. The risk-free interest rate applicable to the life of the option. Notation: r

The Black-Scholes model assumes that the level of volatility and interest rates stays constant, so that changes in these will impact on the value of the option. On the expiry date, the price of the option will be a function of the strike price and the price of the underlying asset. However, for pricing purposes an option trader must take into account all the factors above. From Chapter 16 we know that the value of an option is composed of intrinsic value (IV) and time value (TV); intrinsic ...