Presentation given by Matthew Dodgson and Dherminder Kainth at Risk Training Course, London, September 2006.
Since the introduction of government-issued bonds linked to inflation indices in many major currencies, a liquid market in inflation-linked swaps and other derivatives has grown. The main interest in buying protection from increases in inflation comes from those with inflation-linked liabilities such as pension funds. On the other hand, there are many groups with income linked to inflation (e.g. retail companies), who are well-placed to sell this protection. Inflation-linked derivatives are a convenient way to acquire the desired inflation exposure. In addition there are now several hybrid products available which can guarantee a real (inflation-floored) return, but which still tap into gains in some other asset (e.g. an equity index).
In this talk we will cover the pricing of inflation derivatives within a correlated Hull-White model. Here we consider the short interest rate and the inflation rate as diffusive processes with mean reversion. For constant volatiltiy there are exact results in closed form for simple options. We price more complex derivatives using Monte Carlo sampling. This method also allows us to introduce generalizations to the model (e.g. local volatility) in order to capture the dependence of market prices on, say, the strike of an inflation caplet.
This model naturally includes hybrid products that involve both interest rates and inflation (e.g. a floating rate-inflation rate swap). We also generalize to a third stochastic process to allow other hybrids.