Jerry Marlow, MBA  
 Valuation of Stock Options in Divorce Proceedings

Are the stock options in the divorce you're handling being valued at their full and fair economic value?
In many divorces today, stock options account for a significant portion of the marital wealth to be divided. For anyone not familiar with option-valuation methodologies, the fair economic value of options can be difficult to understand. Consequently attorneys who represent employee spouses all too often get away with valuing options at their so-called "intrinsic value." An option's "intrinsic value" is almost always less than its fair economic value. It is often zero.

The valuation models coming into play under the FASB 123 rules are almost as unfair to non-employee spouses as is "intrinsic-value" methodology. The FASB 123 rules prescribe how corporations should account for employee stock options in their financial reports. People refer to the models being used under FASB 123 as "option-valuation models." But that's not what they are. They are models for estimating the expense that a corporation is likely to incur from issuing options. Most of the models assume that an employee will exercise the options "suboptimally." In other words the models assume the employee will engage in a bad bargain. A model that posits and factors in bad bargains does not produce fair economic values.

When stock options are undervalued in a divorce, the non-employee spouse does not receive her or his fair share of that portion of the marital wealth.

To make it easier for attorneys, their clients, and courts to understand the economic value of options and to ensure that options are valued fully and fairly, I offer two services: seminars and valuations.


Seminar: How to Value Stock Options in Divorce Proceedings
With the publication of Option Pricing: Black-Scholes Made Easy in 2001, I introduced a powerful new way for the non-mathematician to understand option-valuation theory. Computer simulations show clearly that the value of an option is the probability-weighted present value of the option's possible payoffs.

Seminar attendees, finance professors, investors and the financial press all have hailed the educational and analytic power of the simulations I have created.

With the understanding that this technology makes attainable, as an attorney or expert witness, you can say to a judge, “Your honor, to value these options, we looked at how much the price of this company’s stock jumps around in the marketplace. We conservatively assumed that, on average, the stock will perform no better than a government bond. Based on those two factors and using the standard model of how stock prices change over time, we ran a million simulations of what the payoff of these options might be when they expire in seven years. The average payoff for the options was $26.24. The present value of $26.24 is $19.85. Hence, based on conservative assumptions and standard option-valuation methodologies, the fair economic value of these 10,000 options is $198,500. That value is fully consistent with the value of options for sale in the financial markets today."

In seminars on option valuation, I explain and demonstrate the theory, the models, and the methodology that allow an attorney or an expert witness to make this kind of statement. To do so, I use the Option Pricing: Black-Scholes Made Easy simulations and similar software I have developed for binomial pricing models. The technically accurate and highly visual simulations make it easy for anyone to understand the economic value of options and how options are valued in the financial marketplace. Attendees at my seminars are amazed at how quickly they can master heretofore difficult topics.

If you would like for me to conduct a one- or two-day seminar for your firm, colleagues or professional organization, I would welcome the opportunity to do so.

The seminar will teach you to think about options in a new and highly visual way. You will understand how to value stock options at their full and fair economic value. You will learn how to explain mainstream option-valuation methodologies to non-mathematicians.

To arrange for a seminar, contact me at (917) 817-8659 or jerrymarlow@jerrymarlow.com.


Download Seminar Notes
If you would like to know more about the seminar topics and to see screen captures of some of the simulations I use, you can download a copy of my seminar notes.


Valuation of Stock Options in Divorce Proceedings
As usually explained option-pricing theory is difficult for the non-mathematician to understand. Only a small percentage of judges have advanced degrees in mathematics. Unless an attorney or option expert can explain option-valuation methodology in a way that a court can understand, stock options that are part of marital wealth may end up being undervalued.

The fair economic value of any financial asset is the probability-weighted present value of its possible future cash flows. Standard, generally accepted option-pricing theories provide systematic methodologies with which to determine this value. The determinants of an option’s value are the current market price of the underlying stock, how much the market price of the stock is expected to jump around (stock-price volatility), the risk-free rate of return, the option’s strike or exercise price, the option’s length of time to expiration, and the amounts of any dividends the underlying stock is expected to pay.

