This year is a special date for the field of finance and financial derivatives: the iconic Black-Scholes financial model turns 50 years old. Maybe you heard about it in college, at work, or maybe because a friend told you about it. Over the course of what has been half a century, this model transformed the entire industry and paved the way for different professionals and academics. We invite you to learn about the legacy that accompanies us to this day.

How was the Black-Scholes model born?

In 1973, Fischer Black and Myron Scholes introduced their paper "The Pricing of Options and Corporate Liabilities" to the financial world , revolutionizing the financial world of the 1970s . The academics' work introduced a mathematical model that would allow the calculation of the fair price for call and put options. Years later, financial-economics scholar Robert Merton would extend this model to other derivative products.

What was its impact on finance as we know it today?

This model has been important for several reasons, but mainly because of the expansion and development of the options and derivatives market, where it allows the management and transfer of different risks, such as exchange rates, interest rates and commodity prices, among others. When looking at large corporations, talking about derivatives is always important.

By enabling the valuation of options on a sound fundamental basis, it has been of great help to companies for financial innovation, liquidity enhancement and more. 

A simple example:

Imagine you own a company that imports technology into Chile and your core business is selling phones. You do not want to worry about the price at which you will have to buy the phones in the future, as this could affect your income and the stability of your business. To protect yourself against possible price fluctuations, you decide to purchase a European call option that allows you to buy a specific number of phones at a strike price of $110 per unit on a specific date within the next year, say, exactly one year from now. At this point, there are some question marks, but it is also where the Black-Scholes model shines.

Assume that the risk-free interest rate is 3% (for example, the rate of return on a one-year Chilean government bond) and an annual volatility of 25%. The risk-free rate represents the return we could obtain by investing in a risk-free asset, while the volatility represents the variability in the stock price over time. Both factors are fundamental to calculating the fair price of the European call option using the Black-Scholes model.

Using it, we can calculate the fair price of the European call option. For example, if the model tells us that the option price is $10, this means that we should be willing to pay up to $10 per unit to acquire the right to buy the phones at $110 each in one year.

After one year, if the price of the phones increases to $130 per unit, we could exercise the call option and purchase the phones for $110. Although our approach was to protect ourselves for price variations, we even had a gain, which in this case would be $20 per unit ($130 - $110), less the price we paid of $10, leaving us a net gain of $10 per unit.

Now, let us suppose that the price of the phones decreases to $90 per unit. In this case, we would not exercise the call option, since it would not make sense to buy the phones at $110 when the market price is $90. In this case we would have losses, but we would have the peace of mind that they would be limited to the price paid of $10. This is one of the advantages of using call options: our losses are limited to the premium paid, while our potential gains are unlimited if the price of the underlying asset increases significantly.

Perhaps this all seems very simple, but without the Black-Scholes model, it would be very different. Without this model:

1. It would be difficult to determine the fair option price: Investors would have to rely on more rudimentary and subjective methods to estimate the value of options, which could lead to greater uncertainty and reduced efficiency in the options market.
2. Reduced liquidity in the options market: Without a robust mathematical model such as Black-Scholes, market participants may have difficulty finding a fair and acceptable price for options. This could result in lower liquidity in the options market and greater difficulty for investors to manage and transfer risk efficiently.
3. Increased investment risk: Without a robust and widely accepted framework for valuing options, investors could make decisions based on incorrect assumptions or incomplete information, increasing the risk associated with investing in options.

The Black-Scholes model benefits us by providing a robust and widely accepted framework for valuing options, which facilitates informed decision making and improves the efficiency of the options market. This allows you to focus on your core business of selling phones without worrying about fluctuations in the purchase price.

In conclusion, we can say that the Black-Scholes-Merton Model has transformed the financial industry by enabling the accurate valuation of options and financial derivatives. It has been used by leading investors and hedge fund managers, such as Warren Buffett, George Soros and Paul Tudor Jones, to manage risk and profit in financial markets. The model has enabled the expansion and development of the options and derivatives market, improving market efficiency and enabling informed decision making in the financial world. Its wide acceptance in the financial industry has made it a fundamental tool for risk management and profit making.

Cristóbal Martínez, Portfolio Manager Activos Alternativos Fynsa AGF