Risk Simulator Real Options SLS title= Modeling Toolkit PEAT ESO Valuation ROV BizStats
Risk Simulator Runtime ROV Compiler ROV Extractor ROV Optimizer ROV Dashboard ROV Webmodels
Quantitative LSRO SDK rov-visual-modeler


Risk Simulator
Real Options SLS title=
Modeling Toolkit
ESO Valuation
ROV BizStats
Risk Simulator Runtime
ROV Compiler
ROV Extractor
ROV Compiler
ROV Dashboard
ROV Webmodels

Reduce Employee Stock Option (ESO) expenses by millions of dollars using the same software FASB uses to generate its FAS 123 examples

Learn how a FAS 123 preferred customized binomial lattice is calculated and how it compares to the naïve Black-Scholes. The software creator is an advisor to FASB and a professor and consultant in financial analytics, and the software was used by FASB to create the valuation examples in FAS 123. See how considering employee suboptimal exercise behavior, forfeiture rates, blackout periods, vesting, marketability discounts, and changing inputs over time (volatility, dividend yield, risk-free rate, forfeiture rate, and suboptimal behavior exercise multiple) can more accurately reflect reality, reduce expenses, conform to FAS 123 requirements, and pass an audit. See how ESO Valuations are done correctly!

Real Options Valuation, Inc. has created several proprietary software through its partners, including the following software:

  • Employee Stock Options Valuation Toolkit
  • Super Lattice Solver for Real Options Valuation
  • Multiple Super Lattice Solver for Multiple Assets

In most cases, our services include providing these software solutions to our clients at the end of the consulting project, as well as providing customized software, models, and analytical codes that are very specific to the client’s situation. Click here for a sample case study on applying FAS 123 and click here to download the software data sheet. Please contact us directly to obtain a demo version of the software.


  • Our software products were developed by Dr. Johnathan Mun, advisor to FASB on FAS 123.
  • Use the same software FASB uses! Software was used by FASB to create the valuation example in the 2004 FAS 123 (Appendix A87).
  • Our software models both closed-form models (Black-Scholes) as well as different binomial and trinomial lattices.
  • Theories are all covered extensively in the author’s books and articles- use the published books/research to successfully defend an audit
  • All equations are visible within Excel when creating your own option valuation models.
  • Costs a lot less than expensive consultants have the ability to check their work instead!
  • Have the ability to compare the naïve Black-Scholes versus more sophisticated binomial lattice results (FASB’s preferred method).
  • Consulting projects will be implemented by Dr. Johnathan Mun, finance professor, consultant, and author of many well-known books.


  • American Closed-Form Models
  • Binomial and Trinomial Lattices
  • European Black-Scholes


  • Blackout Periods
  • Changing Forfeiture Rates
  • Changing Risk-free Rates
  • Changing Volatilities
  • Forfeiture Rates (Pre- and Post-vesting)
  • Stock Price Barrier Requirements
  • Suboptimal Exercise Behavior Multiple
  • Vesting Periods


FASB Uses This Software! The figure below shows the solution of the case example provided in Appendix A87 of the Final 2004 FAS 123.

  • Specifically, A87-A88 states:
  • “A87. The following table shows assumptions and information about the share options granted on Jan 1, 20X5:
  • Share options granted 900,000;
  • Employees granted options 3,000;
  • Expected forfeitures per year 3.0%;
  • Share price at the grant date $30;
  • Exercise price $30;
  • Contractual term (CT) of options 10 years;
  • Risk-free interest rate over CT 1.5 to 4.3%;
  • Expected volatility over CT 40 to 60%;
  • Expected dividend yield over CT 1.0%;
  • Suboptimal exercise factor 2;

A88. This example assumes that each employee receives an equal grant of 300 options. Using as inputs the last 7 items from the table above, Entity T’s lattice-based valuation model produces a fair value of $14.69 per option. A lattice model uses a suboptimal exercise factor to calculate the expected term (that is, the expected term is an output) rather than the expected term being a separate input. If an entity uses a Black-Scholes-Merton option-pricing formula, the expected term would be used as an input instead of a suboptimal exercise factor.”


From the corporations…

“Veritas has modeled the valuation of its employee stock options for analytical purposes using a proprietary customized binomial lattice, developed by Dr. Johnathan Mun. The valuation based on the customized binomial lattice model allows us to take into account the impacts of multiple vesting periods, employee suboptimal exercise behavior, forfeiture rates, changing risk-free rates, and changing volatilities over the life of the option which are required under the 2004 FAS 123 issued by the Financial Accounting Standards Board. It is not possible to consider these factors in a valuation based on the traditional modified Black-Scholes model. Under the assumptions used by Veritas when modeling the valuation of employee stock option grants both based on the customized binomial lattice model as well as the traditional modified Black-Scholes model, the customized binomial lattice model resulted in a considerably lower expense, considering the expensing guidelines as included in the FAS 123 Statement.”

-Don Rath, VP of Tax & Stock Admin., Veritas Software Corp.

From the consultants…

“This is one of those rare books/software written in anticipation of a major shift in the industry and economy. FAS 123 will throw a lot of public companies in a frantic, however the smart ones are identifying the opportunity to master the process and take over the driving seat. The methodology and the tools developed by Dr. Johnathan Mun are proven, pragmatic, and offer a great deal of value and benefit to those early adopters. IBCOL Consulting AG is using Dr. Mun’s algorithms and methodology because of their applicability, and accuracy, and the fair-market values that we have obtained for our clients are significantly less than traditional Black-Scholes models.”

-Dr. Markus Junginger, Managing Partner, IBCOL Consulting

From the software developers…

“After extensive review of the FASB exposure draft and consideration of a variety of option valuation methodologies, E*TRADE FINANCIAL has decided to implement a binomial lattice model, in consultation with Dr. Johnathan Mun. We found Dr. Mun’s work on employee stock option pricing very valuable.”

– Naveen Agarwal, Director, Product Management , E*TRADE Corporate Services

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Dublin, California 94568