The Derivatives Market

Volatility as an asset class

Introduction

In 2003, the CBOE Volatility Index (VIX) started trading as a proxy to the S&P500 market volatility. More specifically, the VIX “measures the rate of change of S&P500 stocks on a 30 day forward basis” (Crossmark Global). Historical, or realized, volatility can generally be defined as the standard deviation of investment returns. In other words, it reflects the change in prices over time. On the other hand, implied volatility is a function of future price movements based on future option contracts. The VIX, being measured on a forward basis, is a proxy for implied rather than realized volatility and measures volatility in both call and put options of the S&P500. It is important to note, however, that the VIX has not shown any power in predicting future price changes and is used by investors who wish to trade volatility as a measurable asset class.

The impact of selling volatility

To get a return on their investments, investors may consider interest rates, dividends, or price appreciation. However, another indicator that should be considered when valuing an asset over the long term is volatility. The difference between realized and implied volatility is defined as the volatility risk premium, which can be traded for potential diversification benefits. In fact, there is a fundamentally negative correlation between stock prices and their volatility. When prices fall, implied volatility rises. Thus, investors can theoretically achieve maximum diversification benefits, as they would be compensated for their equity losses by volatility gains. By selling volatility, investors can benefit from a reduced standard deviation portfolio that fluctuates less over time than the underlying assets – both up and down, depending on which strategy the shareholder has chosen. This may be a good long stock alternative for investors who want less overall risk. As quoted by Harry Markowitz in his Modern Portfolio Theory, “Don’t put all your eggs in the same basket” meaning that investors should diversify their risk to optimize their returns. Volatility fits this expression as it can become an asset class that offers the portfolio a more diverse return profile in exchange for foregoing upside potential for a period of time.
Trading volatility provides cash flows to investors that is not highly dependent on factors like interest rates or dividends, contrary to stock investments. In simpler terms, “trading volatility is a […] way to find profitable trading opportunities in the market without being right on the direction of the price. Volatility traders are only interested in […] large price-movements in any direction” (My Trading Skills).

Volatility arbitrage strategies

Selling volatility usually means selling options. Options are divided into short and long, and between exercising a call or a put. When selling or buying options, you should receive some positive risk-adjusted return so that you can better manage maximum losses, as with a long call, or maximum gains, as with a short call. When shareholders use an arbitrage strategy, it means they are looking for an opportunity to simultaneously buy and sell an asset in separate markets. Thus, when trading volatility, arbitrage strategies involve looking for options that have implied volatility above or below the estimated forecast volatility of the price of an underlying asset. For example, if the volatility of the stock option is overvalued, you can go short on the call and take a long position on the underlying asset. On the other hand, if the volatility of the stock option is undervalued, the investor can go long on the call and take a short position on the underlying asset. If the prediction is correct, the option will fall to its fair value and the trader will profit. There are many strategies that investors can opt for when trading volatility, such as:

Covered calls: The performance of this strategy is affected by the market volatility and the performance of the underlying asset. In this strategy, the investor takes a long position in an undervalued stock and sells a call on the same underlying. With this strategy, the investor receives a call premium as long as the implied volatilities are higher than the realized volatilities.

Delta neutral: This strategy implies building positions that do not match the price changes of the underlying stock. This strategy is used by option traders who do not want any type of directional bias or risk. This allows investors to profit from factors such as the passage of time and variations in implied volatility.

Volatility arbitrage: In this strategy, the investor enters into a variance swap, receives the implied variance, and pays the realized variance on a rolling basis. Thus, the trader’s return would be the difference between the implied and realized variance. So in this case, the return is not “diluted” by movements in the underlying, as is the case in the first example, the covered call.

Risk Factors

Although trading volatility can provide diversification benefits, investors may need to pay a high price in order to reap such benefits. As such, trading volatility can become an expensive investment in the long run. For this reason, investors will generally sell volatility rather than buy it. Although cost-reducing, it is a highly risky strategy. Being “short gamma” (i.e. selling volatility) is usually achieved by selling options on an uncovered basis and, therefore, investors have limited upside but potentially unlimited downside. Additionally, when trading volatility in the form of covered calls, the investor still incurs the risk that the underlying asset’s price will drop. When the asset’s price drops, implied volatility can rise by a significant amount and the investor shorting implied volatility may incur severe losses in the value of his position.

