Pricing models for inflation-linked bonds?

Question

I need to price an inflation-linked bond issued by italian government. Which models are indicated for this bond? I think I can price bond as a FRN plus an option on inflation rate.

But, first problem: how can I find data on inflation to estimate volatility? Second problem: I have path dependency on the result of the option (if inflation becomes negative, to have the premium inflation has to get higher than the last maximum), how to face this? which kind of option can I use? thanks

Answer 1

I think you are referring to the BTP Italia series of bonds issued by the Italian Treasury, aimed at retail investors and linked to the Italian inflation rate. These bonds are issued in Euro, have a fixed coupon, plus they pay out semi annually any increase in the Italian inflation index, which is the "FOI ex-tobacco" index. Here is a link http://www.dt.tesoro.it/en/debito_pubblico/btp_italia/

Typically these bonds are valued by just discounting the fixed coupons at a fair market real rate of interest. eg if the 10yr bonds carry a 1.75% coupon, but the fair real rate is 1.65%, then they are worth 100% of par plus the present value of 10bp for 10yrs. The fair real rate is usually judged versus other sovereign issuers in a similar way that nominal bonds are compared.

As you mention, a significant complication is the embedded option in the inflation calculations. It is stated in the terms that the Inflation index is effectively protected from going down, so that the inflation payments can never be negative. This is a complicated path dependent option. The way I would value it is to download a history of the relevant index, calculate its historical volatility, and build a monte carlo simulation of the bond value without this feature versus the bond value with this feature. Intuitively I would expect the floor to have some value, since the Eurozone has been flirting with deflation in the last few years.