Inflation derivatives pricing with a forward CPI model

The Zero-Coupon Inflation Indexed Swap (ZCIIS) is a derivative contract through which inflation expectations on the Consumer Price Index (CPI) are actively traded in the US. In this thesis we consider different ways to use the information from the ZCIIS market for modeling forward inflation in a risk-neutral framework. We choose to implement a model using a Monte Carlo methodology that simulates the evolution of the forward CPI ratio. We prefer this approach for its flexibility, ease of implementation, instant calibration to the ZCIIS market and intrinsic convexity adjustment on the inflation-linked payoff. Subsequently, we present a series of results we obtain when modeling a chain of consecutive CPI ratios for simulating the evolution of spot inflation. Furthermore, we use this for pricing inflation caplets and floorlets. Finally, we use the intuition gained from this exercise to analyse our results for pricing inflation caps