## Cap/Floor

A
cap or a floor
provides
a
guarantee
to
the
issuer of
a floating
rate
that
the
coupon
payment
each
period will
be
no
higher or lower
than
a
certain
amount.

The
coupon rate
will
be capped or floored at the strike
rate.

Each payment
date,
the
cap
or a floor pays
the
difference,
if
positive,
between
the
floating rate
and
the
cap or floor
rate,
multiplied
by
the notional amount of
principle
or
par
value,
divided
by
the annual
payment
frequency.

A cap or floor actually consists of a series of options, also known as caplets or floorlets. Each caplet or floorlet successively ensures the buyer protection for a single payment period.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**Start date of the first caplet or floorlet.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional, amount to be invested in the option.**Amortizing Frequency :**this is the amortizing frequency of the notional it can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Bullet with no depreciation during the life time of the option. Cumulative depreciations are counted at the end of the option term.
- Custom where the user can define the different values of each amortization.

**Option Details**

**Currency :**the currency of the option and the underlying. The reference interest rate (IBOR) will be set according to that currency.**Strike :**the interest rate level at which the caplet or floorlet is activated. This level is expressed in percentage.**Interests Frequency :**this is the frequency of the interests perceived or paid. This frequency will determine the tenor of the IBOR (3 months, 6 months …).**Fixing Type :**the fixing can be in advance : at the start of the relevant interest rate period or in arrears : at the end of the period.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

## Collar

A Collar is a security which combines the purchase of a cap and the sale of a floor (from the buyer’s side) to specify a range in which an interest rate will fluctuate. The security insulates the buyer against the risk of a significant rise in a floating rate, but limits the benefits of a drop in that floating rate.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**start date of the underlying cap and floor.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional of the underlying cap and floor.**Currency :**the currency of the option and the underlying. The reference interest rate (IBOR) will be set according to that currency.**Amortizing Frequency :**this is the amortizing frequency of the notional. It can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Bullet with no depreciation during the life time of the option. Cumulative depreciations are counted at the end of the option term.
- Custom where the user can define the different values of each amortization.

**Option Details**

**Option :****Cap :**this is the option to price the collar from the buyer’s side.**Floor :**this is the option to price the collar from the seller’s side.

**Interests Frequency :**this is the frequency of the interests perceived or paid. This frequency will determine the tenor of the IBOR (3 months, 6 months …).**Fixing Type :**the fixing can be in advance: at the start of the relevant interest rate period or in arrears: at the end of the period.**Cap Strike :**this is the strike of the underlying cap.**Floor Strike :**this is the strike of the underlying floor.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

## Cross Currency Swap

A cross currency swap is similar to a vanilla swap, while giving each counterparty access to a different foreign currency. That is, one counterparty makes payments in one currency ; the other makes payments in a different currency.

Because there are two currencies involved (and therefore two notionals) the payments made not only include interest rate payments (on the set payment periods in the relevant currency on the respective principal) but also an exchange of principals at maturity and (optionally) at the start of the swap.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**initial date of the first payment period.**Years/Months :**number of years and months until maturity.**Amortizing Frequency :**this is the amortizing frequency of the notional. It can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Bullet with no depreciation during the life time of the option. Cumulative depreciations are counted at the end of the option term.
- Custom where the user can define the different values of each amortization.

**Receiver/Payer Leg**

**Nominal :**this is the notional ; amount in the index currency that is used for calculating the payments of the leg.**Currency :**currency of the leg.**Rate Type :****Fixed :**if the leg pays a fixed rate.**Floating :**if the leg pays a floating rate (which is set according to the leg’s currency).

