A Plain Vanilla Call is the right (note: not the duty) to buy a certain amount of a currency at a specified time at a specified exchange rate.
In our tool we restrict ourselves to the European Style of that option, which means that the holder of the option cannot buy the specified currency at any time earlier than previously agreed. To put it another way, the holder of the option cannot exercise the option before the specified expiry time in order to buy the agreed currency at the agreed exchange rate (i.e. the specified strike price).

The other version of that option is an American Call, which can be exercised any time before expiry.

A Put option works in the same way as the Call option, with the difference being that now the holder has the right to sell a currency at an agreed exchange rate at expiry.

 

Market Data

Spot Price:		Spot Price: This is the value of the underlying exchange rate today. Accepted Values: ∈(0, n)
Domestic Rate:		Domestic interest rate: If you are not sure about which interest rate is domestic and which foreign, the example at the end of the document will clarify this. Accepted Values: ∈(-0.1, 1)
Foreign Rate:		Foreign interest rate: In general you should use the money market interest rates with the according time to maturity for rf and rd. Accepted Values: ∈(-0.1, 1)
Volatility:		Volatility: This is the market implied volatility of an at-the-money-Call. This figure can be looked up in appropriate tables which are for example provided by banks. ATM is ATM-forward in our calculations. Accepted Values: ∈(0, 10)
Delta Wished:		Delta Wished: This specifies the spot delta (premium unadjusted) of the butterfly and risk reversal - options that are used for vega-hedging. Market standard is the value 0.25. Accepted Values: ∈(0.05, 0.45)
Risk Reversal:		Risk Reversal: This is the market quote of a "risk reversal " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)
Butterfly:		Butterfly: This is the market quote of a "butterfly " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)

Contract Data

Strike:		Strike: This is the agreed exchange rate, at which the holder can buy / sell currency at expiry. Accepted Values: ∈(0, n)
Time trade-to-maturity:		Time trade-to-maturity: This is the time to maturity of the option, measured in years. Our tool accepts times to maturity between one day and 5 years. We recommend using the provided data with appropriate caution if the time is longer than one year, as constant interest rates and volatilities are assumed in the model which is implemented in our program. Accepted Values: ∈(1/365, 5)
Notional:		Notional: Specifies how many units of foreign / domestic currency are bought / sold if the option is exercised at expiry. See also the parameter FOR/DOM. Accepted Values: ∈(0, n)
Call/Put:	Call Option Put Option	Call/Put: Indicates whether the option is a Call or a Put.
FOR/DOM:	Domestic Foreign	FOR/DOM: Determines whether the nominal is in foreign or domestic currency.

Valuation

Output:

Black-Scholes and Vanna-Volga values Previous and Black-Scholes Greeks All

Output: Result selection.

Results

A Vanilla Digital Call pays a previously agreed amount of cash in foreign or domestic currency, if at expiry time the spot rate is higher than a previously agreed barrier. Similarly, the Digital Put pays an agreed amount of cash if at expiry the spot is below a specified barrier.

 

Market Data

Spot Price:		Spot Price: This is the value of the underlying exchange rate today. Accepted Values: ∈(0, n)
Domestic Rate:		Domestic interest rate: If you are not sure about which interest rate is domestic and which foreign, the example at the end of the document will clarify this. Accepted Values: ∈(-0.1, 1)
Foreign Rate:		Foreign interest rate: In general you should use the money market interest rates with the according time to maturity for rf and rd. Accepted Values: ∈(-0.1, 1)
Volatility:		Volatility: This is the market implied volatility of an at-the-money-Call. This figure can be looked up in appropriate tables which are for example provided by banks. ATM is ATM-forward in our calculations. Accepted Values: ∈(0, 10)
Delta Wished:		Delta Wished: This specifies the spot delta (premium unadjusted) of the butterfly and risk reversal - options that are used for vega-hedging. Market standard is the value 0.25. Accepted Values: ∈(0.05, 0.45)
Risk Reversal:		Risk Reversal: This is the market quote of a "risk reversal " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)
Butterfly:		Butterfly: This is the market quote of a "butterfly " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)