Conclusion

Trading volatility has, in recent years, become a popular alternative for investors looking to reap diversification benefits, lower their portfolio’s standard deviation and risk profile as well as providing an additional source of cash flow to their portfolios. There are several strategies to trading volatility, which usually implies selling volatility or being “short gamma”. Despite the benefits, selling volatility can also bring with it several risks, the main one being price risks faced by the underlying asset.

Vanilla, Exotic and OTC Derivative Products

Derivatives

Derivatives are assets in which the value depends, or derives, from the value of another asset called the underlying asset. Generally, derivatives take the form of a contract between two persons, which obliges one of the parties to make a payment, or a set of payments, to the other party at a future date and depending on the evolution of the price of the underlying asset. The duration of the contract can go anywhere from a few months to more than 20 years in some cases. The underlying assets can be as varied as stocks, bonds, commodities, interest rates, exchange rates, among others.

Vanilla derivatives

Like in ice cream, vanilla derivatives, or plain vanilla, are the simplest and most common version of an asset or financial instrument. There are no embellishments, no extras, and no complex features. These are usually applied to options, bonds, futures and swaps and are generally associated with lower risk levels.

Vanillas options:

An option is a financial asset that gives its holder a right, but not the obligation, to buy or sell an underlying asset at a predetermined price, called the strike price, within a period of time. The seller of an option, the writer, is obliged to sell (or buy) the underlying asset to the buyer of the option if the buyer chooses to exercise his right to buy (or sell).
The most common vanilla options are call options and put options. These have no special or unusual features, are standardized and transacted in a stock exchange. Holders of a call option have the right, but not the obligation, to purchase the underlying asset to the strike price.

The owner of a put option has the right, but not the obligation, to sell the underlying asset at the strike price. Calls and puts have a maturity, which set a time limit for the underlying asset transaction. The European type of option can only be exercised at maturity, while in the American type it can be exercised at any time until maturity.

Vanilla swaps:

A swap is a contract between two parties, in which both agree to exchange a set of future and non-active payments or cashflows between them.
As contracts between two parties are usually traded in the OTC markets, vanilla swaps are one of the simplest financial instruments traded on this market. The vanilla swaps, or plain vanilla swap, are essentially an interest rate swap. They normally exchange, for a certain period, a set of payments – one at a fixed interest rate and the other at the variable rate. The amount on which interest is payable, the principal notional, is the same in the two parts of the contract. The only thing that is exchanged is the form of payment, whether at the flat rate or the variable rate.

Futures:

Financial futures consist of a contract between two parties in which both parties agree on a future date to carry out a financial transaction at the agreed price. At maturity, the party buying a futures contract agrees to the future receipt of an asset, thus it acquires a long position on the asset and agrees to buy the asset. The party that sells the futures contract agrees on the future delivery of the asset, thus acquires a short position and agrees to sell the asset.

These derivatives are very similar to forwards, in their concept, but overcome the disadvantages of those, in particular the risks of default and liquidity, since futures are traded in organized markets, therefore being standardized and are associated with the existence of a margin account.

Exotic derivatives

An exotic derivative is a more complex derivative than those normally transacted, or relative to plain vanillas. This complexity is usually how the return and the characteristics of the contract are defined. Exotic derivatives include, for example, derivatives whose contract is not standardized in the sense that the underlying asset is not common and can be made for a particular customer or market.
In addition to that, the advanced structure presented by exotic derivatives allows holders to have significant returns that they wouldn’t have with the hold of plain vanilla derivatives. These types of derivatives are associated with a high risk.

Exotic swaps:

For simplification purposes we are going to explain two one of the most common exotic swaps, the delayed start swaps and the collapsible swaps. For the delayed start swaps, these are just plain vanilla swaps that exchange assets on a non-immediate, or on a forward, start date.
Regarding the collapsible swaps, these are simply a combination of a plain vanilla swap with a swaption (an option that grants its owner the right to enter into an underlying swap) on that swap. It is more commonly used when the interest rates are uncertain.

Exotic options:

Exotic options can be customized to the investor’s likings to meet the risk and profit they wish to be submitted to. Although we have to keep in mind that they do not guarantee any profits, despite the flexibility provided. We can mention some exotic options examples like compound options or asian options, which each have their own characteristics.
Besides, exotic options are often traded over-the-counter (OTC), which leads us to our next section.

