In our patent valuation practice, we are constantly seeking to improve the reliability of the analytical methods we apply in valuing intellectual property, particularly the challenging area of patents.

In this post, we’ll be discussing the application of the contingent claims analysis framework to patent valuation, illustrating specific principles and approaches from the field of the financial analysis of stock options.

The basic definition of a financial option in general can be expressed as follows:

The right, but not the obligation, at or before some specified time, to purchase or sell an underlying asset whose price is subject to some form of random variation.

This generalized definition can, and has, been applied to a number of other situations other than financial assets directly. The most common of such non-financial applications of the concept of options is known as “Real Options,” and substantial literature has been built around the application of Option Pricing Theory to the valuation of managerial flexibility, untapped mineral reserves, and the like.

In the field of Intellectual Property, it is notable that there are multiple parallels between the abstract characterization of financial options on stocks and the basic concept of a utility patent. This makes contingent claims analysis attractive theoretically as a way of pricing distinct potentially useful patented products or technologies. Consider the following analogies:

- Patents and stock options represent a right to exploit an asset in the future, and to exclude others from it.
- A stock option may be exercised by its owner, or it may be allowed to expire. If it is exercised, the owner of the stock option obtains an equity interest in the underlying firm; thus, gaining exclusive title to a pro-rata share in the stream of dividends.
- Similarly, a patent gives its owner the right to exclude others from using the underlying invention, and further investment is typically required to exploit its commercial potential.
- Stock options and patents have a limited timeframe: stock options are valid up to an exercise date, and patents have a statutory expiration date.
- Both instruments have a direct and precise pricing relationship with an underlying asset: a company in the case of stock options, and an innovation in the case of a patent.
- Either type of right can be transferred to other parties. A license transfers the right to an invention, and a stock option has organized markets. The price at which the transfer occurs comes at something less than the full value of the underlying asset. The licensee, in the case of patents, will only enter the transaction with the expectation of reaping the difference between the full value of the patent and the license price (paid-up or ongoing royalty).

These parallels have been drawn for some time now and a good reference for an overview of these approaches is R. Pitkethly’s work on *The valuation of patents: a review of patent valuation methods with consideration of option based methods and the potential for further research*, and M. Reitzig’s *Valuing Patents and Patent Portfolios from a Corporate Perspective*, both published by the UNECE (*Intellectual Assets: Valuation and Capitalization*, United Nations, Geneva and New York, 2003).

### Prototypical Valuation Model

The best-known approach to the valuation of financial options is the Black-Scholes-Merton model. Although the actual equation utilized in this model is complex, the model can be explained as a rigorous (mathematical) approach to answer two key questions that arise when pricing an option on a stock. Although the market value of a (publicly traded) stock can be ascertained easily by referring to the appropriate organized market, the proper price of the right to buy it at a specified price at some point in the future is not straight forward. Similarly, despite the fact that the profitability of implementing a patented product or process in practice can be achieved with conventional financial tools, the proper valuation of the right to exclude other from doing the same is more complex. The buyer of the (financial) option has to consider two key questions:

- Given the volatility of the stock price, what is the “likely” range of variation for that price in the future; and
- What is the proper return on the amount invested with buying the option (even if it expires unexercised).

The option will have value to the buyer only to the extent that the “likely” price in the future exceeds the opportunity cost of earning just as much in a risk-less alternative. The Black-Scholes model gives a precise answer to the term “likely,” by applying the statistical model of the Normal distribution to the variations of the stock price. This summarizes the volatility of stock prices in a single number, or parameter, called the variance. On the other hand, the amount invested in the future to exercise the option should provide revenue comparable, at a minimum, to a suitable risk-free rate of return, conventionally the yield on certain government bonds.

For stock options, their value is the current stock price multiplied by a probability minus the present value of the exercise price multiplied by another probability. Within this framework, the option price (maximum expected profit) stands for the value of the patent. In effect, a patent is valuable today to the extent the probability-adjusted potential net income from practicing (or licensing) it exceeds the probability-adjusted additional expense of maintaining its validity and developing the ancillary assets required to implement it.

The application of this approach requires consideration of the applicability of the option-patent parallel, and due attention to the actual negotiated context in which the patent licensing transaction is deemed to take place, the commercialization commitments of the parties, and other factors of the dilution of the value of the patent. Applying many of the observations and assumptions introduced for this purpose by Frank R.F. Russell Denton and Paul J. Heald in: “Random Walks, non-cooperative games, and the complex mathematics of patent valuation” 55, Rutgers Law Review, 1175-1288 (2003).

Expressed as a proportion of the anticipated profits from the patent protection, the price of the option in this method, divided by the net present value of the patent’s addressable revenue is directly interpreted as the optimal royalty rate attributable to the patent.

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Additional material based on this approach, with examples and additional tools will be developed in future posts and in IPmetrics’ Patent Value Guide.