On the Pricing of Inflation-Indexed Caps
16 Pages Posted: 30 Nov 2006 Last revised: 23 Apr 2009
Date Written: April 22, 2009
We consider the problem of pricing inflation-linked caplets in a Black-Scholes-type framework as well as in the presence of stochastic volatility. By using results on the pricing of forward starting options in Heston's Model on stochastic volatility, we derive closed-form solutions for year-on-year inflations caps which aim to receive smile-consistent option prices. Additionally we price options on the inflation development over a longer time horizon. In this paper we develop a new and more suitable formula for pricing inflation-linked options under the assumption of stochastic volatility. The formula in the presence of stochastic volatility allows to cover the smile effects observed in our Black-Scholes type environment, in which the exposure of year-on-year inflation caps to inflation volatility changes is ignored. The chosen diffusion processes reflect the macro-economic concept of Fisher making a connection between interest rates on the market and the expected inflation rate.
Keywords: Inflation-indexed options, year-on-year inflation caps, Heston model, stochastic volatility, option pricing
JEL Classification: G13
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