Main categories of derivative products

• Forward agreements
  • Forward contracts
  • Futures contracts
• Swaps
  • Interest rate swaps
  • Currency swaps
  • Asset swaps
  • Credit default swaps
  • Total return swaps
  • Other types of swap agreements
• Options

FORWARD AGREEMENTS

A forward agreement is an agreement between two parties for the consignment of a specific quantity of a certain underlying product at a pre-established price (consignment price) and on a pre-established date (maturity date).

The underlying product can be of various types:

• financial assets, such as shares, bonds, currency, financial instruments, derivatives, etc;
• goods, such as oil, gold, grain, etc..

The purchaser of the forward agreement (in other words the party who undertakes as of the maturity date to pay the consignment price in order to receive the underlying products) opens a long position, while the seller ( the party who undertakes on maturity to hand over the underlying product in order to receive the consignment price) opens a short position.

The forward agreements are generally structured in such a way that, at the time of their finalization, the two services are equivalent. This is obtained by setting the consignment price, in other words that established in the agreement, as equal to the forward price. The latter is equal to the current price of the underlying products (so-called spot price) increased by the financial value of the time running between the date of stipulation and the maturity date. If this condition occurs, in other words if the services are equivalent, on conclusion of the agreement the exchange of any compensatory service does not need to take place between the parties.

It goes without saying that, if the forward price initially coincides with the consignment price, subsequently, over the duration of the agreement, it will change in relation, essentially, to the changes in the current price which the underlying product will gradually adopt.

The changes in the value of the underlying product determine the risk/return profile of a forward agreement, which can be summarized as follows:

• for the purchaser of the agreement, in other words the party which must buy a certain asset on a certain date and at a price already established in the agreement, the risk is represented by the depreciation of the asset. In this case, in fact, the party would in any event be obliged to pay the price already established in the agreement for the assets whose market value is lower than the price to be paid: if the purchaser was not bound by the agreement, it could purchase the asset on the market at a lower price more advantageously. For the opposite reason, in the case of appreciation of the underlying product, the party will accrue a profit, since it will purchase at a certain price that which is worth more;
• for the seller of the agreement, in other words the party which must sell a certain asset on a certain date and at a price already established in the agreement, the risk is represented by the appreciation of the asset. The contractual commitment, in fact, obliges the party to sell the asset at a lower price than that which could be achieved on the market. The party would by contrast generate a profit in the event of the depreciation of the underlying product, since thanks to the agreement entered into, it will sell the asset at a price higher than the market one.

The decision to stipulate a forward agreement can be associated with the following aims:

• hedging purpose: let us pose the case of holding a certain asset, for example ten-year Government securities, which we already know we will have to sell at a future date, for example to pay the instalment of a mortgage loan which falls due on 30 September and whose amount is equal to the current value of the securities. In this situation, we are exposed to the risk of depreciation which the Government securities could suffer, with the consequence that, as of 30 September, the amount from their sale will not be enough to make the mortgage payment. The stipulation of a forward agreement covered us from this risk. In detail, we will sell forward the Government securities with a maturity of 30 September at a consignment price equal to their current price, By doing this, even if as of 30 September our securities have sharply depreciated, by virtue of the agreement we can sell them at the price already established, and thus make the mortgage payment without any problem.
• speculative purpose: if we are convinced that a certain asset, for example Alfa shares, will follow a certain future trend, for example a considerable increase in price, by means of the stipulation of a forward agreement we can undertake the exposure on the Alfa shares on a consistent basis with our expectations. It will be sufficient to purchase a forward agreement with the consignment price equal to the forward price and, if as we expect, the security increases its value, on maturity of the agreement we will acquire the Alfa shares at a price which is clearly lower than the market one. If our expectations are by contrast bearish, we will have to sell the forward agreement;
• arbitrage purpose: let us pose the case of being professional experts, capable of detecting that on the market there is the possibility of stipulating forward agreements which concern a certain asset, such as Beta bonds, where the consignment price (in other words the price established in the agreement) is higher than the forward price (in other words the current market price increased by the financial value of the time as from now until the maturity of the forward agreement) of the bonds. If we are so clever as to identify this difference, by means of the forward agreement we can set up operations which permit us to achieve a profit without risk. In fact, we will straight away purchase the Beta bonds at the current market price and, at the same time, sell the forward agreement. On maturity, the cost we have incurred for our Beta bonds will be equal to the price originally paid plus the financial value of the time, in essence the forward price, but via the agreement we could receive a higher sum, represented by the consignment price, thereby generating a profit without risk deriving from the difference between the consignment price and the forward one. Vice versa, if we have Beta bonds in our portfolio and we note that the consignment price is lower than the forward price, it is worth our while selling the Beta bonds straight away at the current price and at the same time purchasing the forward agreement: on maturity, we will regain the same bonds against payment of a lower amount than that obtained from their sale.

