2017/10/02 by Kamil Kladívko, Kladivko, Kamil, Mihail Zervos +1
Business, Management and Accounting · Economics, Econometrics and Finance · #Capital Investment and Risk Analysis #Corporate Finance and Governance #FOS: Economics and business #FOS: Mathematics #Financial Reporting and Valuation Research #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1710.00897
openalex publication_date 2017/10/02 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
We consider the problem of ESO valuation in continuous time. In particular,\nwe consider models that assume that an appropriate random time serves as a\nproxy for anything that causes the ESO's holder to exercise the option early,\nnamely, reflects the ESO holder's job termination risk as well as early\nexercise behaviour. In this context, we study the problem of ESO valuation by\nmeans of mean-variance hedging. Our analysis is based on dynamic programming\nand uses PDE techniques. We also express the ESO's value that we derive as the\nexpected discounted payoff that the ESO yields with respect to an equivalent\nmartingale measure, which does not coincide with the minimal martingale measure\nor the variance-optimal measure. Furthermore, we present a numerical study that\nillustrates aspects or our theoretical results.\n