The value of a covered warrant represents forecast earnings linked to the possibility of usefully exercising the incorporated right. This possibility is linked to the performance of prices of the underlying in relation to the set strike price.

The value of a covered warrant following exercise of the right, which, for a call warrant, consists in the difference between the spot price and the strike price, and for a put warrant, in the different between the strike price and the spot price, is commonly called the intrinsic value. This cannot take on negative values because, as previously explained, the bearer has the right but not the obligation to buy or sell. Thus, if the spot price is lower than the strike price of a call warrant (or vice versa for a put warrant), the bearer simply refrains from exercising the right, with his loss limited to the amounts paid for the premium.

The relationship between the spot price and the strike price also determines the moneyness of a covered warrant. This concept describes the distance of the spot price from the strike price.

A covered warrant is at-the-money when its strike price is equal to the spot price (thus, its intrinsic value is nil); in-the-money when the investor earns a profit from exercising the warrant (positive intrinsic value, known as a positive pay off). Thus, a call warrant is in-the-money when the strike price is less than the spot price while, on the contrary, a put warrant is in-the-money when the strike price is greater than the spot price (when this difference is very wide, warrants are described as deep in-the-money). A call warrant is out-of-the-money when the different between the spot price and the strike price is negative, and thus it does not attribute any gain to the investor (generally, as the intrinsic value cannot be negative, is nil). If the difference is very wide, the warrant is described as deep out-of-the-money.

Thus, summarizing:

Thus, the intrinsic value does not represent the entire value of a covered warrant. Looking through published listings, it can be noted that even deep out-of-the-money warrants have a price. This price represents the time value, and expresses the likelihood that the warrant may take on a positive intrinsic value within the maturity date or, if it is already in-the-money, the likelihood that the intrinsic value will increase, thus increasing earnings for the investor.

The value of a covered warrant is, therefore, the sum of two components:+ intrinsic value and time value. These two components come together to form the market price, which expresses the likelihood that the bearer will receive more or less high earnings. This explains why, generally, warrant are not exercised but sold on the market. In exercising warrants, the bearer only earns the intrinsic value, and gives up the time value. The above is true for call warrants, but, at least theoretically, not for put warrants.

The fact that, at least theoretically, there may be cases where it is cost-effective to exercise a put warrant early explains why, with all other conditions being equal, the value of an American-style put warrant is greater than a European-style put warrant which, as you remember, does not allow for early exercise.

In order to calculate the theoretic value of a covered warrant, probabilistic models are used, which combine several parameters. Specifically, the value depends on:

a) the strike price;

b) the spot price;

c) the duration (time from the valuation date to the maturity of the option);

d) the risk free interest rate;

e) the volatility of the underlying asset;

f) any yield on the underlying asset (for example, expected dividends, for shares).

Changes in any of the parameters will lead to a change in the price of the covered warrant, and is more or less correlated to changes in the other parameters. For the sake of simplicity, here we study the effect of each parameter, assuming the others are fixed.

The influence of the strike price in relation to the spot price can be understood intuitively: in the case of out of-the-money options, the greater the gap between the spot price and the strike price at the moment of purchase, the lesser the value of the warrant, as there will be lower likelihood that the spot price will reach useful values for the investor. Vice versa, in the case of in-the-money options, the greater the gap between the spot price and the strike price at the moment of purchase, the greater the value of the warrant, as there will be greater likelihood that the spot price will remain at useful values for the investor.

The performance of the spot prices takes on particular importance:

• the price of the call warrant has a direct relationships with the performance of the underlying asset. with all other conditions being equal, increases in the price of the underlying correspond to increases in the price of the warrant, and vice versa in case of decreases:

• the price of put warrants have an inverse relationship with the performance of the underlying. Thus, with all other conditions being equal, an increase in the price of the underlying leads to a decrease in the price of the put warrant, and vice versa.

For a more detailed explanation of the reactivity of covered warrant prices to the performance of the underlying, see the paragraph regarding Delta in the following section "The greeks".

Another determining factor for the valuation of covered warrants is time.