Over the counter (OTC) derivatives

Depending on where we trade our derivatives, there are two categories, those being over-the-counter or exchange-traded derivatives. Focusing on over-the-counter derivatives, these are usually traded between two parties and without the supervision of an exchange or a third party, which means it can, sometimes, lack of transparency because there is no check up being done. It also means that the transaction is more exposed to counter-party risk, since each party only depends on the other to perform it.
Just like exotic derivatives, OTC derivatives can be shaped to fit the investor’s needs, which means they can be adapted in order to meet each party’s desired risk and return. With that said, OTC derivatives don’t follow a pattern due to the adaptability they show and are not listed on the market.
Although this type of derivative offers flexibility, it presents a high risk of default since there is no clearing house involvement.

Some OTC derivatives examples include forward contracts and swaps, and also exotic options, which were already mentioned. Furthermore, the OTC market has usually a bigger focus on interest rates or foreign exchanges, for instance.
Let’s draw our attention to the forwards. These contracts usually relate to two parties and mean to set the financial transaction in the future.
OTC derivatives can be used for hedging purposes, transferring or trading risk or even as leverage.

What are the advantages of using derivatives?

The main reason as to why investors chose to use derivatives is the possibility these ensure to reduce or eliminate the risk, although they are also widely used for speculation purposes. Some main advantages of using derivatives besides for hedging and speculating purposes, are the price determination of the underlying asset, tax benefits and moreover it is also considered that derivatives increase the efficiency of the markets. Finally, we can say that the main benefit of using derivatives is the fact that it creates room for income growth that would not be possible otherwise.

Major scandals involving derivatives

Metallgesellschaft

Metallgesellschaft was one of the largest German industrial companies, employing over 20 thousand people and bringing in revenues of over 10 billion USD. One of Mettalgesellshaft’s business streams was commodity trading, and in 1993 it lost north of 1.3 billion dollars due to long hedge strategy, eventually leading to the company getting restructured and becoming a part of “Aktiengesselshaft”.

At the time, the company had 5- and 10-year forwards heating oil and gasoline contracts with its clients (at fixed, locked in prices), and to hedge against a possible increase in oil price, which would be detrimental to the company, they opened long positions on short-term contracts. This is usually a good strategy, if not for the fact that from 1991 to 1994, oil prices went down 25%, from 20$ to 15$ (nominal prices). The company had to cover their margin calls and was short in cash. Mettallgesellshaft’s financial counsellors remained confident in their strategy since the forward fixed price contracts would eventually offset the losses. In spite of this, senior management decided to pull the plug and close out all the positions, resulting in a 1.3 billion USD loss.

Procter & Gamble

Also in 1993, Procter & Gamble (P&G) entered an interest rate swap with Bankers Trust (BT). An interest rate swap is a derivative contract between two parties that agree to exchange payments of different specific rates, based on a pre-set amount of money, called the notional principal. In most cases, one of the parties pays a set rate whereas the other pays a floating rate (this is called a Vanilla Swap). These contracts can be used to alter exposure to interest rate fluctuations or get better interest rates on loans.
P&G signed a leveraged “5/30” swap on a 5-year contract with biannual payments and a 200 million USD notional principal.
The contract stated that every 6 months, Bankers Trust would pay a rate of 5,30% to P&G, in exchange of P&G’s payment of commercial paper’s (CP) monthly daily average rates, minus 75 basis points (-0.75%). In addition, P&G would also have to pay a spread that was calculated based on the 5-year CMT’s yield (Constant-Maturity Treasury note) and the TSY’s price (30-year treasury bond) (1) (e.g.: if the spread were 0,2 P&G would have to pay an interest of 20%)

Consequently, it suited P&G if the spread were zero or close to it, meaning that they would be getting funded at a 5.30% interest rate, minus the CP rate, with the 75-basis points discount. Unfortunately for them, in early 1994 bond prices fell, increasing yields, thus making the contracts extremely expensive for P&G.
P&G sued BT on the basis that the bank had not fully disclosed the entire risk underlying these contracts. BT argued that P&G’s experts had reviewed the contracts and signed them. Nevertheless, Bankers Trust and P&G settled out of court for 78 million USD.

Societé Generale

As derivatives are very versatile instruments, there is always the possibility that an employee who is responsible to hedge or to find arbitrage opportunities become a speculator.
That was exactly what happened to Jérôme Kerviel in Société Général (SocGen). He usually traded equity indices such as the German DAX one, the French CAC40 and the Euro Stoxx 50 and his job was to find arbitrage opportunities. This might happen when an equity index future price is trading for a different price on two different exchanges; or if equity index futures prices are not consistent with the price of the shares of the constituting index.
Kerviel used his knowledge of the bank’s procedures to speculate while giving the appearance of arbitraging. He then took large positions in equity indices and created a lot of fictitious trades to make it appear that he was hedged. In fact, what he was doing was to create large bets on the direction in which the indices would move and the size of his unhedged position grew over time to tens of billions of dollars.
Later, in January 2008, his scheme was uncovered by SocGen. For three days, the bank unwound his position for a loss of 4.9 billion euros. This was the biggest loss created by fraudulent activity in the history of finance, at that time (Later, Bernard Madoff’s Ponzi scheme came to light)

