An option pricing by eliminating observation noise when the model parameters are unknown

Abstract

The stock price that is observed in the market contains irregular fluctuations that cannot be explained by the theory. We assume this kind of fluctuation to be observation noise. By eliminating observation noise from the underlying stock price, we can evaluate the option that better reflects the entity price. We define the stock price that eliminates observation noise as the entity stock price. The most important problem in eliminating the observation noise is the choice of unknown constant parameters of the market model. We develop a parameter estimation method by using the relationship between stock price and its option price or future price. We obtain satisfactory results in testing the algorithm by some simulations. We apply the parameters obtained by this method to estimate the stock price by eliminating observation noise from the real market data. We then calculate the call option price based on the estimated entity stock price.