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Lenos Trigeorgis, A Log-Transformed Binomial Numerical Analysis Method for Valuing Complex Multi-Option Investments, The Journal of Financial and Quantitative Analysis, Vol. 26, No. 3 (Sep., 1991), pp. 309-326

Abstract We extend the Fama-French (1992) model by considering growth option (as well as distress/leverage) variables in explaining the cross section of stock returns. We find that growth option variables, namely growth in capital investment and yet-unexercised growth options (GO), are significantly and negatively related to stock returns. Investors may be willing to accept lower average returns from growth stocks in exchange for a more favorable (positively skewed) risk-return profile. Book-to-market (BM) ratio seems to proxy for omitted distress/leverage variables. When these are explicitly accounted for, BM is not that significant. Our growth options variables have added explanatory power.

We provide a real options framework for the analysis of product development that incorporates research and exploration actions, product attribute value-enhancing actions with uncertain outcome, as well as preemption and innovation options. We derive two-stage analytic formulas and propose a general multi-period solution using a numerical lattice approach. Our analysis reveals that exploration actions are more important when the project is out or at-the-money (near zero NPV) and less important for high project values. In a multi-stage setting, exploration actions are important even for in-the-money projects, when follow-on actions exist that can enhance the expected value of the project. With path-dependency, early actions are more valuable since they enhance the impact or reduce the cost of subsequent actions. Preemptive controls affecting rare event (jump) frequency and innovations that introduce positive jumps are more valuable for firms with higher frequency of competitive threats involving low volatility.

We examine the empirical properties of the theoretical Black–Scholes–Merton (BSM) bankruptcy model. We evaluate the predictive ability of various existing modifications of the BSM model and extend prior studies by estimating volatility directly from market-observable returns on firm value. We show that parsimonious models using our direct market-observable volatility estimate perform better than alternative, more sophisticated, models. Our findings suggest the adoption of simpler modelling approaches relying on market data when implementing the BSM model.