The market price calculator for currency options / currency barrier options calculates current market values, time values, and future market values (the future point in time is the horizon).

A currency option is an option on a forward exchange transaction. There are both call and put options. A currency barrier option is a currency option, for which there is an additional condition known as a barrier Currency barrier options also come in both the call and put variety. We distinguish between four main types of barrier options:

• The "up & in", which means that a currency option becomes valid only when the currency rate in the underlying rises above a certain level (barrier).

• The "up & out", which means that a currency option becomes invalid when the currency rate in the underlying rises above a certain level.

• The "down & in", which is where a currency option becomes valid when the currency rate in the underlying falls below a certain level.

• The "down & out", which is where a currency option becomes invalid when the currency rate in the underlying falls below a certain level.

Both the American and the European types of currency and currency barrier options can be created. The buyer has the right to exchange one currency for another at a price agreed upon earlier (with a currency barrier option, this assumes that the currency option is valid). The optional exchange takes place on a particular date (when exercised according to European standards), or during a specified period up to the expiration date (when exercised according to American standards). Only those currency and currency barrier options whose expiration date is after the horizon will be valued.

The future currency rate is modeled in the valuation. Currency options, like other types of options, are calculated using the option price formulae: Black for European options, and the binomial tree (using 30 or 31 periods) for American options. These formulae require the strike price (the agreed upon exchange rate in the case of currency options), the spot rate (the current or forward exchange rate), the term of the option, and the volatility. In addition, currency options also require two risk free interest rates (corresponding to the two transaction currencies).

In order to value a currency option, you need the transaction data, and alternatively a par coupon or zero coupon yield curve in the transaction currency (ask or bid rate) for the evaluation date.

You will also need a currency volatility curve for the term of the option. The given currencies represent the two transaction currencies (currencies of the call and put sides of the underlying transactions).

The currency rates (bid and ask rates) of both transaction currencies in relation to the display currency are needed. If the horizon comes after the evaluation date and the transaction currency differs from the display currency when calculating a forward currency rate on the horizon (currency of the put side of the underlying / display currency), a par or zero coupon yield curve structure will have to be entered in the display currency (ask or bid rate).

You need zero coupon rates and zero bond discounting factors for use in later determining the risk free interest rates (both of which go into the price formula).

If the horizon is later than the evaluation date, the corresponding forward currency rates (bid or ask price) of the transaction currencies (currency on the put side of the underlying) are calculated for the evaluation date using the yield curves from the transaction and display currencies. The relevant forward currency rate (bid or ask price) of the transaction currency on the horizon is calculated using the yield curve from the transaction currency, based on the exchange rate on the evaluation date.

Depending on the type of option (American or European), the option price calculator uses the Black Scholes formula (for European options) or the binomial tree (for American options), along with the following parameters (some of which are taken from the input parameters):

• Call/Put: Call/Put:
• Term: term of the option in days (expiration date of the option to the horizon)
• Spot: current currency rate or forward currency rate on the horizon of the two transaction currencies (currencies on the call and put sides of the underlying transaction)
• Strike: fixed currency rates of both transaction currencies in the underlying transaction of the option (currencies of the call and put sides of the underlying transaction)
• Interest rate 1: risk free interest of the call side of the underlying transaction = zero interest rate of the given yield curve corresponding to the currency of the call side of the underlying transaction and the option term
• Interest rate 2: risk free interest of the put side of the underlying transaction = zero interest rate of the given yield curve corresponding to the currency of the put side of the underlying transaction and the option term
• Volatility: currency volatility of both transaction currencies from a volatility curve with a term corresponding to the option term

The result calculated will be the NPV (on the horizon) of the currency difference (DZ) between the currency rate and the currency rate fixed in the underlying transaction on the exercise date of the option. This difference (DZ) is standardized to the nominal volume of the put side of the underlying transaction, and has a lower limit of zero.

The NPV of the currency option (in the currency of the put side of the underlying transaction) is the nominal volume (NV) of the put side of the underlying transaction multiplied by the currency difference (DZ).

Along with the symbols given already, the following are also used:

where:

K: call/put-marker

If the display currency differs from the put side of the underlying transaction of the currency option/currency barrier option, the NPV is calculated using the (forward) currency (bid/ask) rate.