Contract Data

Level:		Level: This is the agreed exchange rate,(1) above which a Call pays out the notional amount of money, (2) under which a Put pays out the notional amount of money at expiry. Accepted Values: ∈(0, n)
Time trade-to-maturity:		Time trade-to-maturity: This is the time to maturity of the option, measured in years. Our tool accepts times to maturity between one day and 5 years. We recommend using the provided data with appropriate caution if the time is longer than one year, as constant interest rates and volatilities are assumed in the model which is implemented in our program. Accepted Values: ∈(1/365, 5)
Notional:		Notional: Nominal amount of cash that is paid if the barrier is hit. Accepted Values: ∈(0, n)
Call/Put:	Call Option Put Option	Call/Put: Indicates whether the option is a Call or a Put.
FOR/DOM:	Domestic Foreign	FOR/DOM: Determines whether the nominal is in foreign or domestic currency.

Valuation

Output:

Black-Scholes and Vanna-Volga values Previous and Black-Scholes Greeks All

Output: Result selection.

Results

A OneTouchOption pays a fixed amount of money, called the rebate, if a previously determined exchange rate ever trades at a previously determined touch-level until a specified expiry time T.

Similarly, a NoTouchOption pays a certain rebate if the exchange rate never trades at a touch-level until T. The rebate can be specified in foreign or domestic currency.

A OneTouch-option is also sometimes called one-touch-digital or hit option. Furthermore, this option can be interpreted as an American Cash-or-nothing-digital option, if the rebate is in domestic currency, or as an American Asset-or-nothing-digital option, if the rebate is in foreign currency.

 

Market Data

Spot Price:		Spot Price: This is the value of the underlying exchange rate today. Accepted Values: ∈(0, n)
Domestic Rate:		Domestic interest rate: If you are not sure about which interest rate is domestic and which foreign, the example at the end of the document will clarify this. Accepted Values: ∈(-0.1, 1)
Foreign Rate:		Foreign interest rate: In general you should use the money market interest rates with the according time to maturity for rf and rd. Accepted Values: ∈(-0.1, 1)
Volatility:		Volatility: This is the market implied volatility of an at-the-money-Call. This figure can be looked up in appropriate tables which are for example provided by banks. ATM is ATM-forward in our calculations. Accepted Values: ∈(0, 10)
Delta Wished:		Delta Wished: This specifies the spot delta (premium unadjusted) of the butterfly and risk reversal - options that are used for vega-hedging. Market standard is the value 0.25. Accepted Values: ∈(0.05, 0.45)
Risk Reversal:		Risk Reversal: This is the market quote of a "risk reversal " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)
Butterfly:		Butterfly: This is the market quote of a "butterfly " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)

Contract Data

Touch Level:		Touch Level: This is the touch level. Accepted Values: ∈(0, n)
Time trade-to-maturity:		Time trade-to-maturity: This is the time to maturity of the option, measured in years. Our tool accepts times to maturity between one day and 5 years. We recommend using the provided data with appropriate caution if the time is longer than one year, as constant interest rates and volatilities are assumed in the model which is implemented in our program. Accepted Values: ∈(1/365, 5)
Notional:		Notional: Specifies how many units of foreign / domestic currency are bought / sold if the option is exercised at expiry. See also the parameter Fd. Accepted Values: ∈(0, n)
Barrier Position:	Lower Barrier Upper Barrier	Barrier Position: This parameter indicates whether the barrier is an upper or lower barrier.
Payment Time:	Pay at hitting time Pay at expiry	Payment Time: This parameter indicates whether the rebate is paid at hitting-time or at expiry.
FOR/DOM:	Domestic Foreign	FOR/DOM: Determines whether the nominal is in foreign or domestic currency.