As we have seen, one of the components of the price of a warrant is the time value. We have also seen that this component represents the likelihood that the security will achieve earnings (or greater earnings) for the bearer, within the maturity date. Thus, it can be intuitively understood that the time value decreases as time goes on, because the nearer the maturity date, the lesser the likelihood that the warrant will increase in value, until the warrant zeroes upon maturity, when the value of the warrant simply coincides with the intrinsic value, if positive.

This results in a fundamental characteristic of these financial instruments: with the other parameters remaining the same, the price of a warrant decreases as time goes on, and this decrease accelerates as the maturity nears. It’s like a melting ice cream cone: if you hold it without eating it, it melts, first slowly, then ever more quickly. The chart below illustrates the development of the price of an option as the time available decreases, in the cases at-the-money (ATM), in-the-money (ITM), and out-of-the-money (OTM), and also illustrates that upon maturity, only in-the-money warrants maintain value (equal to the intrinsic value).

Among the elements that contribute to forming the value of a covered warrant, it is worth mentioning the volatility of the underlying. This concept expresses the degree of variability in the prices of an asset: the quicker and greater the fluctuation in prices, the higher the volatility.

Volatility has a direct influence on both call and put warrants, in the sense that increases/decreases in volatility correspond to increases/decreases in the warrant prices. The greater the volatility of a security, the more likely that its price will move and that, among the possible values it could reach, it will reach favourable values for the investor. In other words, with greater volatility, if a warrant is out-of-the-money, it is more likely that it moves to in-the-money or, if it is already in-the-money, that it becomes more deep in-the-money, resulting in possibly large earnings. However, it is important to be aware that with increased volatility, it is also likely that an in-the-money can move out-of-the-money or, even deep-out-of-the-money, even though its loss is still limited to the value of the premium.

Keep in mind that volatility, as a measure of the variability in prices, does not provide any indication of upwards or downwards trend in the security. To better understand this concept, we compared the performance of the MIB30 index (the index of the top thirty securities in terms of liquidity and capitalisation on the Italian stock exchange) and the related 30-day volatility from January 1999 – November 2000. The chart illustrates that the volatility of the MIB30 index had upwards and downwards trends which were not directly related to the performance of the index. For example, from June – October 2000, against substantial stability of the index, its volatility decreased significantly.

Up to this point, volatility has been determined with reference to past values. In this sense, we refer to historical volatility, which can be objectively calculated retrospectively.

However, historical volatility is not necessarily indicative of the future volatility of the underlying. For this purpose, implicit volatility is also commonly used. This does not represent a historical datum, but expresses the expectations of market operators regarding the variability of the underlying. Implicit (referring to prices) is used as the volatility is extrapolated from the prices of options contracts formed on the market. It is determined using the same calculation models for the options prices, considering, however, the price as a known variable, and volatility as unknown.

Implicit volatility plays a significant role in the options market. Frequently, in operations between professional investors and intermediaries, the implicit volatility is quoted instead of the price.

Implicit volatility is also an important tool for guiding investor choices: as we have seen, this allows for an effective comparison of the cost-effectiveness of the various covered warrants on the market, also compared to other similar products (such as options contracts listed on the derivatives market).

Lastly, the elements that contribute to forming the price of covered warrants also include the risk free interest rate and expected yield of the underlying.

Considering the average life of warrants and the current stability of rates, the interest rate is a marginally important element. It is enough to know that an increase in the interest rate positively influences the value of a call warrant, and negatively influences the value of a put warrant (and vice versa in case of a decrease).

An increase in the expected yield lowers the price of a call warrant and increases the price of a put warrant (and vice versa).

We have seen that investments in covered warrants are exposed to the performance of several economic parameters and, more specifically, to those which combine to form the price (price, volatility and expected yield of the underlying, and risk free interest rate). The effect of these parameters on the economic result of the investment depends on how these parameters combine with the structural features of each warrant (call or put, strike price, maturity, ratio). This "combination" is clearly not static, but continuously changes as a result of the changes in the economic parameters.

The complexity of these financial instruments requires (especially from professional operators) the adoption of sophisticated monitoring procedures capable of identifying the impact of each economic parameter on the price of the instruments. Financial analysts have introduced several coefficients (known as the "greeks") to measure this impact: Delta and Gamma for the performance of the underlying, Theta for the time value, Vega for volatility and Rho for the interest rate.