The execution of the agreement on maturity may take place:

• by means of the effective consignment of the underlying assets by the seller to the purchaser, against payment of the consignment price: in this case, this involves physical delivery;
• by means of the payment of the differential in cash between the current price of the underlying product, on maturity, and the consignment price indicated in the agreement. This difference, if positive, will be payable by the seller to the purchaser of the agreement, or vice versa if negative: in this case, this involves consignment by way of differential or cash settlement.

The main types of forward agreements are forward contracts and futures contracts.

Forwards contracts

Forward contracts are characterized by the fact that they are stipulated outside organized markets. In technical jargon, we say that they are traded OTC (over-the-counter). The consignment price is also called for the forward price.

In order to comprehend the function of this instrument, it is useful to analyse the cash flows which derive therefrom, or the payments which are exchanged between the two parties over the entire duration of the contract.

In the forward contract, the only cash flows appear on maturity, when the purchaser receives the underlying assets in exchange for the price agreed in the contract (physical delivery), or the two parties exchange the difference between the market price of the asset on maturity and the consignment price indicated in the contract which, if positive, will be payable by the seller to the purchaser and vice versa if negative (cash settlement).

By contrast, intermediate cash flows are not envisaged over the duration of the contract, even if during this period the forward price of the underlying asset is subject to changes essentially in relation to the performance of the related current market price. As a rule, cash flows are not envisaged even as of the stipulation date, considering that, like all forward agreements, they are generally structured in such a way as to render to two services equivalent.

 

Future contracts

Futures are also forward agreements. They differ from forward contracts since they are standardized and traded on organized markets. Their price – which emerges, as for all listed securities, from trading – is also called the future price.

The future price corresponds to the consignment price of the forward contracts but, since it is listed, it is not really negotiated between the parties in that, like all listed securities, it is the result of the meeting of the purchase proposals introduced by whomever wants to purchase with the sales proposals introduced by whomever intends to sell. As a rule, it is indicated in "index points".

In relation to the underlying asset, the futures contract adopts different names:

commodity future, if involving a good, and financial future if involving a financial asset.

The standardization of the futures contracts means that series of contracts exist which are the same with regard to:

• object (in other words the underlying assets of the contract);
• dimension (in other words the nominal value of the contract). This is obtained by multiplying the price, usually indicated in index points, by a conventionally established multiplier;
• maturity date: a pre-established calendar is observed with a limited number of maturities, as a rule four times a year;
• trading rules including:
  • the dealing hours;
  • the minimum price change which can be listed on the futures market (so-called tick);
  • the formalities for settling the transactions;
  • the consignment locations.

The standardization of the contracts and the possibility of trading them on organized markets involves important effects:

• the parties can "negotiate" just the price of the contract (even if, since the security is listed, a genuine negotiation between the parties does not exist);
• the possibility of an early closure of a futures position, without waiting for the maturity, by means of its trading;
• a considerable profit in terms of liquidity of the trading and, as a consequence, a reduction in the costs incurred by the operators.