Valuation

Output:

Black-Scholes and Vanna-Volga values Previous and Black-Scholes Greeks All

Output: Result selection.

Results

A OneTouchOption pays a fixed amount of money, called the rebate, if a previously determined exchange rate ever trades at a previously determined touch-level until a specified expiry time T.

Similarly, a NoTouchOption pays a certain rebate if the exchange rate never trades at a touch-level until T. The rebate can be specified in foreign or domestic currency.

A OneTouch-option is also sometimes called one-touch-digital or hit option. Furthermore, this option can be interpreted as an American Cash-or-nothing-digital option, if the rebate is in domestic currency, or as an American Asset-or-nothing-digital option, if the rebate is in foreign currency.

 

Market Data

Spot Price:		Spot Price: This is the value of the underlying exchange rate today. Accepted Values: ∈(0, n)
Domestic Rate:		Domestic interest rate: If you are not sure about which interest rate is domestic and which foreign, the example at the end of the document will clarify this. Accepted Values: ∈(-0.1, 1)
Foreign Rate:		Foreign interest rate: In general you should use the money market interest rates with the according time to maturity for rf and rd. Accepted Values: ∈(-0.1, 1)
Volatility:		Volatility: This is the market implied volatility of an at-the-money-Call. This figure can be looked up in appropriate tables which are for example provided by banks. ATM is ATM-forward in our calculations. Accepted Values: ∈(0, 10)
Delta Wished:		Delta Wished: This specifies the spot delta (premium unadjusted) of the butterfly and risk reversal - options that are used for vega-hedging. Market standard is the value 0.25. Accepted Values: ∈(0.05, 0.45)
Risk Reversal:		Risk Reversal: This is the market quote of a "risk reversal " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)
Butterfly:		Butterfly: This is the market quote of a "butterfly " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)

Contract Data

Touch Level:		Touch Level: This is the touch level. Accepted Values: ∈(0, n)
Time trade-to-maturity:		Time trade-to-maturity: This is the time to maturity of the option, measured in years. Our tool accepts times to maturity between one day and 5 years. We recommend using the provided data with appropriate caution if the time is longer than one year, as constant interest rates and volatilities are assumed in the model which is implemented in our program. Accepted Values: ∈(1/365, 5)
Notional:		Notional: This is the amount of money that is paid if the exchange rate touches / does not touch the specified exchange rate level. Accepted Values: ∈(0, n)
Barrier Position:	Lower Barrier Upper Barrier	Barrier Position: This parameter indicates whether the barrier is an upper or lower barrier.
Payment Time:	Pay at expiry	Payment Time: Payment occurs at expiry.
FOR/DOM:	Domestic Foreign	FOR/DOM: Determines whether the nominal is in foreign or domestic currency.

Valuation

Output:

Black-Scholes and Vanna-Volga values Previous and Black-Scholes Greeks All

Output: Result selection.

Results

A DoubleOneTouch pays off 1 unit of domestic currency if the underlying exchange rate ever hits the lower or upper barrier until expiry.

A DoubleNoTouch pays off 1 unit of domestic currency if the underlying exchange rate never hits any of the upper and lower barriers until expiry.

 

Market Data

Spot Price:		Spot Price: This is the value of the underlying exchange rate today. Accepted Values: ∈(0, n)
Domestic Rate:		Domestic interest rate: If you are not sure about which interest rate is domestic and which foreign, the example at the end of the document will clarify this. Accepted Values: ∈(-0.1, 1)
Foreign Rate:		Foreign interest rate: In general you should use the money market interest rates with the according time to maturity for rf and rd. Accepted Values: ∈(-0.1, 1)
Volatility:		Volatility: This is the market implied volatility of an at-the-money-Call. This figure can be looked up in appropriate tables which are for example provided by banks. ATM is ATM-forward in our calculations. Accepted Values: ∈(0, 10)
Delta Wished:		Delta Wished: This specifies the spot delta (premium unadjusted) of the butterfly and risk reversal - options that are used for vega-hedging. Market standard is the value 0.25. Accepted Values: ∈(0.05, 0.45)
Risk Reversal:		Risk Reversal: This is the market quote of a "risk reversal " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)
Butterfly:		Butterfly: This is the market quote of a "butterfly " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)

