Pricing Stock Options with Stochastic Interest Rate

This paper constructs a closed-form generalization of the Black-Scholes model for the case where the short-term interest rate follows a stochastic Gaussian process. Capturing this additional source of uncertainty appears to have a considerable effect on option prices. We show that the value of the stock option increases with the volatility of the interest rate and with time to maturity. Our empirical tests support the theoretical model and demonstrate a significant pricing improvement relative to the Black-Scholes model. The magnitude of the improvement is a positive function of the option's time to maturity, the largest improvement being obtained for around-the-money options

Pricing Stock Options with Stochastic Interest Rate

This paper constructs a closed-form generalization of the Black-Scholes model for the case where the short-term interest rate follows a stochastic Gaussian process. Capturing this additional source of uncertainty appears to have a considerable effect on option prices. We show that the value of the stock option increases with the volatility of the interest rate and with time to maturity. Our empirical tests support the theoretical model and demonstrate a significant pricing improvement relative to the Black-Scholes model. The magnitude of the improvement is a positive function of the option's time to maturity, the largest improvement being obtained for around-the-money options

Non-Standard Errors

In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence-generating process (EGP). We claim that EGP variation across researchers adds uncertainty: Non-standard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for better reproducible or higher rated research. Adding peer-review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants

Taxation and the value of employee stock options

Purpose – This paper aims to derive firm value implications for various kinds of employee stock options (ESOs) in a framework that considers uncertainty, non-diversification and the US statutory tax treatment. Design/methodology/approach – The authors extend the analysis of ESOs from the case of perfect capital markets to two cases of imperfect capital markets using the Benninga-Helmantel-Sarig framework. Findings – It is found that ESOs are inferior to cash compensation and that the degree of option inferiority depends on employee diversification. In addition, incentive stock options (ISOs) are generally inferior to non-qualified stock options (NSOs). This relative profitability of the NSO versus ISO increases as market imperfections are added. The authors also find that in general firm hedging of ESOs is suboptimal. Originality/value – The paper highlights the firm value of employee stock options.Corporate finances, Pay structures, Stock options, Taxation, United States of America