Lattice Method of Real Option Analysis - Solving the Curse of Dimensionality and Strategic Planning

Abstract

The deregulation policy introduces uncertainties into the power market. The power market uncertainties have increased the significance of two factors in decision analysis: financial risks and managerial flexibility. Real option analysis enables such flexibility to management. There are several major methods under real option analysis: traditional black-Scholes option-pricing method, lattice (binomial and trinomial) methods, Monte Carlo simulation method, and finite element (explicit, implicit, and Crank-Nicolson) method. This paper concentrates on the lattice method. Lattice model is easy to implement, appreciate and understand. However, when the investment duration is large (or the length of model period - step size is small), the lattice model becomes a massive bush of lattice, which is known as the curse of dimensionality. This paper proposes a new efficient methodology of solving the curse of dimensionality for the lattice model. The massive bush of lattice model can be reduced by analyzing the boundary of the lattice where the decision changes. This can be achieved via the implementation of value at risk into the lattice model. Besides reducing the degree of dimensionality, this new methodology also specifies "when" a decision changes. This is a very critical part in strategic budgeting planning. Timing and simplification yet maintaining high accuracy in analysis are essential in the new deregulated power economic uncertainties.