Contract Data

Lower Barrier:		Lower Barrier: This is the lower barrier for the underlying. Accepted Values: ∈(0, n)
Higher Barrier:		Higher Barrier: This is the upper limit for the underlying exchange rate. Accepted Values: ∈(0, n)
Time trade-to-maturity:		Time trade-to-maturity: This is the time to maturity of the option, measured in years. Our tool accepts times to maturity between one day and 5 years. We recommend using the provided data with appropriate caution if the time is longer than one year, as constant interest rates and volatilities are assumed in the model which is implemented in our program. Accepted Values: ∈(1/365, 5)
Notional:		Notional: This is the amount of money that is paid if the exchange rate touches / does not touch the specified exchange rate level. Accepted Values: ∈(0, n)
FOR/DOM:	Domestic Foreign	FOR/DOM: Determines whether the nominal is in foreign or domestic currency.

Valuation

Output:

Black-Scholes and Vanna-Volga values Previous and Black-Scholes Greeks All

Output: Result selection.

Results

A DoubleOneTouch pays off 1 unit of domestic currency if the underlying exchange rate ever hits the lower or upper barrier until expiry.

A DoubleNoTouch pays off 1 unit of domestic currency if the underlying exchange rate never hits any of the upper and lower barriers until expiry.

 

Market Data

Spot Price:		Spot Price: This is the value of the underlying exchange rate today. Accepted Values: ∈(0, n)
Domestic Rate:		Domestic interest rate: If you are not sure about which interest rate is domestic and which foreign, the example at the end of the document will clarify this. Accepted Values: ∈(-0.1, 1)
Foreign Rate:		Foreign interest rate: In general you should use the money market interest rates with the according time to maturity for rf and rd. Accepted Values: ∈(-0.1, 1)
Volatility:		Volatility: This is the market implied volatility of an at-the-money-Call. This figure can be looked up in appropriate tables which are for example provided by banks. ATM is ATM-forward in our calculations. Accepted Values: ∈(0, 10)
Delta Wished:		Delta Wished: This specifies the spot delta (premium unadjusted) of the butterfly and risk reversal - options that are used for vega-hedging. Market standard is the value 0.25. Accepted Values: ∈(0.05, 0.45)
Risk Reversal:		Risk Reversal: This is the market quote of a "risk reversal " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)
Butterfly:		Butterfly: This is the market quote of a "butterfly " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)

Contract Data

Lower Barrier:		Lower Barrier: This is the lower barrier for the underlying. Accepted Values: ∈(0, n)
Higher Barrier:		Higher Barrier: This is the upper limit for the underlying exchange rate. Accepted Values: ∈(0, n)
Time trade-to-maturity:		Time trade-to-maturity: This is the time to maturity of the option, measured in years. Our tool accepts times to maturity between one day and 5 years. We recommend using the provided data with appropriate caution if the time is longer than one year, as constant interest rates and volatilities are assumed in the model which is implemented in our program. Accepted Values: ∈(1/365, 5)
Notional:		Notional: This is the amount of money that is paid if the exchange rate touches / does not touch the specified exchange rate level. Accepted Values: ∈(0, n)
FOR/DOM:	Domestic Foreign	FOR/DOM: Determines whether the nominal is in foreign or domestic currency.

Valuation

Output:

Black-Scholes and Vanna-Volga values Previous and Black-Scholes Greeks All

Output: Result selection.

