How is the value of an unlisted option determined?

Background

An option is an agreement between an option issuer and an option holder that gives the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price within a defined future period. Such an option has a value.

Determining the value of unlisted options is important for several reasons. First, it can help investors understand the value of their investment and make informed decisions about buying or selling options. In addition, it may be necessary to determine a tax value, for example in connection with employee option programs. An estimate of an option’s market value aims to approximate as closely as possible the value that would have applied if the relevant asset had been traded between independent parties under market conditions.

Value at maturity

The value of a call option at maturity is equal to the higher of the underlying asset’s value minus the predetermined price, and zero.

Let us illustrate with an example. A call option with a predetermined strike price of SEK 50 is purchased, and the underlying asset is a share. At maturity, the share is considered to be worth SEK 60. The option therefore gives the right to buy a share worth SEK 60 for SEK 50, and such a right is worth SEK 10, which corresponds to the value of the option.

On the other hand, if the share is considered to be worth SEK 40 on the exercise date, the option holder still has the right to buy the share for SEK 50. That right has no value because the share is valued at a lower amount, so the option is not exercised and its value is zero. Since an option represents a right and not an obligation, an option’s value is never negative for the option holder.

The value of an option before maturity

Determining the value of an option at a point in time before maturity, for example when the option is issued, is not quite as intuitive.

Because the value of the option at maturity is known for different prices of the underlying asset, the option’s value prior to maturity can often be calculated using numerical models. One well-known valuation model is the Black–Scholes model. The Black–Scholes model is a mathematical model used to calculate a fair price or theoretical value.

According to the Black–Scholes model, the price of a European equity option is influenced by five factors:

1. The price of the underlying asset, i.e. the current share price. A share that is traded regularly and in high volumes on a stock exchange has a market-determined fair value. For shares that are traded infrequently or are unlisted, the fair value must be estimated, usually by an independent external valuer. Fair value is defined as the amount for which an asset could be transferred or a liability settled between knowledgeable parties who are independent of each other and willing to carry out the transaction.
2. The predetermined price, i.e. the price the option holder will pay for the share in the future. The higher the predetermined price relative to the current share price, the lower the value of the option.
3. The volatility of the underlying asset. Volatility is a statistical concept used in finance to describe price movements in shares and other financial assets. Simply put, volatility describes how much the price of a financial asset fluctuates. The greater the price movements, the higher the volatility. A share that is traded regularly on an exchange has an observable volatility. For shares that are traded infrequently or are unlisted, volatility must be estimated. Higher volatility leads to a higher option value, as larger price movements increase the probability that the share price will exceed the strike price during the term of the option.
4. The risk-free interest rate. The risk-free rate is the return that can be achieved without taking any risk over a given period. It is a cornerstone of valuation models for financial instruments, but remains a theoretical concept, as truly risk-free investments do not exist in practice. Typically, the yield on a government bond with a maturity corresponding to the option’s remaining term is used. A higher risk-free rate negatively affects the option premium and increases the cost of the right.
5. The remaining time to maturity. The longer the time to maturity, the higher the option value. This is because a longer term increases the probability that the share price will exceed the strike price, making the right more attractive and therefore more valuable.
   

Advantages and limitations of the Black–Scholes model

The Black–Scholes model involves relatively advanced mathematics and is a classic example of a situation where a value can be calculated with great precision, while at the same time relying on several variables that must be estimated. Of the five factors listed above, only the risk-free interest rate cannot be adjusted to any significant degree, even though the model requires the assumption that the risk-free rate remains constant over the option’s term. The other four factors can be adjusted relative to one another, resulting in significantly different – yet mathematically precise – option values.

Additional limitations include the fact that the model applies only to European options, assumes that many of the input variables remain constant over the term, and ignores transaction costs and taxes.

Despite these limitations, it is important to emphasize the model’s significance and strengths. The Black–Scholes model has had a major impact on financial economics and has contributed to the development of a wide range of derivative products, such as futures, swaps, and options.

The model has also been successfully implemented and widely used by financial professionals due to the many advantages it offers, including:

1. Provides a framework. The Black–Scholes model offers a theoretical framework for pricing options, enabling investors to determine a reasonable option price using a structured and well-tested method.
2. Enables risk management. By knowing the theoretical value of an option, investors can use the model to manage their risk exposure to different assets. It is therefore useful not only for evaluating potential returns, but also for understanding portfolio vulnerabilities and weaknesses.
3. Facilitates portfolio optimization. The model can be used to optimize portfolios by providing measures of expected return and associated risks for different alternatives, allowing investors to make more informed decisions aligned with their risk tolerance and return objectives.
4. Improves market efficiency. The Black–Scholes model has contributed to greater market efficiency and transparency, as investors are better able to price and trade options. This simplifies the pricing process by improving understanding of how prices are derived.
5. Standardizes pricing. The model is widely accepted and used across the financial industry, enabling comparability between different markets and jurisdictions.
   

Disclaimer: This article is intended for informational purposes only and should not be interpreted as legal advice. It is recommended to consult a qualified professional for specific guidance on legal matters.