仿射通货膨胀市场模型
The affine inflation market models
摘要：
利率市场模型，如LIBOR市场模型，具有基本模型量在金融市场中可直接观察的优点。通货膨胀市场模型将这种方法扩展到通货膨胀市场，其中零息和同比通货膨胀指数掉期是基本的可观察产品。对于通货膨胀市场模型，迄今为止，只存在一种互换的封闭公式，但不存在两种。本文中的模型使用仿射过程，使得两种类型的掉期价格都可以显式计算。此外，看涨期权和看跌期权的两种类型的互换利率可以使用一维傅立叶反演公式计算。使用导出的公式，我们提出了一个例子校准市场数据。
英文摘要：
Interest rate market models, like the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where zero-coupon and year-on-year inflation-indexed swaps are the basic observable products. For inflation market models considered so far closed formulas exist for only one type of swap, but not for both. The model in this paper uses affine processes in such a way that prices for both types of swaps can be calculated explicitly. Furthermore call and put options on both types of swap rates can be calculated using one-dimensional Fourier inversion formulas. Using the derived formulas we present an example calibration to market data.
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