In the option valuations that I do, I use the technology I have developed to demonstrate how these factors translate into an option’s probability-weighted present value: The greater the uncertainty about a stock’s future value, the greater the value of an option written on that stock. The longer an option’s time to expiration, the greater the option’s value. (An option’s so-called “intrinsic value” is the value the option would have if its time to expiration were zero.) At their time of issue, employee stock options typically have times to expiration of seven to ten years.

The option values I arrive at are fully consistent with the values of options traded in the financial marketplace. The documentation I provide is easy to understand.

If you are handling a divorce in which stock options are a significant part of the marital property and you would like for the options to be valued at their full and fair economic value, then have me value the options for you. I can show you, your client, and the court how the value of the options is obtained in a way that you and they can understand.

You can contact me at (917) 817-8659 or jerrymarlow@jerrymarlow.com.


Sample Option Valuation
To download a sample valuation, click sample option valuation.

Information I Need
To find out what information I need you to gather so I can value your or your spouse's options, click information I need to value your options.

Fee Schedule
For my fee schedule and payment terms, click fee schedule.
Valuation Methodology
If you would like to know more about the methodology I use to value stock options, download a copy of my seminar notes.
Jerry Marlow, MBA
Valuation of Stock Options in Divorce Proceedings
(917) 817-8659
jerrymarlow@jerrymarlow.com

 

 

What seminar attendees, finance professors, investors, and the financial press have to say about Jerry Marlow's seminars, simulations and approach to teaching option-pricing methodologies

Just a brief thank you for the two-day course on valuing options (with an emphasis on divorce valuation) that you presented to my group last week. The group consisted of a number of my peers/competitors, all of us moderately to heavily experienced in forensic accounting and business valuations. Thus, it was not an easy audience to satisfy. However, you did it. We all recognize how dry the options valuation topic is, but nonetheless, my personal reaction and those of my fellow attendees was most positive. All of us felt that we got considerable value out of the program, and insight into how to best approach the issue of the valuation of options.

We certainly all appreciate your offer to stay in touch, and to bounce questions off you, and to in general continue to exchange information for our mutual benefits.

Once again, thanks and best wishes.
Kalman A. Barson, CPA/ABV, CFE
The Barson Group

Thank you for presenting the Black-Scholes Made Easy and option-valuation seminar. It was interesting and informative, and as the title of your book suggests, your presentation skills and graphics, did make it easy to follow and understand.

My dozen CPA colleagues attending the seminar from other firms, all came away with the same impression: you were able to take a subject that is, at best, difficult to understand and make it intelligible.

I look forward to future seminars, and wish you much success with the option-valuation program.
Marshall A. Morris

I have tried Jerry Marlow's Black-Scholes Made Easy and plan to make it a requirement for my investments classes. Its animations provide intuitively clear visual explanations of the fundamental nature of stock market risk. It is an ideal complement to textbooks such as my own (Bodie, Kane, and Marcus, Investments). I have been using my own Excel simulations to illustrate this material in the past, but Marlow's animations blow mine away. Simply wonderful stuff!!"
Zvi Bodie, Professor of Finance,
Boston University School of Management

Extremely easy to follow. I can't praise it highly enough. Any student or trainee having to study this topic really should buy this tutorial.

Having a degree in Mathematics and a professional accountancy qualification did not prepare me for the explanations of Black Scholes to be found in most text books. They may have got a Nobel prize for their option pricing model but Black and Scholes were never going to get an award for clarity of explanation.

Having grappled with this area for a few months, I decided I needed a little more innovative help; hence my purchase of Jerry Marlow's interactive tutorial.

Two days later and I feel I could go for the next Nobel prize myself! So many things click into place so quickly, it's marvelous. Jerry gives his email address which I had to resort to for one query. He answered most helpfully within a couple of hours.
Peter Stewart

The simulation is a good one. A deep insight into the price process pops out clearly. In my next semester course "Black-Scholes Made Easy" will be a useful tool for giving the necessary intuitive view of the matter.
Lucio Geronazzo, Professor
Mathematical Models for Financial Markets
Il Dipartimento di Matematica per le Decisioni
Università degli Studi di Firenze
Florence, Italy

I thoroughly enjoyed the presentation. I am looking forward to receiving all the "goodies" which you promised.
I. Alan Hirschfeld CPA/ABV MBA
RosenfarbWinters, LLC
Forensic Accountants & Business Consultants

Thanks for a grand tutorial on Friday, and for making a huge contribution to the investment community. You are truly an "explainer extraordinaire."
Dennis A. Webb, MAI, ASA
Primus Valuations
Marina Del Rey, CA

Futures Magazine calls the Black-Scholes animation "A joy to use" and of "enormous value as a teaching tool for students, novice traders and those who suddenly find themselves in need of a reference for option behavior."

