Abstract: We suggest an approach to parametric estimation of the drift function mu(t) in a one-dimensional Ito stochastic differential equation representing a stock price with a variable diffusion parameter sigma such that dSt = mu(t)Stdt + sigmaStdWt from a portfolio consisting of the stock, a call option and a forward contract. The parametric charactrisation of mu(t) is derived from non-arbitrage arguments used to price derivatives. The stock price process is expressed in terms of discretely observed derivative prices and the unobservable discrete market risk premium, the later modeled using the Ornstein-Uhlenbeck process. To address the time variation of volatility sigma, the Black-Scholes implied volatility of the option is used. The resulting system of prices and market risk premium dynamics is then be cast into the state space framework from which the time varying conditional distribution of the market risk premium can be estimated using the Kalman filter. Numerical analysis are carried out using simulated market prices.