Derivative Securities

What is a Derivative Security?

A derivative security is an agreement or contract with a value contingent upon the value or price of an underlying asset or set of assets, dependent on a market or index price, or dependent on certain events (“underlying basis or bases”).  Derivative securities may be settled (if exercised or effective) by either delivery of the underlying asset or assets or by cash settlement based upon a formula with the underlying bases determined at the exercise date.  The most common underlying bases for widely traded derivative securities include: market common equity share prices; market currency exchange rates or currencies; and market prices for commodities (most often mining commodities, including metals or energy, or agricultural commodities).

  • The most commonly valued derivative securities are options. A common, or “vanilla,” call option is a right (but not an obligation) to purchase an asset or a quantity of assets at a specified price per unit (the “strike” or exercise price) within a specified time period.
  • A futures contract is an agreement between two parties to a future exchange of an asset for a cash price at a specified date. A forward contract is a private contract that is similar to a futures contract.
  • A swap is an agreement to exchange two assets at a future date at a specific exchange rate or to exchange the terms of two securities (typically to exchange interest rates on fixed income securities or currencies at some specific exchange rates) over a period of time or at certain specified dates.
  • A convertible security is a security that may be converted into another security (in whole or in part) upon certain events or actions of either the holder or the issuer. Convertible securities are securities with an “embedded” or attached derivative.

Valuing Complex Derivative Securities

Both investors and issuers should know and understand the value and cost of complex securities.  Unfortunately, too often the values being derived and reported are wrong, and the consequences of these errors can be significant.  Valuing complex derivative securities is one of the most difficult and challenging tasks confronted by business valuation experts.  In performing these tasks, the valuation expert must consider the following:

  1. the specific terms of the subject derivative in terms of the mix of rights and obligations of the holder and the issuer of the derivative security;
  2. the likely range of payoffs (or consequences) to the holder and issuer and how they relate to the value of the underlying asset (or assets or index price) at some future date or dates; and,
  3. the likely distribution of probable future outcomes that would affect the realized value of the derivative security.

What Makes a Derivative Security Complex?

We refer to a complex derivative security as a derivative security that is more difficult to value because it has certain unique additional contingencies or variable features as part of the agreement, or the derivative security is, or must be, valued as a compound derivative security.

Common examples of exotic options that often require more extensive valuation analyses, include:

  1. Warrants or options with variable exercise prices, payoffs, or quantities:
    1. Warrants with “reset” features.
    2. Look-back options are options where the exercise price, payoff, or quantities to be purchased are contingent on future events or prices.
  2. Warrants and options with contingent or restricted exercise periods:
    1. A vesting period is common for stock options issued by companies to employees and directors. With a vesting option, a specified time must pass, and certain conditions must be met (continued employment) in order to be able to exercise the option.
    2. Barrier options are options where the right to exercise is triggered based on the underlying asset price hitting a certain threshold (often on certain specified dates or in specified time periods).
    3. Forfeiture (or premature expiration) conditions are similarly a part of stock options granted by companies to employees or affiliates.
    4. Early exercise of a warrant or option is another contingent issue often not adequately considered. This issue often arises when the holder is more risk averse, has significant wealth in the derivative, or is impatient and the derivative has gained sufficient intrinsic value that the holder seeks to exercise the option well prior to the expiration date because there is little additional “option” value to be realized by waiting and there is greater “perceived” relative risk to the holder associated with waiting to exercise the option.
    5. Contingent exercise or expiration dates and awards are often observed particularly in private companies. These are like barrier options except that the options rights are triggered (knock in) or are lost (knock out) out upon certain events.
  3. Securities with multiple rights or embedded derivatives:
    1. Convertible securities with both “put” and “call” features, such as the right of the issuer to prematurely retire principal (or “call” the security) prior to maturity and the right of the holder to “put” the security back to the issuer for repayment or assets upon certain events have such multiple events.
    2. Convertible securities with various forfeiture, barrier, participation rights, and/or anti-dilution features.
    3. “Chooser” options or conversion features that entitle the holder or issuer to choose which asset (from a set of choices) to receive (in general or upon certain conditions).
  4. Compound options and unusual underlying asset distributions:
    1. Most commonly, mezzanine debt (with or without conversion features) becomes a compound option when valued in the context of highly leveraged companies (companies with significant debt or default risk) or in connection with more highly leveraged assets (such as real estate).
    2. Stock options and warrants (including embedded derivatives in securities convertible into common or preferred equity) to purchase or sell equity securities should be similarly valued as compound options when the underlying company or asset is highly leveraged, has a substantial risk of reaching a value of zero (or very close to zero), or is subject to certain discrete event risks.
    3. Even a vanilla call option or put option may become a complex derivative or require more effort to model and value when the underlying asset does not have a well-defined or easily modeled distribution or characteristics.

Modeling Complex Derivatives for Valuation

Complex derivative securities typically cannot normally be valued (or solved) based on a formula or solution provided in a book. While books of option pricing formulas exist, the formulas provided are often merely approximations, require very specific assumptions about the characteristics of the underlying asset and the likely distributions over time, and often do not match the exact terms of the derivative security of interest. When a formula (or solution) is not readily available, then one is required to employ some form of simulation modeling to solve the problem and derive a value for the derivative security.

Estimating Volatility

The famous Black-Scholes option pricing model and its various extensions and applications, for example, assumes that the distribution of the underlying asset follows a process called geometric Brownian motion (assets provide a log-normal return distribution). In this process, the standard deviation (volatility assumption) is constant over time as a percentage of the underlying asset or basis value, transactions may be made continuously over time at no cost to investors, and there are no discrete events. Additionally, the price of the underlying asset or basis and its distribution is not contingent on other possible future events.

In valuation assignments, the derivative securities being evaluated are often long-term in nature (two to ten years to expiration). Volatility within an industry or company can vary significantly as a result of numerous changes over time such that the observed historical volatilities may not be reflective of expected future volatility and the implied volatilities observed may be limited to options expiring in the near term. Thus, a valuation analyst needs to use considerable judgment and experience and may need to understand how volatility has changed over time in the past or is likely to change in the future within the industry as a function of leverage, general market volatility, a company’s development, and other factors.

Additional Dilution & Volatility Considerations

Once an analyst has examined and estimated how volatility is likely to change over time in general, or as a function of the underlying asset price, or as related factors such as the state of development or enterprise value are taken into consideration, the next step is to model the valuation of the subject derivative security.  A variety of models may be constructed given the tradeoff being capturing the essential elements that affect valuation and creating a model that is tractable and can be replicated in practice.


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