ABS securities and crisis of 2007

To talk about major derivatives scandals is to talk about the crisis of 2007 and the complex structured products that were widely used at that time. To better understand that, is necessary to briefly explain some concepts.
In the 1960s, the U.S banks could not keep the pace with the demand for residential mortgages with this type of funding. This led to the creation of the mortgage-backed security (MBS), which is no more than a portfolio of mortgages and its cash flows (interest and principal payments) that were packed as securities (securitization) and sold to investors.
A securitization of this type was used during the 2000-2007 period (see figure 3). This is known as asset-backed security or ABS. A portfolio of assets such as loans is sold by the origination banks to a special purpose vehicle (SPV) and the cash flows from the asset are then allocated to tranches. Figure 3 represents only 3 tranches, usually more are used.

Finding investors for Senior tranches were not hard. However, for the Mezzanines ones, it was difficult, and that led to the creation of ABSs of ABSs (ABS CDO) (see figure 4).

With that said, subprime mortgages were frequently securitized in the way shown in both figures above. The investors in tranches created from these subprime mortgages generally had no guarantees that interest and principal would be paid. Securitization played a part in this crisis. When considering new mortgage applications, the question was not “Is this a risk we want to assume?” but instead “Is this a mortgage that we can sell to someone else”?
Finally, when the U.S housing bubble burst, investors in tranches that were formed from the mortgages incurred in big losses. As an example, tranches originally rated as BBB loss 80% of their value by the end in 2007 and 97% by mid-2009. Some financial institutions such as UBS, Merrill Lynch and Citigroup had big positions in some tranches and incurred in huge losses. The insurance giant AIG that provided protection against losses on ABS CDO tranches (rated AAA), followed the same wave and ended up with massive losses.
There have been few worse years in financial history that 2008. Government rescued several financial institutions. Merrill Lynch was taken over by the Bank of America, Bear Stearns was taken over by JP Morgan Chase and Goldman Sachs and Morgan Stanley were forced to act as commercial banks as well. Lastly, Lehman Brothers was allowed to fail and entered in bankruptcy.

Discretionary and Quantitative Strategies

Reflexivity in the Markets

The Wall Street Crash of 1929, the Nifty Fifty of 1970’s, the Dot.com bubble of the late 1990’s, and so many other. Again and again, we notice this trend of “Rise and Fall” of the markets, of speculation and return to real prices. Why does this phenomenon happen so frequently over history, instead of markets presenting a more continuous performance?
One theory that may explain it is Reflexivity, with its primary proponent being George Soros. It states that investors act not on reality, but on their perception of reality, which has a desired outcome that is different for every single person. These actions have an impact on reality, which then affects investors’ perceptions and thus prices. This positive feedback loop will make prices tend towards disequilibrium, as the perceptions of reality become increasingly detached from reality itself.
The cycle ends when participants acknowledge that their perception of reality has indeed become detached from reality and adjust their portfolios accordingly. As such, prices increase steadily until they drop abruptly, marking the beginning of a new cycle.
This seems like an easy method for predicting market crashes, by disconnecting yourself of others’ perception and unbiasedly analyse how much other participants’ perceptions are detached from reality and exit the market timely.

Chaos in the Markets

But can someone truly predict events in the markets? Not according to Chaos Theory, that states that small occurrences impact greatly seemingly unrelated events. This is also known as the “Butterfly Effect”.
To understand Chaos Theory is attempting to understand the underlying order and logic of vast, complex systems that may appear disorganized, or its events unrelated. If we look at a company as one of these systems, there are numberless small situations occurring in day-to-day operations. Employees switching buttons, operating machines, making cold calls, having meetings, reporting sales, etc. In fact, there are so many, that it is virtually impossible to keep track of them, even more so to forecast what impact they can have in the operations of the company if something goes wrong.
Picture a sphere, and everything inside it is the realm of the known. What you perceive to be probable is inside, and what you perceive to be highly unlikely is at the edges. Contrary to what you might think, there are other outcomes outside that sphere, that you would never think of unless they happened. The best investors can capture these unknown realities and use them to their advantage.
Now, picture the stock market as one of these systems. Hundreds, thousands of companies listed, all with their own employees, suppliers, networks and all, and every single one of them connected to the other in some degree. Whatever perception of reality you may have, can you now imagine how disconnected it is from reality itself? Being impossible to know all these small factors, it is also impossible to forecast the impact of all of them. What most investors do is educated forecasts, which they themselves know to be faulty, but are the best approximation of reality they can calculate.
Volatility arbitrageurs use reflexivity and chaos to their advantage as discretionary methods.