Another distinguishing element with respect to forward contracts, associated with their trading on organized markets, is the presence of a sole counterpart for all the transactions, the clearing house, which for the Italian market is the Cassa di Compensazione e Garanzia. Its task is to ensure the satisfactory conclusion of the transactions and the daily clearing (understood to be the calculation) and settlement of the profits and losses generated by the parties

The clearing house intervenes in all the transactions concluded on the futures market: when two parties purchase/sell a contract, they immediately inform the clearing house which takes steps to buy the future from the party which has sold and sell it to the party which has purchased. In this way, in the event of the default of one of the two parties, the clearing house takes over their obligations, guaranteeing the satisfactory outcome of the transaction, subject to it then making good its losses on the defaulting party.

In order to acquit its duties on a systematic and on-going basis and ensure the efficiency of the system, the clearing house adopts a series of measures:

• it never undertakes, on its own account, open positions on the markets: the number and the type of contracts acquired are exactly equal to those of the contracts sold, so that the risk of unfavourable changes in the prices of the underlying assets does not encumber the house;
• it is exclusively the counterpart of the intermediaries who are members of said clearing house (mainly banks and asset management and investment firms), endowed with specific capitalization and professionalism requisites. Therefore, if an investor wishes to open a futures position, and is not a member of the clearing house, it will have to contact one of the member intermediaries which will act as broker and apply the same mechanisms to the investor, protecting against the risk of default, envisaged by the clearing house for its members;
• it adopts the system of margins, protecting open positions on the market from the risk of default, which envisages the payment by the parties of an initial margin and variation margins over the duration of the contract.

In detail, it functions as follows: at the time of opening a position (long or short) in futures, both the parties will have to pay over the so-called initial margin (guaranteeing the satisfactory conclusion of the transaction, a margin which will be returned on the day of settlement of the futures contract) into a specific account held with the clearing house (or opened on their behalf at the clearing house by the respective brokers). This margin is usually a percentage of the nominal value of the contract (multiplied by the number of the contracts stipulated) and, in general, it is proportionate to the volatility of the price of the underlying product, in the sense that greater volatility (and in other words greater probability that the underlying product undergoes extensive price fluctuations) corresponds to a higher margin. In addition to the initial margin, the clearing house calculates another margin, the variation margin, which corresponds to the gain or the loss generated by each of the two parties at the end of the business day. The variation margin is calculated by means of the marking-to-market mechanism: at the end of the day, the clearing house determines the closing price of the future and, calculating the difference between this and the closing price on the previous day, determines the profit and the loss of each party as if the position had been settled at that moment. The party who has suffered an unfavourable price variation pays the clearing house the related variation margin and the latter takes steps to transfer it to the party for whom the price variation was positive.

If the balance of the account of a party should drop below the minimum level, the so-called maintenance margin, this party would receive a margin call from the clearing house, or rather an invitation to make an adequate payment so as to restore the margin.

In the case of futures contracts, there are cash flows both at the time of stipulation of the contract (initial margin), over the duration of the same (variation margins), and on maturity (settlement of the contract).

 

SWAPS

The literal translation of swap, in other words exchange, identifies the essence of the contract: two parties agree to exchange payments flows between them (also called cash flows) on certain dates. The payments can be expressed in the same currency or in different currencies and their amount is determined in relation to an underlying element. The swaps are OTC (over-the-counter) contacts and, therefore, not traded on organized markets.

The underlying element can be of various types and considerably influences the features of the contract which may, in practice, adopt different forms.

Swap contracts are generally established in such a way that, at the time of stipulation, the envisaged services are equivalent. In other words, the initial value of the contract is made null, so as not to generate any initial cash flow for offsetting the portion encumbered by services of greater value.

If at the time of stipulation, the two services are equivalent, it is not guaranteed that they will remain so for the entire duration of the contract. On the contrary, it is precisely the change in the value of the services which generates the risk/return profile; the party who is obliged to perform a service whose value has depreciated with respect to the initial value (and, therefore, with respect to the counter-service), will accrue a profit and vice versa.