**Interests Frequency :**this is the frequency of the interests perceived or paid. This frequency will determine the tenor of the IBOR (3 months, 6 months …) of the leg.**Day count Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

**Fixed Rate :**value of the fixed rate in percentage.**Spread :**value of the spread in bp.

## Dual

In this option the underlying is an FX rate. An example for the payoff (at each payment date of the tenor structure) is given at the end of this note.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**initial date of the first payment period.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional, amount to be invested in the option. It’s used for calculating the payment at each time of the tenor structure.**Currency :**this is the currency used for the payments of the option.**Amortizing Frequency :**this is the amortizing frequency of the notional. It can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Custom where the user can define the different values of each amortization.

**Details**

**Interests Frequency :**this is the frequency of the interests perceived.**Index Fixing :**the fixing can be in advance : at the start of the relevant interest rate period or in arrears : at the end of the period.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

**Payoff**

**Example :**

If FX Rate Sup 2 (in percentage)

then 3

else 2,5 + 0,5 * [(2-FX Rate) / FX Rate]

## Dualys

In this option the underlying is the spread between two FX rates. An example for the payoff (at each payment date of the tenor structure) is given at the end of this note.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**initial date of the first payment period.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional, amount to be invested in the option. It’s used for calculating the payment at each time of the tenor structure.**Payout Currency :**this is the currency used for the payments of the option.**Amortizing Frequency :**this is the amortizing frequency of the notional. It can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Custom where the user can define the different values of each amortization.

**Details**

**Interests Frequency :**this is the frequency of the interests perceived.**Index Fixing :**the fixing can be in advance : at the start of the relevant interest rate period or in arrears : at the end of the period.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

**Payoff**

**Example :**

If (FX Rate1- FX Rate2 – 2 < 0)

Then 3

Else 2,5 + 0,5 * (FX Rate1 – FX Rate2 – Strike (2 in our example))

## European Barriers Options

A Cap or Floor with a Knock-In or Knock-Out interest rate level.

At the maturity of each Caplet or Floorlet, if the Knock-In barrier level is reached, the option (Cap or Floor) pays
the
difference,
if
positive,
between
the
floating rate
and
the
cap or floor
rate.

If the Knock-Out barrier level is reached there is no payment.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**Start date of the underlying Cap/Floor.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional ; amount to be invested in the barrier option, it’s used for calculating the barrier option payment.**Currency :**the currency of the option and the underlying. The reference interest rate (IBOR), will be set according to that currency.**Amortizing Frequency :**this is the amortizing frequency of the notional it can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Custom where the user can define the different values of each amortization.

**Option Details**

**Barrier Type :****In :**for a Knock-In barrier.**Out :**for a Knock-Out barrier.

**Interests Frequency :**this is the frequency of the interests perceived or paid. This frequency will determine the tenor of the IBOR (3 months, 6 months …).**Fixing Type :**the fixing can be in advance : at the start of the relevant interest rate period or in arrears : at the end of the period.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

**Strike :**this is the exercise rate level of the underlying cap or floor. This level is expressed in percentage.**Trigger :**this is the rate level at which the barrier will be activated(discativated) in the case of a KI(KO) barrier.

## Fixed Rate with Ibor KO

This option is similar to the fixed leg of a swap but with a Knock-Out interest rate level. At each payment date of the tenor structure if the IBORreaches the KO interest rate level there is no payment.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**initial date of the first payment period.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional, amount to be invested in the option. It’s used for calculating the payment at each time of the tenor structure.**Currency :**the currency of the option and the underlying. The reference interest rate (IBOR) for the barrier will be set according to that currency.**Amortizing Frequency :**this is the amortizing frequency of the notional. It can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Custom where the user can define the different values of each amortization.

**Option Details**

**Interests Frequency :**this is the frequency of the interests perceived. This frequency will determine the tenor of the IBOR (3 months, 6 months …).**Fixing Type :**the fixing can be in advance : at the start of the relevant interest rate period or in arrears : at the end of the period.**Fixed Rate :**value of the fixed rate in percentage.**Trigger :**this is the rate level at which the payment at the constatation date will be cancelled.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

## Fixed Rate on Spread CMS

In this option the underlying is the spread between the yields of two different swap rates, one is called ‘High CMS Index’ and the other ‘Low CMS Index’. An example for the payoff (at each payment date of the tenor structure) is given at the end of this note.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**Initial date of the first payment period.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional, amount to be invested in the option. It’s used for calculating the payment at each time of the tenor structure.**Currency :**the currency of the option and the underlying. The underlying CMS swap rates will be set according to that currency.**Amortizing Frequency :**this is the amortizing frequency of the notional. It can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :

Linear for constant depreciation. It’s the most common method.