Results

This name is used for all options with knock-in or knock-out barriers: They are basically Calls or Puts, but they can only be exercised if a barrier has / has not been reached anytime until expiry (American style).
A very liquidly traded example is the Up-And-Out-Call, which has the same payoff as a plain vanilla Call if a barrier B has not been reached until expiry, otherwise the option expires worthless.
In the European style - version the option can only be exercised if the barrier has / has not been reached at expiry.

 

Market Data

Spot Price:		Spot Price: This is the value of the underlying exchange rate today. Accepted Values: ∈(0, n)
Domestic Rate:		Domestic interest rate: If you are not sure about which interest rate is domestic and which foreign, the example at the end of the document will clarify this. Accepted Values: ∈(-0.1, 1)
Foreign Rate:		Foreign interest rate: In general you should use the money market interest rates with the according time to maturity for rf and rd. Accepted Values: ∈(-0.1, 1)
Volatility:		Volatility: This is the market implied volatility of an at-the-money-Call. This figure can be looked up in appropriate tables which are for example provided by banks. ATM is ATM-forward in our calculations. Accepted Values: ∈(0, 10)
Delta Wished:		Delta Wished: This specifies the spot delta (premium unadjusted) of the butterfly and risk reversal - options that are used for vega-hedging. Market standard is the value 0.25. Accepted Values: ∈(0.05, 0.45)
Risk Reversal:		Risk Reversal: This is the market quote of a "risk reversal " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)
Butterfly:		Butterfly: This is the market quote of a "butterfly " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)

Contract Data

Strike:		Strike: This is the agreed exchange rate, at which the holder can buy / sell currency at expiry. Accepted Values: ∈(0, n)
Barrier:		Barrier: This is the agreed exchange rate, at which the option either knocks out or knocks in. Accepted Values: ∈(0, n)
Time trade-to-maturity:		Time trade-to-maturity: This is the time to maturity of the option, measured in years. Our tool accepts times to maturity between one day and 5 years. We recommend using the provided data with appropriate caution if the time is longer than one year, as constant interest rates and volatilities are assumed in the model which is implemented in our program. Accepted Values: ∈(1/365, 5)
Notional:		Notional: Specifies how many units of foreign / domestic currency are bought / sold if the option is exercised at expiry. See also the parameter Fd. Accepted Values: ∈(0, n)
Call/Put:	Call Put	Call/Put: Indicates whether the option is a Call or a Put.
Knock In/Out:	Out In	Knock In/Out: Specifies whether it is a knock-out or a knock-in option.
Barrier Above/Below:	Below Above	Barrier Above/Below: Eta takes the value +1 if the barrier B is approached from above (e.g. down-and-out) and ?1 if the barrier is approached from below (e.g. up-and-out).
Barrier Style:	American European	Barrier Style: A European barrier is valid only at maturity, an American barrier is observed continuously at all times from trade time.
FOR/DOM:	Domestic Foreign	FOR/DOM: Determines whether the nominal is in foreign or domestic currency.

Valuation

Output:

Black-Scholes and Vanna-Volga values Previous and Black-Scholes Greeks All

Output: Result selection.

Results

This option type includes all kinds of Call - and Put - Options that can only be exercised, if until expiry the underlying exchange rate never trades at a pre-specified lower and upper barriers (double barrier knock-out) or alternatively ever trades at least one of those barriers (double barrier knock-in).

 

Market Data

Spot Price:		Spot Price: This is the value of the underlying exchange rate today. Accepted Values: ∈(0, n)
Domestic Rate:		Domestic interest rate: If you are not sure about which interest rate is domestic and which foreign, the example at the end of the document will clarify this. Accepted Values: ∈(-0.1, 1)
Foreign Rate:		Foreign interest rate: In general you should use the money market interest rates with the according time to maturity for rf and rd. Accepted Values: ∈(-0.1, 1)
Volatility:		Volatility: This is the market implied volatility of an at-the-money-Call. This figure can be looked up in appropriate tables which are for example provided by banks. ATM is ATM-forward in our calculations. Accepted Values: ∈(0, 10)
Delta Wished:		Delta Wished: This specifies the spot delta (premium unadjusted) of the butterfly and risk reversal - options that are used for vega-hedging. Market standard is the value 0.25. Accepted Values: ∈(0.05, 0.45)
Risk Reversal:		Risk Reversal: This is the market quote of a "risk reversal " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)
Butterfly:		Butterfly: This is the market quote of a "butterfly " in terms of volatility with a delta which is specified in the variable delta_wished. Also see Vol. Accepted Values: ∈(-1, 1)

