Nonparametric pricing of interest rate derivative securities. (English) Zbl 0844.62094

Aït-Sahalia, Yacine

Econometrica 64, No. 3, 527-560 (1996).

Summary: We propose a nonparametric estimation procedure for continuous-time stochastic models. Because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process, we leave the volatility function unrestricted and estimate it nonparametrically. Only discrete data are used but the estimation procedure still does not rely on replacing the continuous-time model by some discrete approximation. Instead the drift and volatility functions are forced to match the densities of the process. We estimate the stochastic differential equation followed by the short-term interest rate and compute nonparametric prices for bonds and bond options.

MSC:

62P05	Applications of statistics to actuarial sciences and financial mathematics
62G07	Density estimation
62M05	Markov processes: estimation; hidden Markov models
91G20	Derivative securities (option pricing, hedging, etc.)

Keywords:

estimation of stochastic differential equations; kernel estimation; discrete-time sampling; option pricing; term structure of interest rates; continuous-time stochastic models; derivative securities; volatility function; drift; short-term interest rate; bond options