Progressive according to a progressivity rate defined by the user.

Bullet with no depreciation during the life time of the option. Cumulative depreciations are counted at the end of the option term.

Custom where the user can define the different values of each amortization.

**Details**

**Interests Frequency :**this is the frequency of the interests perceived.**Index Fixing :**the fixing can be in advance : at the start of the relevant interest rate period or in arrears : at the end of the period.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

**Payoff**

**Example :**

If Spread > 2

Then 3 – 0 ( * Spread)

Else 5 – 0,5 ( * Spread)

## Ibor Probabilities Level

This function gives the probability for an Ibor to be higher than a Strike between the Market Date and the Estimation Date. The probabilities are calculated according to the Constatation Frequency.## Quanto Fixed Rate with Ibor KO

This option is similar to the Fixed Rate with Ibor KO but where the payout currency is different than the index currency used to determine the payoff and the IBOR of the barrier.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**initial date of the first payment period.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional, amount in the index currency to be invested in the option.**Payout Currency :**this is the currency used for the payments of the option.**Amortizing Frequency :**this is the amortizing frequency of the notional. It can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Custom where the user can define the different values of each amortization.

**Option Details**

**Index Frequency :**The reference interest rate (IBOR) tenor will be set according to that frequency.**Index currency :**The reference interest rate (IBOR) will be set according to that currency.**Interests Frequency :**this is the frequency of the interests perceived.**Fixing Type :**the fixing can be in advance : at the start of the relevant interest rate period or in arrears : at the end of the period.**Fixed Rate :**value of the fixed rate in percentage.**Trigger :**this is the rate level at which the payment at the constatation date will be cancelled.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

## Quanto Option

A Cap/Floor Quanto is an option similar to a regular Cap/Floor whose underlying asset is measured in one currency and the payoff is quoted in another currency.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**Initial date of the first payment period.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional, amount in the index currency to be invested in the option.**Amortizing Frequency :**this is the amortizing frequency of the notional. It can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Custom where the user can define the different values of each amortization.

**Option Details**

**Currency :**this is the currency used for the payments of the quanto option.**Index Currency :**this is the currency used in the cap/floor. The reference interest rate (IBOR) will be set according to that currency.**Strike :**the interest rate level at which the caplets or floorlets are activated. This level is expressed in percentage.**Interests Frequency :**this is the frequency of the interests perceived or paid. This frequency will determine the tenor of the IBOR (3 months, 6 months …).**Fixing :**the fixing can be in advance: at the start of the relevant interest rate period or in arrears: at the end of the period.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

## Range Accrual

The Range Accrual Option pays at each payment date a minimum coupon plus a coefficient. That is, this coefficient only accrues on days (for each payment period) when an IBOR index falls within a specified range, set using an upper and a lower barrier, or is greater or smaller than a strike in the simple case.

**Characteristics :**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**initial date of the first payment period.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional, amount to be invested in the option. It’s used for calculating the payment at each time of the tenor structure.**Currency :**the currency of the option and the underlying. The reference interest rate (IBOR) will be set according to that currency.**Amortizing Frequency :**this is the amortizing frequency of the notional it could be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Custom where the user can define the different values of each amortization.

