Learning Resources

In my eyes, interest rate modeling is one of the most interesting areas of mathematical finance. Interest rate (IR) models are more…

The archetypal fixed income security is the bond . A bond is an instrument of indebtedness of the issuer to the holder . The holder…

Crucial to the modeling of interest rate derivatives is the risk-neutral pricing framework. This framework is expressed in the language…

Some derivatives depend on multiple currencies. If this is the case, the challenge of modeling such derivatives becomes more difficult. In…

In this section, we assign dynamics to the major quantities we have defined thus far. Specifically, we look at the ZCB prices and the…

In this section, we will introduce the various fixed income markets along with an overview of the most basic products that trade . The…

In the previous section we covered the most basic rates derivatives. In the world of fixed income, these products are known as linear…

The plain vanilla swap market has grown into such an active and liquid market that quotes for corresponding swap rates are themselves often…

Bermudan swaptions are a common form of option on swaps. They are similar to standard vanilla swaptions, except the holder has the right…

Investors have grown familiar with the swap or bond format of payout on fixed income securities. Sophisticated market participants seeking…

While standard Bermudan swaptions are Bermudan-style options giving the holder the right to enter into a regular fixed-for-floating swap…

Volatility derivatives are contingent claims where the underlying asset is the volatility of another financial observable, rather than a…

Fundamentally, the goal of an interest rate model is to describe the random movement of a curve of discount bond prices (known as the…

In the previous section, we explored different methodologies of constructing yield curves, in particular, through the use of different…

As we saw in post 6 of this series, European swaptions can be valued as European options on a forward swap rate. Consequently, a full term…

Bonds and Forward Rates