The "greeks" are normally used by professional operators to manage the risk of portfolios incorporating derivatives and securities. They are not extremely significant for individual investors. In any event, for the sake of completeness, we will look at the main greeks.

DELTA AND GAMMA COEFFICIENTS

The Delta coefficient indicates the change (in absolute value, not percentage) in the price of a covered warrant in relation to increases or decreases in the spot price. Increases/decreases in the underlying which refer to the value of the Delta must be extremely small (±1%) to avoid erroneous interpretation of this value, because, as the change in the underlying increases, the error in the Delta calculation increases. Thus, the value of the Delta represents how much of the change in the underlying adds or subtracts from the price of the warrant. The Delta ranges from 0% to 100% for call warrants, and from 0% to -100% for put warrants (the minus sign is due to the fact that increases in the underlying correspond to decreases in put warrants, and vice versa).

Specifically:

• a Delta near zero expresses substantial stability in the price of the option (in absolute terms) against small changes in the underlying;

• a Delta near ±100% (depending whether the warrant is call or put) expresses high variability (always in absolute values and not percentages) in the price in relation to (small) changes in the underlying.

These examples introduce two points to be considered. The first is that the Delta is not constant, but varies depending on moneyness and, specifically, takes on higher values (irrespective of the ± sign) for in-the-money warrants compared to out-of-the-money warrants (in the examples, 90% and 10%, respectively).

Thus, the more the warrant is out-of-the-money, the nearer the Delta moves toward zero, while as the warrant moves in-the-money, the Delta nears ±100%.

The second consideration is that the Delta measures price reactivity in absolute, not percentage terms: it tells you the amount of change in Euro in the price of the warrant against small changes in the underlying.

In answer the question of how much this change amounts to in percentage terms, the leverage must be taken into account. Leverage is the number of times the percentage change in the underlying must be multiplied to obtain the corresponding percentage change to be applied to the price of the covered warrant.

It is very simple to calculate the leverage: multiply the Delta by the gearing (which is simply the ratio of the spot price to the price of the covered warrant multiplied by the cover ratio).

In example 1 (an in-the-money call warrant) above, the leverage would
be:

an increase of 1% in the underlying would correspond to an increase of 3.9% in the warrant price.

In example no. 2 (an out-of-the-money put warrant) the leverage would be:

an increase of 1% in the underlying would correspond to a decrease of 9.1% in the warrant price (as it is a put warrant).

As the examples demonstrate, if, in terms of absolute value, in-the-money covered warrants are the most reactive to changes in the underlying (Delta near ±100%), the situation changes radically if the percentage change is considered, where out-of-the-money warrants show the greatest sensitivity.

Moreover, it is important to consider that the Delta is also influenced by the time factor: as the maturity of the covered warrant nears, the Delta tends to progressively take on values near ±100% and 0% depending on whether the warrants are in-the money or out-of-the-money, respectively.

If the Delta continuously changes in relation to the time, it can be said that this provides and instant analysis of the sensitivity of the covered warrant.

The "instant" value of this parameter is confirmed by the fact that Delta values vary also in relation to the performance of the underlying. There is a coefficient for measuring this change. It is called Gamma, and it expresses the degree of change in Delta in relation to a unit change in the spot price. If its value is low, it means that the Delta is not very sensitive to the performance of the underlying. If the Delta is high, the reverse is true.

Vega Coefficient

We have taken a look at the significance of the volatility of the underlying in determining the value of a covered warrant. Thus, it is important to know how sensitive the covered warrant is to changes in volatility, specifically in order to understand the degree of risk in your warrants. The volatility of a security (as well as its price) changes dynamically, determining sometimes considerable effects on the value of the warrant (remember that an increase in volatility results in an increase in the value of a call warrant and a put warrant, and vice versa).

For this purpose, the Vega (or Kappa) coefficient is helpful. Vega expressed the expected change (in absolute value and not percentage) in the value of a covered warrant following a unit change in volatility (as volatility is expressed as a percentage, unit change is considered one percentage point).

The Vega of a covered warrant is always a positive number because, as previously explained, the volatility directly influences both call warrants and put warrants, and reaches a maximum value when the covered warrant is at-the-money, while it decreases as the warrant moves towards in or out-of-the-money.