The essential feature of the swap transactions – in other words that of exchanging the cash flows, associated with an underlying asset, with other cash flows of another type – determines the creation of new financial opportunities which otherwise would not be achievable. These opportunities can be exploited in relation to numerous needs, which may be hedging, speculation or arbitrage related, according to the purposes the operator sets itself.

The main swap agreements observed on financial markets are illustrated as follows.

 

Interest rate swaps

Interest rate swaps (IRS) are agreements in which two counterparts exchange periodic interest payments, calculated on a sum of money, called notional principal amount, for a pre-established period of time equating to the duration of the agreement, and in other words until maturity (maturity or termination date) of said agreement. The name interest rate swap derives from the fact that the payments made are similar to interest payments on a debt.

There are numerous types of IRS. The most common – known as plain vanilla swaps – presents the following features:

• the duration of the swap is a complete number of years;
• one of the two payment flows is based on a fixed interest rate, while the other is index-linked to a floating interest rate;
• the notional principal remains constant for the entire duration of the agreement.

The fundamental elements of a plain vanilla swap, to be indicated in the agreement, are:

• the date of stipulation of the agreement (trade date);
• the notional principal amount, which is not exchanged between the parties and is used only for calculating the interest;
• the start date (effective date), or rather as from when the interest starts to accrue (normally two business days after the trade date),
• the maturity or termination date of the agreement;
• the payment dates, or rather the dates when the interest flows are exchanged;
• the level of the fixed rate;
• the reference floating rate (very often the Libor or other interbank rates are used, or the interest rates paid on Government securities) and the related determination date (so-called fixing date).

In practice, the purchaser of the swap is the party who makes the payments at the fixed rate and receives those at the floating rate; it can also be said that this party adopts a long swap position. Likewise, the seller is the party which in exchange for the floating rate receives a fixed rate and is said to adopt a short swap position.

The flow of the interest payments at the fixed rate is called "fixed leg"; the equivalent value of each payment derives from the product of the notional principal for the fixed rate contractually established, referring to the portion of the pertinent year (fixed rate day count fraction).

The flow of the payments at the floating rate is called the "floating leg"; the related unit equivalent value is the result of the product of the notional principal for the floating rate fixed as of the date of determination in the agreement (fixing date), referring to the portion of the pertinent year (fixed rate day count fraction).

The value of the fixed rate which renders the value of the agreement null at the time it is stipulated is called the so-called swap rate. It comes about by equalizing the current value of all the payments of the fixed leg to the current value of all the payments of the floating leg. Under such conditions, the two services – at the time of stipulation – are equivalent and an at-the-money par swap is achieved.

Over the duration of the agreement, the valuation at a given moment of a swap derives from the difference between the current values of the payment flows of the two legs – fixed and floating – still due on the basis of the contractual provision.

The changes in the floating rate, with respect to the levels hypothesised at the time of finalization of the agreement, determine the risk/return profile of the plain vanilla swap. In detail, if the floating rate is higher than expectations, the purchaser of the swap – in other words the party who is obliged to pay the fixed rate – accrues a profit (since, without prejudice to the fixed rate payments it is obliged to make, it will receive floating rate payments at an amount greater than envisaged) and the seller will accrue a loss, while if the floating drops the seller will achieve a profit.

 

Currency swaps

Currency swaps, literally "exchange of currency", are agreements where two parties exchange the principal and the interest expressed in one currency against principal and interest expressed in another currency.

A recurrent feature of currency swaps is that both the payment flows are at a floating rate and that the notional principal amounts are exchanged once at the start of the agreement and then on the date of maturity of the swap.

The two notional amounts, denominated in different currencies, are usually chosen so as to be approximately equal if valued at the current exchange rate observed on the market as of the agreement stipulation date. If, for example, one Euro is worth 1.23 dollars (and thus it can be said that the Euro/dollar exchange rate equates to 1.23), a notional amount of Euro 100,000,000 will have to correspond to a notional amount of 123,000,000 dollars.

