Multiple Time Scales Stochastic Volatility Modeling Method in Heath-jarrow-morton Model of Interest Rate Market

Download or read book Multiple Time Scales Stochastic Volatility Modeling Method in Heath-jarrow-morton Model of Interest Rate Market written by Feiyue Di and published by . This book was released on 2011 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: We utilize multiple time scales processes in consistent dynamic modeling to capture main time scales and heterogeneity features of the volatility process of Heath-Jarrow-Moton models in the fixed income market. The Black-Scholes type HJM models are prevailing in both industry and academy. However since these models assume that the volatility process of the underlying financial contract is constant during the term period, they are not able to incorporate some implied volatility phenomenons emerging after the Crash of 1987. Stochastic volatility modeling is one of the main approach to overcome the above defects of the Black-Scholes type models. By applying the time scale separation, that is, the singular perturbation method, we show that the stochastic volatility HJM model we proposed are parsimonious and robust effective models. In fact, we carry out this framework on the linear finite dimensional realizable HJM models, derive the explicit pricing formulas of floorlet contracts under this stochastic volatility HJM models and estimate the accuracy of the result. Meanwhile, as a specific example, we studied the stochastic volatility Hull-White model explicitly. Besides the pricing function of the floorlet contracts, we also obtain the explicit form of the pricing function of the swaption. Following the calibration procedures we proposed, we calibrated this model by a group of daily swaption data from PIMCO. The calibration result shows that the mutliple time scales stochastic volatility Hull-White model is able to capture the implied volatility smile and this model is stable statically.