I am new to options and will be using the book and software to learn about them. I have started to read the first chapters and using the software and I am pleased to report that it has made understanding options so much easier. Thank you.
Robert Lim

Financial Engineering News says,
"If you're well versed in the stochastic mathematics underlying Black-Scholes-Merton option pricing theory, this book will interest you as a way of visually demonstrating how the value of options vary with the key input parameters such as time to maturity, strike price, dividends paid, stock price volatility, etc. And if you're relatively new to the field (or a student), this book offers a unique tool for learning about option pricing in a way that blends theory (albeit with minimal math) with an easy to use, graphics rich program which runs on Windows based PCs."

I've read several books on options and have traded options on a regular basis. I felt like I had a pretty good handle on the concepts and mechanics. Black-Scholes Made Easy took these abstract ideas and provided a concrete visual experience to solidify them in my head. To see the probabilities and assumptions expressed graphically really enhanced my understanding of options as well as stocks. I believe anyone wanting to get a firm grasp on options, whatever their current level of knowledge, would benefit from Black-Scholes Made Easy. I wish that this program had been available when I first starting learning options.
Kirk Guillebeau
Financial Analyst

Download

Seminar Notes:
How to Value Stock Options in Divorce Proceedings
By Jerry Marlow

Below are a list of the topics covered in the seminar notes. To see what the seminar notes are like, you can download for free any or all of the first three sections.

 

To download a complete copy of all 165 pages in a pdf file, click on the buy-now button at right. The charge to download the entire book is $9.95 payable through PayPal with your credit card.

The seminar itself uses advanced simulation software. The notes contain screen captures from some of the simulations. Consequently, the complete notes file is large: 3.1 megabytes.

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Section Topics

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How to Value Employee Stock Options in Divorce Proceedings

An option’s payoff is uncertain.

An option’s value is related to its potential payoffs and the probability of those payoffs.

If we tabulate the outcomes of thousands of price-path simulations with little squares, the squares form a pattern.

Every financial forecast is a probability distribution. A stock forecast is a bell-shaped curve.

MarlowOptionsDivorcePages001To009

To calculate the value of an option, we can evaluate the payoffs produced by the squares that fill up the bell-shaped curve.

Payoffs near the strike price add little to the value of the option.

Payoffs below the strike price add nothing to the value of the option.

We get an option value half way between the marketplace bid and ask prices.

MarlowOptionsDivorcePages010To016.pdf

The spread of the bell-shaped curve and how high it sits on the price axis determines the option’s value.

A more spread out bell-shaped curve centered at the same height gives a higher option value.

A less spread out bell-shaped curve centered at the same height gives a lower option value.

To draw a stock forecast, we need to know its expected return, standard deviation of expected volatility, current stock price, dividend forecast and the forecast’s time horizon.

A stock’s expected return is the average of all the returns in its probability distribution.

Standard deviation of expected volatility tells us how spread out the bell-shaped curve is.

In the bell-shaped curve, the median return is less than the average or expected return.

We can expect 99.87% of outcomes to fall between three standard deviations below the median return and three standard deviations above.

The longer the forecast horizon, the more spread out the bell-shaped curve.

The longer an option’s time to expiration, the greater its value.

If a stock pays dividends, its price path will be lower than it otherwise would have been.

If a stock pays dividends, the price bell-shaped curve will sit lower than the return curve.

This methodology allows us to value options fairly in the face of uncertainty.

MarlowOptionsDivorcePages019To033.pdf

How does an option’s probability-weighted present value compare to its Black-Scholes value?.

The Black-Scholes-Merton formula for call options.

An option’s Black-Scholes value is the cost to a trader of setting up a delta hedge against the sale of the option.

When a trader sets up a delta hedge, his liabilities are the money he has borrowed to buy the shares of stock and the value of the options.

