C# for Financial Markets

17

Swaption, Cap and Floor

17.1 INTRODUCTION AND OBJECTIVES: A CLOSED FORMULA WORLD

In this chapter we introduce some very simple interest rate options, namely cap floor and swaption. For many traders the Black formula represents the market practice to price these instruments, considering rates as tradable assets. We discuss some simple approaches for building a caplet's volatility surface and to manage a given swaption matrix. The Black formula is used to calculate the Greeks and it is the accepted formula to compute implied volatility starting from brokers' markets prices. Of course, the calculated implied volatility depends not only on the option price but also on how the money forward rates are estimated and discount factors are calculated. Brokers directly quote Black volatilities. It is assumed that market participants are able to calculate prices from volatilities using formulae presented in Section 17.2. In this chapter we discuss a traditional approach using the single-curve methodology; we do the same for estimating forwards and for discounting. Several formulae and a short explanation for the multi-curve framework are described. A possible solution for managing the pricing and volatilities stripping process using C# code is also presented. More complex and advanced market models are not illustrated here since they are outside the scope of this book.

17.2 DESCRIPTION OF INSTRUMENTS AND FORMULAE

Caps, floors and swaptions are the most popular OTC interest rate options. ...