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Two dimensional chirp signal has been used for modeling gray scale symmetric images in the statistical signal processing literature. In this paper we propose a computationally efficient algorithm for estimating different parameters of a two dimensional chirp signal model in presence of stationary noise. Starting from a suitable initial guess value, the proposed method produces estimators which are asymptotically equivalent to the corresponding least squares estimators. We also discuss how to obtain the initial estimates suitably. Some simulation experiments have been performed to see the effectiveness of the proposed method, and it is observed that the proposed estimators perform very well.

Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had been obtained by Necula (2002) under constant drift and volatility. We obtain option prices under time varying volatility model. The expression depends on volatility and the Hurst parameter in a complicated manner. We derive a central limit theorem for the quadratic variation as an estimator for volatility for both the cases, constant as well as time varying volatility. That will help us to find estimators of the option prices and to find their asymptotic distributions.