The sensitivity of the price of a covered warrant to volatility is, therefore, at the maximum when the warrant is at-the-money. This is true in terms of absolute values, but be aware that it is no longer true if you consider the impact of the change in volatility on the price in percentage terms. In this case, out-of-the-money covered warrants are the most affected by the change in volatility. This is due to the fact that prices of out-of-the-money warrants are lower than those of at-the-money or in-the-money warrants.

This situation is similar to that previously illustrated in the first part of this section, regarding the Delta. The second consideration set forth in the examples demonstrated that lower absolute values of the coefficient for out-of-the-money covered warrants did not correspond to lower sensitivity in their prices, in percentage terms. This situation should draw attention to the considerable risk of out-of-the-money warrants, as their high degree of sensitivity can result in enormous losses if the economic parameters move in the opposite direction that that hoped for by the investor.

Another characteristic of Vega is that its value decreases over time. Thus, with all other conditions being equal, warrants near maturity are less sensitive to changes in volatility.

Other coefficients

We have illustrated that covered warrants are subject (with other conditions remaining the same) to a natural loss of value over time, as the time value nears zero. This effect is measured by the Theta coefficient, which indicates the amount of loss (in absolute, not percentage value) the value of the covered warrant is subject to in a given period (one day, one week, etc.). For this reason, the Theta is always negative.

We have also seen that covered warrants depreciate at an increasing pace and thus, Theta takes on increasing values as warrants near their maturity.

Theta, like Vega, reaches its maximum value for at-the-money warrants. The considerations set forth for Delta and Vega also apply to Theta, in that it expresses the change due to the time value in terms of absolute value, and not percentage. In percentage terms, the situation changes considerably, and out-of-the-money warrants demonstrate the greatest sensitivity to the passing of time.

It is important to highlight once again the extreme risk of out-of-the-money warrants, which are extremely sensitive not only to unfavourable trends in the price and volatility of the underlying, but also to the time factor. While the price and volatility trends can be favourable, the passage of time is always negative for the results of the investment.

Lastly, the sensitivity of covered warrant prices to changes in interest rates is measured by the coefficient Rho.

Currently, in Italy, covered warrants are listed on a specific section of the "Borsa" called the CWM (Electronic Covered Warrants Market), managed by Borsa Italiana spa. This market is divided into three main segments:

• "plain vanilla", which includes covered warrants consisting in a call or put option;
• "structured/exotic", which includes covered warrants that combine call and/or put options or incorporate exotic options;
• "certificates", which replicate the performance of the underlying asset.

The covered warrants described herein are typical warrants, which belong to the "plain vanilla" segment.

The company managing the market – in case of the single market currently operating, "Borsa Italiana"- is also responsible for the admission to listing of covered warrants once the requirements set forth by its regulations have been ascertained, regarding both the issuers and the financial instruments.

Different to other financial instruments, there is no minimum free float (and thus, circulation among the public). Once listed, this security is circulated among the public through trading on the stock exchange, where the issuer sells the warrants on a continuous basis.

The issuer (or delegated party) must also carry out the role of market maker, to ensure a minimum level of liquidity by committing to display bid (the price at which it is willing to buy) and ask (the price at which it is willing to sell) prices for a minimum trading lot, or for a different quantity set by the market management company for each covered warrant.

The limitation of the commitment to a single trading lot and the requirement (contained in the accompanying instructions to the regulations of Borsa Italiana) that when a transaction is carried out on the warrants displayed the market maker has 5 minutes to insert new bid and ask prices sometimes makes it unprofitable to disinvest the warrants, especially in the case of deep out-of-the-money warrants, whose extremely low price results in a paltry countervalue of the minimum lot.

At this time (April 2003), there is no spread limit, meaning the difference between bid and ask prices. Thus, some market makers could propose significant gaps between the prices at which they are willing to buy and sell. However, it should be noted that the regulations in this regard is being revised, and a maximum bid-ask spread will soon be introduced, in order to control the difference between market makers’ bid and ask prices.

Trading is automatically suspended in case of a deviation exceeding a certain amount (currently 30%) between two contracts concluded in sequence. In specific cases, market makers can also request to be temporarily exonerated by Borsa Italiana from displaying bid and ask prices.

