Faculty of Economics and Business Administration Publications Database

Optimal Trend Estimation in Geometric Asset Price Models

Volume: 24
Number: 1
Pages: 51 - 70
Link External Source: Online Version
Year: 2005
Keywords: Geometric asset price model; Trend estimation; Wiener process; Ornstein-Uhlenbeck process; Kernel reproducing Hilbert space; Exogeneous shocks; Compound Poisson process

In the general geometric asset price model, the asset price P(t) at time t satisfies the relation

P(t) = P0 ·e  a·f(t) + s·F(t)  ,     t Î [0,T],

where f is a deterministic trend function, the stochastic process F describes the random fluctuations of the market, a is the trend coefficient, and s denotes the volatility.

The paper examines the problem of optimal trend estimation by utilizing the concept of kernel reproducing Hilbert spaces. It characterizes the class of trend functions with the property that the trend coefficient can be estimated consistently. Furthermore, explicit formulae for the best linear unbiased estimator [^(a)] of a and representations for the variance of [^(a)] are derived.

The results do not require assumptions on finite-dimensional distributions and allow of jump processes as well as exogeneous shocks.