This equality is not guaranteed to remain over the duration of the agreement, since the variation of the exchange rate between the currencies leads to a change in the value of the notional amounts.

 

Asset swaps

Asset swaps are agreements where two parties exchange periodic payments paid in relation to a bond (asset) held by one of them (and not, for example, in relation to a mere sum of money, as for IRS).

The determination of the cash flows exchanged therefore presupposes the identification of a bond which, as a rule, is at a floating rate; by means of the asset swap, whomever holds the bonds can exchange the associated floating rate with a fixed rate.

The underlying bond can also be at a fixed rate and, in this case, the agreement makes it possible to exchange the fixed rate with a floating rate and is thus called a reverse asset swap. However, this distinction with regards to name is not always adopted in practice, where the term asset swap is used indiscriminately.

The party which holds the bond is called the asset swap buyer and pays the interest associated with the bond, which can be fixed or floating. Vice versa, the asset swap seller receives the interest on the bond and pays a rate of a different kind (if the bond is fixed rate, it will pay a floating rate and vice versa).

In the event of default of the bond, the asset swap buyer will cease to make payments, while the asset swap seller will continue to pay the agreed interest.

The function of these agreements is therefore to exchange a fixed rate with a floating rate, and as a result of this they are similar to IRS. Moreover, there is a partial hedge against the risk of default of a specific bond.

The asset swaps are generally established in such a way so that the value of the agreement as of the start date of the same is nil. This circumstance, in the case of bonds lacking credit risk, occurs, alternatively, in the following cases:

• the current value of the two legs of the swap - if the discounting back is carried out discounting both the payment flows by means of the same curve of the current market interest rates (spot rates) – is the same;
• the price of the underlying security is exactly equal to 100 (which is generally the price of the security lacking credit risk with interest corresponding to market interest) and a leg of the swap is represented by the risk free rate (in other words, the interest rate paid for an asset completely lacking risk).

If this does not occur, the value of the contract is not nil. In order to take the value to zero, one can operate as follows:

• a spread (know as an asset swap spread) is inserted on the rate which defines the periodic payment flows paid in exchange for those deriving from the bond;
• a one-off contribution (known as a par adjustment) is established.

These two methods are not necessarily alternative, but can also contribute together towards achieving the objective of cancelling the value of the agreement.

Again by means of these operative methods (insertion of an asset swap spread or determination of a par adjustment), the eventual presence of a credit risk of the bond, involving the possibility that not all the coupons will be paid, is also handled, by means of calculations which are necessarily very complex.

The matters stated above explain how the existence of an asset swap spread or of a par adjustment acts as a signal on the features of the underlying security in terms of rating class and coupon structure, in other words in terms of assessment of the credit and interest rate risk paid by the bond. In fact, it is evident how the asset swap spread (or the par adjustment) is eventually envisaged for offsetting specific characteristics of the underlying security which involve an additional risk with respect to risk free securities or involve different returns, higher or lower, with respect to the curve of the market rates (spot rates) present at the time the agreement is stipulated.

 

Credit Default Swaps

Credit default swaps (CDS) are agreements where a party (so-called protection buyer), against periodic payments made in favour of the counterpart (so-called protection seller), protects itself from the credit risk associated with the specific underlying product, generally referred to as a reference asset, which may be represented by a specific issue, an issuer or an entire portfolio of financial instruments.

The risks covered by the CDS are associated with certain events (so-called credit events) indicated in the agreement (for example: the insolvency of the issuer of the bond, so-called default), on occurrence of which payment flows between the parties are created. These flows, effectively, can take place according to two operating methods:

- the protection seller pays the counterpart the nominal value (or that contractually established) of the financial instrument forming the subject matter of the CDS, net of the residual market value of the same (so-called recovery value), and the protection buyer ceases to make the periodic payments (cash settlement);

- the protection seller pays the counterpart the nominal value (or that contractually established) of the financial instrument forming the subject matter of the CDS and the protection buyer, besides ceasing to make the periodic payments, hands over the reference assets (physical delivery). In practice, the protection buyer has the faculty to choose the reference asset to be handed over from a basket of assets identified within the sphere of the agreement and, in this case, will exploit this faculty choosing that which is most convenient for it (so-called cheapest-to-delivery).