The complete regulations concerning trading on the covered warrant market are contained in the Rules of the Borsa Italiana and in the related instructions contained on the website www.borsaitaliana.it, in the section Rules and Instructions.

At times, covered warrants which have not yet been listed are traded on alternative trading systems (ATS), pursuant to Article 78 of the Consolidated Law on Finance. Listed warrants are traded on ATS when the market is closed. It is also possible to issue warrants traded exclusively on ATS. However, this type of trading might not provide the same guarantees, in terms of transparency of price formation and liquidity, offered by trading on an official market.

These notes are intended as a sufficiently detailed, sufficiently simple and effective description of covered warrants. They are also intended to offer a technical tool to assist investors in choosing between warrants from different issuers, facilitating the comparison of cost-effectives, also in relation to other products, as will be explained further on.

We have already mentioned the fact that cost-effectiveness cannot be easily valued on the basis of price, given the difficulty in comparing prices of covered warrants which are similar, but not identical.

We have also noted that implicit volatility is a precious tool for comparison, which can be used to compare the prices of several covered warrants with characteristics that are similar, but not an exact match.

An example may assist in clarifying this issue

It should be clarified that the implicit volatility calculated as above does not necessarily correspond to that effectively quoted by the market maker, which could have different expectations of the interest rate and dividends (expectations which could result in different values of volatility). Nonetheless, in terms of a relative comparison, implicit volatility is an excellent measuring tool (provided that the same values are used for the other parameters – interest rate and yield of the underlying asset, for all covered warrants compared).

How is implicit volatility calculated? It has already been mentioned that the same calculation models are used as those for determining the price, inserting the price as a known variable and volatility as unknown. To this end, it is possible to use our preset calculator to determine the implicit volatility, by inserting the data requested. Our calculator provides a figure that is not intended to be the effective and sole value of implicit volatility that traders should negotiate, but is exclusively to be used as a tool for comparing several covered warrants (and understand the cost-effectiveness) provided that they have similar strike prices and maturities. The user is not required to enter specific dividend and interest rate information, as the calculator uses several properties of the differential stochastic equation underlying the calculation. Provided that these figures are the same for all the warrants compared, higher implicit volatility means higher price, and thus, less cost-effectiveness (the calculator is on www.consob.it).

Covered warrants are not the only instruments available providing the right to buy or sell a certain assets at maturity For decades, a more diffuse instrument has been options contracts, whereby one party pays a premium to acquire the future right to sell or buy a specific asset at present conditions.

As you can see, options contracts have financial characteristics which are highly similar to covered warrants. You could say that from a certain financial point of view, the position of an investor purchasing a covered warrant is equivalent to that of a party who acquires, through an options contract, the right to buy or sell a certain asset.

In fact, covered warrants were created in order to package the options contract mechanism into a "box" more suitable for small investors. The financial content is the same, however, there are "structural" differences: the presence of a certificate which can be traded between investors (the box) and, specifically, an issuer of the certificate.

On the contrary, options contracts are not represented by certificates, and simply consist in a commitment agreed between the buyer and seller. These contracts are rendered fungible by the intermediation of a clearing house which acts as the central counterparty.

Carrying out the role of central counterparty means that, though the contracts are formally executed between any two parties, the clearing house guarantees their fulfilment, thus eliminating the risk linked to the solvency of the contracting parties. This risk, known as counterparty risk, is present for covered warrants. This in addition to the risk that, upon maturity, the issuer may not be able to fulfil the performance incorporated in the warrant. Thus, in the second case, we can refer to issuer risk.

The guarantee is also granted through a "margining" system, based on recording the daily value of profits and losses originating from the open contractual positions with the clearing house (marking- to-the-market). Investors operating in options have to deposit margins with the clearing house in order to guarantee their commitments. Margins are proportionate to the exposure of the operator’s position, and are adjusted to the changes in the exposure on a daily basis.

The requirement to deposit margins is applied only to investors who undertake the commitment by contract, and not to those who acquire the right to buy or sell. The latter position is similar to that of an investor holding a call and put warrant, respectively. The reason for this is clear: Only the first risks a margin call for an undeterminable amount a priori. The second only risks losing his premium which, in any event, was already paid upon conclusion of the contract.