The best and arguably the most talk about example was the GameStop story. How many of us thought that with GameStop being at $75 for the first time after a 2 or 3 Standard Deviation move thought it could not go any higher and become a 6+ Standard Deviation move ? Well, these people that were acting inside their sphere and perception of reality and decided to short because “the stock had disconnected from fundamentals” were caught in the cross fires. They completely disregarded the reflexivity of the positive feedback loop of aggressive call buying that made dealers hedge out by buying the underlying stock, making for a pure Gamma move and exacerbating the short squeeze. There are so many lessons in the GameStop story, but the main one is that just because a stock is high, it does not mean it can’t go any higher. Just by looking at the flows it was evident that the probable outcomes had changed, but so many people failed to recognize it because they were so focused on their desired outcomes.

Simple Straddle Strategy

What’s most appealing about derivatives is that the payoff is customizable. The needs are tailored to the approach, as there are several ways to express a hedge or a trade. Buying a call option and a put option with the same strike price, expiring at the same date may seem counter-intuitive at first glance if you are not familiar with options. When you start to dive into the dynamics it makes more sense. As a derivative, options are priced according to the underlying asset, under a set of different “Greeks”.
This strategy, called a Straddle, does not have a directional bias in the underlying asset, that is, up or down. The Straddle benefits from a rise in volatility, more specifically implied volatility (Vega) and realized volatility (Gamma).
A Straddle is appropriate when an investor is expecting a large move in a stock price, but does not know which direction the move will be. This could be due to an earnings announcement, a takeover bid or something more on the macro level. This position is highly sensitive to any change in Vega, which makes it vulnerable to a volatility crush, meaning a sudden drop in volatility after an event unfolds and does not produce the expected impact in the stock. But if the event has a large impact on the move of the stock, the investor can capture the mispricing of the volatility and profit from it.

Vanna & Charm

Vanna and Charm are two overlooked Greeks in the volatility space that have a very large impact in really understanding the flow dynamics of Dealer Hedging and can be of good assistance to build a quantitative strategy.
Essentially, Dealer positioning can drastically change the probability outcomes, and this needs to be modelled. You usually wouldn’t bet against a person that is being challenged to do complicated things. If everyone owns puts, the market is less likely to go down, as market makers and dealers are pre-hedged. If everyone is short puts, then the market is more likely to go down.
Vanna and Charm are viewed as a function of dealer positioning. Dealers are generally short puts and long calls, which makes it a short stock underlying position. This is not empirical though. Different market dynamics affects dealer positioning. As time passes, the position expires and the volatility declines, making it possible to measure Vanna, which is the effect in Delta relative to the rate of change in implied volatility, as well as Charm, which is the effect that time has on Delta. By measuring this you can see the effect of these flows on dealer positioning on the market. Let’s suppose that a dealer is short calls in Tesla.

To hedge this, the dealer needs to buy Tesla stocks. This can cause a temporary rise in the stock. But at some point, call buying starts to lose momentum, the premium starts to decay and through Vanna and Charm you can quantify that momentum loss and use it to your advantage. This was exactly how some of the best volatility arbitrageurs predicted the top in Tesla stocks in February of 2021.
A retail investor does not have the same tools as these professionals of course, but you can take in the volume and the look at the open interest and model the volatility surfaces.
But the key is to look at the flows that come in and have a clear understanding if these dealers are hedged or not, how the market makers are going to react and when they are rebalancing their portfolios (normally towards OPEX). If the dealers are insufficiently hedged it is more likely that a big move in the underlying might happen.

Sources

Volatility as an asset class

Vanilla, Exotic and OTC Derivative Products

Major scandals Involving Derivatives

Hull, John C. (2014) Options, Futures and Other Derivatives (9th Edition). Pearson.
Smith, Donald J. (1997) Aggressive Corporate Finance: A Close Look at the Procter & Gamble-Bankers Trust Leveraged Swap
Taleb, N. (1996). Taleb on risk: Dynamic hedging. New York: Wiley.

Discretionary and Quantitative Strategies