Contract Data

Strike:		Strike: This is the agreed exchange rate, at which the holder can buy / sell currency at expiry. Accepted Values: ∈(0, n)
Lower Barrier:		Lower Barrier: This is the lower barrier for the underlying. Accepted Values: ∈(0, n)
Higher Barrier:		Higher Barrier: This is the upper limit for the underlying exchange rate. Accepted Values: ∈(0, n)
Time trade-to-maturity:		Time trade-to-maturity: This is the time to maturity of the option, measured in years. Our tool accepts times to maturity between one day and 5 years. We recommend using the provided data with appropriate caution if the time is longer than one year, as constant interest rates and volatilities are assumed in the model which is implemented in our program. Accepted Values: ∈(1/365, 5)
Notional:		Notional: Specifies how many units of foreign / domestic currency are bought / sold if the option is exercised at expiry. See also the parameter Fd. Accepted Values: ∈(0, n)
Call/Put:	Call Put	Call/Put: Indicates whether the option is a Call or a Put.
Knock In/Out:	Out In	Knock In/Out: Specifies whether it is a knock-out or a knock-in option.
Barrier Above/Below:	Below Above	Barrier Above/Below: Eta takes the value +1 if the barrier B is approached from above (e.g. down-and-out) and -1 if the barrier is approached from below (e.g. up-and-out).
FOR/DOM:	Domestic Foreign	FOR/DOM: Determines whether the nominal is in foreign or domestic currency.

Valuation

Output:

Black-Scholes and Vanna-Volga values Previous and Black-Scholes Greeks All

Output: Result selection.

Results

The Iteration that is used needs an initial value which is used as a first guess for the correct implied volatility. In doubt you should enter the at-the-money-volatility.
Note that the implied_vol - routine calculates the volatility for a plain vanilla Call or Put with notional 1 in foreign currency. If the implied volatility is below 0.1 % or bigger than 200%, the function returns the error code -992, if the input data are not consistent, e.g. StartVol > 100%, the function returns the error code -999.

 

Market Data

Spot Price:		Spot Price: This is the value of the underlying exchange rate today. Accepted Values: ∈(0, n)
Domestic Rate:		Domestic interest rate: If you are not sure about which interest rate is domestic and which foreign, the example at the end of the document will clarify this. Accepted Values: ∈(-0.1, 1)
Foreign Rate:		Foreign interest rate: In general you should use the money market interest rates with the according time to maturity for rf and rd. Accepted Values: ∈(-0.1, 1)

Contract Data

Strike:		Strike: This is the agreed exchange rate, at which the holder can buy / sell currency at expiry. Accepted Values: ∈(0, n)
Time trade-to-maturity:		Time trade-to-maturity: This is the time to maturity of the option, measured in years. Our tool accepts times to maturity between one day and 5 years. We recommend using the provided data with appropriate caution if the time is longer than one year, as constant interest rates and volatilities are assumed in the model which is implemented in our program. Accepted Values: ∈(1/365, 5)
Call/Put:	Call Put	Call/Put: Indicates whether the option is a Call or a Put.

Valuation

Option Price:

Option Price: Option price in DOM per 1 unit of FOR. Accepted Values: ∈(0, n)

Volatility Guess:

Volatility Guess: Initial value to start iteration. Accepted Values: ∈(0, 1)

Results