**Ibor Frequency :**This frequency will determine the tenor of the IBOR (3 months, 6 months …).

**Option Details :**

**Range Accrual Type :****Simple :**in this case, we count the number of days where the index Ibor is greater (or smaller, it depends on the chosen Range) than the strike. The option pays the minimum coupon plus the coefficient multiplied by this number of days divided by the total number of days of the payment period.**Tunnel :**in this case, we count the number of days where the index Ibor is inside (or outside, it depends on the chosen Range) the tunnel composed by the Low Barrier and the High Barrier. The option pays the minimum coupon plus the coefficient multiplied by this number of days divided by the total number of days of the payment period.

**Minimum Coupon :**value of the minimum coupon in percentage.**Coefficient :**value of the coefficient in percentage.**Interests Frequency :**this is the frequency of the interests perceived.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

## Vanilla Swap

Vanilla European Call or Put for foreign exchange is the option to buy or sell a foreign currency at a predetermined Strike price (exchange rate).

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Expiry :**this is the maturity date of the FX Option. On that date the option will be exercised or expired.**Foreign Currency :**the underlying currency that we want to buy (for a call) or sell (for a put).**Domestic Currency :**local currency that we want to buy (for a put) or sell (for a call).**Notional :**This is the nominal, amount to be invested in the option.**Currency :**Currency of the notional. The premium will be paid or received in this currency.

**Details**

**Strike :**Exchange rate level at which the option can be exercised. This rate is usually compared to the spot rate to determine the moneyness of the option.

## Vanilla Swaption

The option to enter into an interest rate swap. In exchange for an option premium, the buyer gains the right but not the obligation to enter into a specified swap agreement with the issuer on a specified future date.

The buyer of the Swaption can be a fixed rate receiver or payer.

If the holder elects to exercise, a swap contract begins, and if not then the only exchange of payments is the premium.

**Characteristics**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**this is the start date of the underlying swap.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional ; amount to be invested in the underlying swap, it’s used for calculating the underlying swap payment.**Currency :**the currency of the option and the underlying. The reference interest rate (IBOR) will be set according to that currency.**Amortizing Frequency :**this is the amortizing frequency of the notional it can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Custom where the user can define the different values of each amortization.

**Fixed Leg**

**Swaption Type :**gives the owner of the swaption the right to enter a swap contract where he pays or receive the fixed rate.**Strike :**the exercise rate of the option indicates a fixed rate that will be swapped versus the floating rate.**Interests Frequency :**this is the frequency of the interests perceived or paid.**Day count Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

**Floating Leg**

**Interests Frequency :**this is the frequency of the interests perceived or paid. This frequency will determine the tenor of the IBOR (3 months, 6 months …).**Day count Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

## Year on Year Inflation Swap

An Inflation Swap is similar to a Vanilla Swap with a leg which pays (or receives) an inflation rate which is calculated Year on Year (YoY) from an inflation index.

**YoY Inflation Swap**

**Market Date :**date on which the option will be priced. The value of the option will be given on that date.**Start Date :**initial date of the first payment period.**Years/Months :**number of years and months until maturity.**Nominal :**this is the notional, amount to be invested in the option. It’s used for calculating the payment at each time of the tenor structure.**Currency :**the currency of the option which determines the types of inflation. The reference interest rate (IBOR), if the IR Leg is set float, will be set according to that currency.**Amortizing Frequency :**this is the amortizing frequency of the notional. It can be monthly (every month), quarterly (every 3 months), semi annually (every six months) or annually (every year).**Amortizing Method :**the notional or nominal depreciation over the life of the option can be :- Linear for constant depreciation. It’s the most common method.
- Progressive according to a progressivity rate defined by the user.
- Custom where the user can define the different values of each amortization.

**Inflation Leg**

**Index :**The inflation rate will be set according to that Index.**Interests Frequency :**this is the frequency of the interests perceived.**Daycount Convention :**this is the number of days in a year that we use to calculate periodic amortization :- Actual/360 : we take the actual number of days in the corresponding year divided by 360.
- EU30 360 : This convention assumes there are 30 days in a month and 360 days in a year.

**IR Leg**

See the Vanilla Swap note.