The typical function of the agreement is therefore the hedging of the risks associated with a specific asset: a function very similar to the insurance-related one.

The following elements are generally specified in the definition of a credit default swap agreement:

• the notional principal in relation to which the payments due by the protection buyer are calculated, generally corresponding to the nominal value of the reference asset;
• the amount of each of these payments, equating to the result of the product of a fixed rate (so-called CDS rate) for the notional principal;
• the frequency of these payments and the maturity of the same agreement;
• the events relating to the reference asset identifiable as credit events (insolvency, declassing by a rating agency, etc.).

In the event that the CDS has a specific bond issue as its underlying element, the maturity of the agreement tends to coincide with the residual duration of the bond and, above all else, the amount of each of the payments made by the protection buyer is closely linked to the return spread implicit in the issue with respect to that of the securities lacking credit risk (so-called credit spread). In other words, the more risky the security is, the higher the fixed rate requested for offering the hedge will be. For this reason, the CDS can also act as a signal for the riskiness of the assets covered by them.

 

Total Return Swaps

Total return swaps (TRS) are agreements were a party (so-called protection buyer) transfers to the other party (so-called protection seller) the entire risk/return profile of an underlying element (so-called reference asset), against a flow of period payments. These periodic payments, as a rule, are a floating rate increased by a spread (so-called TRS spread).

The function of this instrument is the same as the credit default swap: cover the risks associated with a security. The methods for achieving it are different. By means of the TRS, the holder of a security, for example a bond, does not make a periodic payment in exchange for protection, as occurs for the credit default swap, but pays the entire return of its security (coupons and capital increases) in exchange for periodic payments, established at the time the agreement is stipulated, and the compensation of any capital losses on the underlying element, including therein the ultimate loss in the event of default. In this sense, the holder of the security, i.e. the protection buyer, is also called total return seller, while the protection seller is also called the total return buyer.

On occurrence of a default event, as a rule two operating methods are envisaged in TRS:

• the protection seller pays the other party the equivalent value of the loss generated, so-called loss given default, equating to the difference between the nominal value of the security and the residual market value after the default (cash settlement);
• the protection buyer hands over the security forming the subject matter of the TRS to the protection seller, who pays the former the nominal value, or that established contractually, of said security (physical delivery).

The elements which are generally contained in a total return swap agreement are as follows:

• the notional principle with respect to which the payments due by the protection seller are calculated, generally corresponding to the nominal value of the reference asset;
• the amount of each of the afore-mentioned payments, equating to the result of the product of a floating rate increased by a spread for the notional principal;
• the frequency of these payments;
• the maturity of said agreement.

 

Other Types of Swap Agreements

The types of swaps traded are countless, and this is due to the considerable flexibility of this instrument. A number of additional types are listed which, due to their popularity, are worth a mention:

2. equity swaps, where the dividends and capital profits on a share index are exchanged against a fixed or floating rate;
3. zero-coupon swaps, where a payment in a single solution is exchanged with a flow of periodic payments;
4. domestic currency swaps, where two parties purchase/sell two forward contracts on two notional reference amounts expressed in different currencies, thereby establishing an initial exchange rate. On maturity, they undertake to exchange just the differences which have arisen between the exchange rate observed as of that date and that established at the start of the agreement;
5. forward swaps or deferred swaps, in which a significant interval of time is inserted between the date of stipulation of the swap and the effective maturity start date of the interest of the swap’s legs;
6. basis swaps, where the two payment flows exchanged are both floating rate;
7. differential swaps, where a payment flow at a floating rate denominated in national currency is exchanged with a payment flow at a floating rate denominated in foreign currency and both the flows are calculated on the same notional amount denominated in national currency.

