Non-Transferable Non-Hedgeable Executive Stock Option Pricing

David B. Colwell, David Feldman, Wei Hu
2013 Social Science Research Network  
We introduce a method of valuing non-transferable non-hedgeable (NTNH) contingent claims and use it to price executive stock options (ESOs). We use NTNH constraints to break local co-linearity, caused by derivative assets, that renders common portfolio optimization methods ineffective. We are, thus, able to translate portfolios that include NTNH derivatives into portfolios of primary assets (only). We achieve this by replicating derivatives using primary assets, and then integrating NTNH
more » ... grating NTNH constraints into a single rectangular constraint. Solving the constrained portfolio optimization facilitates the identification of stochastic discount factors that price any contingent claim in such portfolios. Implementing our method, we find subjective prices of NTNH European and American ESOs, both for block exercise and for a continuum of exercise rates. We identify executives' optimal exercise policies. We use these to find the objective price/cost of ESOs to firms. We then run a simulation study of price sensitivities and changes to optimal exercise policies with respect to model parameters and obtain policy implications regarding ESOs' incentivizing efficiency. We identify comparative statics results and policy implications that are sensitive to (high/low) volatility regimes. Moreover, for the first time, we demonstrate that unlike under the block exercise of European and American ESOs, with the continuous partial exercise of American ESOs, under a low volatility regime, subjective prices may be higher than objective ones.
doi:10.2139/ssrn.2325601 fatcat:tneaei65bnduddz45vqzeezqpm