Kalman filter approach to real options with active learning

Abstract

Technological innovations often create new markets and this gives incentives to learn about their associated profitabilities. However, this decision depends not only on the underlying uncertain profitability, but also on attitudes towards risk. We develop a decision-support tool that accounts for the impact of learning for a potentially risk-averse decision maker. The Kalman filter is applied to derive a time-varying estimate of the process, and the option is valued as dependent on this estimation. We focus on linear stochastic processes with normally distributed noise. Through a numerical example, we find that the marginal benefit of learning decreases rapidly over time, and that the majority of investment times occur early in the option holding period, after the holder has realized the main benefits of learning, and that risk aversion leads to earlier adoption. We find that risk-aversion reduces the value of learning and thus reduces the additional value of waiting and observing noisy signals through time.