 

OPTIONS

An option is an agreement which assigns the right, but not the obligation, to purchase (call option) or sell (put option) a certain quantity of an asset (underlying) at a pre-established price (strike price or exercise price), by a certain date (maturity), in which event we are dealing with an American option, or on reaching said date, in which case we are dealing with a European option.

The underlying asset of the option agreement can be:

• a financial asset, such as shares, bonds, currency, financial derivative instruments, etc.;
• a good, such as oil, gold, grain, etc.;
• an event of various kinds.

In any event, the underlying element must be swapped on a market with official listings or a publicly recognized one or, in the case of an event, an objectively verifiable one.

The two parties of the option agreement are called the purchaser (so-called holder) and the seller (so-called writer) of the option. The purchaser, against the payment of a sum of money, called a premium, acquires the right to sell or purchase the underlying asset. The seller receives the premium and, in exchange, is obliged to sell or purchase the underlying asset upon the request of the purchaser.

According to the terminology used by the operators, the purchaser opens a long position, while the seller opens a short position.

When the purchaser of the option exercises the right, in other words decides to purchase (call) or sell (put), the following scenarios occur:

• in the case of a call option, the purchaser of the call option will receive the difference between the current price of the underlying product (so-called spot price) and the exercise price, from the seller:
• in the case of a put option, the purchaser of the option will receive the difference between the exercise price and the spot price.

The difference between the spot price and the exercise price, in the case of the call, and the exercise price and the spot price, in the case of a put, is commonly known as the intrinsic value.

The intrinsic value cannot adopt negative values since the bearer has the right, but not the obligation, to purchase or sell; therefore, in the event that the current price of the underlying product at the time of exercise is lower than the exercise price of the call (or vice versa for the put), it will merely avoid exercising the right, incurring a limited loss on the sums paid for the premium.

The relationship between the spot price of the underlying asset and the exercise price also determines the so-called moneyness of an option. This concept expresses the distance between the two prices.

The moneyness separates the options into:

• at-the-money when its exercise price is exactly equal to the current price (the intrinsic value is therefore nil);
• in-the-money when the purchaser perceives a profit from the exercise (positive intrinsic value, so-called positive pay-off): therefore, a call is in-the-money when the strike is lower than the spot, while, to the contrary, a put is in-the-money when the strike is higher than the spot (when this difference is very large, we refer to deep in-the-money options);
• out-of-the-money when the exercise of the right would not provide any positive pay-off for the purchaser (the intrinsic value would have a negative value which, therefore, as already mentioned, does not take place since the purchaser of the option decides not to exercise it): therefore, a call is out-of-the-money when the strike is higher than the spot, while a put is out-of-the-money when the strike is lower than the spot. In the event that the difference is very large, we refer to deep out-of-the-money options.

The execution of the agreement, for in-the-money options, may take place:

• by means of the effective consignment of the underlying asset, and then we can talk of physical delivery;
• by means of the consignment of the differential in cash between the current price of the underlying assets and the exercise price (cash settlement).

The decision to stipulate an option agreement can be traced back to all the purposes typical of derivatives. In detail:

• hedging purpose: an operator has sold a financial asset short and wishes to cover itself from the risk of appreciation of said asset since on a certain date it will have to purchase the securities so as to close the position. By means of the purchase of a call option, whose strike price is equal to the price at which it sold the financial asset short, it can protect itself from the risk of the security’s appreciation;
• speculative purpose: an operator has specific expectations on the future price performance of an asset and, by stipulating an option agreement, can adopt a position consistent with these expectations, so as to achieve a positive pay-off if these expectations come true and to limit the loss to the payment of the premiums if they do not;
• arbitrage purpose: in finance, there are mathematical equivalences between the options, the forward agreements and the underlying securities. An operator – having noted a disparity between these theoretical equivalences – can set up operations capable of achieving a profit lacking risk, following methods similar to those illustrated in the most simple case of forward agreements.

Diagram 1 provides a graphic representation of the example.

Diagram 1. Pay-off of a European call