When a trader sets up a delta hedge, his assets and liabilities are in balance. Delta hedging keeps them in balance with no additional infusion of cash from the trader.

When an option expires, the trader’s assets and liabilities go to zero.

Delta Hedging— An Example.

The financial marketplace enforces options’ arbitrage-free values.

Risk-neutral valuation gives us arbitrage-free values for market-traded options.

Modeling the evolution of a stock price on a binomial tree.

Backward induction:
Walking values back down the tree.

Using backward induction to value a European-style put option.

Using backward induction to value an American-style put option.

Binomial models translate forecasts of expected return and volatility into up and down rates of return and probabilities.

The Equal Probabilities Model sets the up probability and the down probability equal to.5.

The Cox, Ross, and Rubinstein Model makes the up and down jumps equal.

The General Additive Model makes the up and down jumps equal.

Where do these formulas come from?

In general, the translation of the geometric-Brownian-motion model into the binomial model is more accurate as the option’s time to expiration is divided into shorter time intervals; but beware!

Risk-neutral models evaluate probability distributions against strike prices.

When an underlying pays a dividend yield, the price-path evolution is depressed below what it otherwise would be.

Payment of quarterly or other lumpy dividends depresses price paths at the time of the payments.

If investors in a stock are risk averse, then the stock offers a risk premium.

If a stock offers a risk premium, then the probability-weighted present value of a call option written on that stock is greater than its Black-Scholes or risk-neutral value.

Under risk-neutral valuation, a stock and an option on that stock have the same expected return.

The financial world relies upon Black-Scholes and risk-neutral-valuation models.

Reality does not conform exactly to the Black-Scholes or binomial-modeling theories.

Black-Scholes and risk-neutral valuation offer courts the fairest methodology with which to value employee stock options in divorce proceedings.

Valuation of stock options in divorce proceedings.

Valuing employee stock options requires complete information.

An example: Value 5,000 XYZ options.

Selection of a valuation as-of date is a question of law.

If options identical to an employee stock option are available in the marketplace, then the market price is the fair value.

If employee stock options are otherwise identical to market-traded options but have a different strike price or time to expiration, then either Black-Scholes or risk-neutral models can be used to value the options.

To value options, use the continuously compounded risk-free rate for a term equal to the option’s time to expiration.

Which volatility measure to use: historical or implied?

Historical volatility is a backward-looking measure.

The term structure of implied volatility.

Selection of a volatility value with which to value the options requires some exercise of judgment.

Calculation of option value if the options are vested and have a clear and clean expiration date.

Probability distributions and simulations show the financial forecast and expectations on which the value is based.

What if the options are not yet vested?.

What if the options are vested but the grant requires that, upon leaving the company, the employee exercise the options within a specified amount of time?.

“Intrinsic value”.

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Share your thoughts with the author and seminar leader
This seminar benefits from the thoughts and observations of its participants and from the critiques of other professionals. Send me your comments, criticisms, suggestions and inquiries. Let me know how I can make this seminar more useful to courts, attorneys, valuation professionals, and divorce financial planners.

Contact me at jerrymarlow@jerrymarlow.com or (917) 817-8659.

If you find this site valuable, please copy and add to your web site the following link: How To Value Stock Options In Divorce Proceedings.

Arrange for a seminar
To arrange a seminar for your firm or professional organization on how to value stock options in divorce proceedings, call Jerry Marlow at (917) 817-8659 or e-mail jerrymarlow@jerrymarlow.com.

Valuation of Stock Options in Divorce Proceedings by the Seminar Leader
When I perform option valuation for divorce proceedings, I follow the principles taught in the seminar and summarized in these notes. I can write a valuation report that is as detailed or as terse as suits the case at hand. I can present the valuation methodology in a way that is easy for the judge to understand. If you would like for me to perform a valuation of stock options for a divorce case that you have, call me at (917) 817-8659 or e-mail jerrymarlow@jerrymarlow.com.

Jerry Marlow


Getting divorced? Don’t let the court value your spouse’s stock options at their so called “intrinsic value”!
by Jerry Marlow

Jerry Marlow, MBA
Valuation of Stock Options in Divorce Proceedings
(917) 817-8659
jerrymarlow@jerrymarlow.com

 

 
 

 

 

 

 

 

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