In Italy, the clearing house for the options market is Cassa di Compensazione e GaranziaS.p.a..

There are other differences between covered warrants and options. Covered warrants usually have longer maturity, generally more than one year, while options usually have a maturity of less than one year.

In addition, options require a minimum investment. While this is not an excessive amount, it is greater than the investment for covered warrants, which are mainly targeted to small and medium investors. It should also be noted that the fees charged by the intermediary for dealing in options could significantly exceed those for covered warrants.

In Italy, the options most similar to covered warrants are those traded on the Italian Derivatives Market (IDEM), managed by Borsa Italiana, where contracts on the MIB30 index (MIBO30) and on the primary shares are traded.

On the IDEM market, as on the covered warrant market (CWM), contract liquidity is favoured by the existence of market makers. However, on the IDEM market, there are usually several market makers. This is an element of competition which differentiates IDEM compared to the CWM, where there is a sole market maker, that is usually the issuer of the covered warrants.

Lastly, IDEM options cannot be settled through cash settlement (with the exception of options on the MIB30). The option is held until maturity, followed by the physical delivery of the securities, unless the investor closes his positions before maturity by carrying out offsetting transactions.

If you keep in mind the differences illustrated above, investing in IDEM options can represent an alternative to the purchase of covered warrants with short-medium duration. However, it is essential to note the high level of risk of options and warrants near maturity, due to the high Theta values).

Yet again, however, the individual investor must assess the cost-effectiveness of various investments. With this initiative, Consob simply intends to provide useful knowledge instruments to aid investors in making informed choices. These elements include the calculator presented in the previous chapter. Follow the same steps: insert the information requested (in this case) on the IDEM option, to calculate the implicit volatility. This can be used to compare products which may be alternatives to covered warrants, due to their characteristics. 

As with any financial instrument, the public offer of covered warrants is subject to the regulations on public offering.

Nonetheless, the absence of the free float requirement for listing covered warrants, and thus, the fact that the security is directly sold to the public on the stock exchange ensures that in Italy (except in unusual cases), public offers of warrant, understood as preliminary placement for the circulation of the security, are not carried out. In any event, as a result of the exemption set forth in Article 100 (1)(f) of the Consolidated Law on Finance, these regulations would not be applied to any issues of warrants with cash settlement issued by banks and carried out over the counter. Therefore, in effect, the regulations on public offers does not apply, except in very few cases.

As a result, the issuer is neither required to draw up an investment prospectus, nor to submit its advertising campaigns to Consob’s approval. It remains understood that when Consob becomes aware of such disclosure, it verifies the correctness of the information disclosed by persons under its supervision. The Italian Antitrust Authority has the ultimate authority as regards issues of deceptive advertising.

If their warrants are admitted to the CWM, issuers then must draw up a listing prospectus to be submitted to Consob. The prospectus comprises an informative document on the issuer and explanatory notes regarding the product being listed.

Consob has the duty to ensure that the prospectus provides transparency regarding the characteristics of the issuer, the products (with specific attention to risks), as well as the contractual and listing terms and conditions. The prospectus also provides examples of the possible return on these investments as a result of changes in the investment scenario (change in prices and volatility of the underlying and residual life).

The information prospectuses are made available to the public at Borsa Italiana and at the issuers' premises. The original of the prospectus is filed in the Consob prospectus archive. They can also be viewed on the site www.consob.it.

Once the information prospectus is published and Borsa Italiana has listed the security, trading on the stock exchange may begin. Supervision of the regularity of trading, and thus, of the conduct of operators (including market makers) is the direct responsibility of Borsa Italiana.

Consob must, in any case, supervise the work of Borsa Italiana and, within the scope of this activity, approve the regulations of the markets Borsa Italiana manages.

For those interested in more information on the topics covered herein, Consob has published several Quaderni di Finanza on these matters. Specifically, we recommend reading the following:

No. 25 - Volatilità dei titoli industriali e volatilità dei titoli finanziari: alcuni fatti stilizzati (M. Bagella and L.Becchetti);

No. 34 - Opzioni sul MIB30: proprietà fondamentali,volatility trading ed efficienza di mercato (L. Cavallo, P. Mammola, D. Sabatini).