FX Option

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Currency Option or FX Option Introduction and Pricing Guide

FinPricing provides valuation tools for the following FX products:

1. Currency Option Introduction

A currency option, also known as FX Option, is a derivative contract that grants the buyer the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified future date. The FX options market is the deepest, largest and most liquid market for options of any kind. Most FX derivatives trading is over the counter (OTC) and is lightly regulated.

There are call options and put options. Also a currency option could be European style or American style. Call options provide the holder the right but not the obligation to purchase an underlying currency at a specified FX rate on a future date, while Put options give the holder the right to sell an underlying currency at a specified FX rate on a future date. A European option can be exercised only at the expiration date of the option, whereas an American option can be exercised anytime during its life.

FX options contain Vanilla FX option and Listed FX option. Although both have similar characteristics, they differ mainly in two respects: First, Vanilla options are traded OTC while Listed options are exchanged-traded. Secondly, the underlying of Vanilla options is FX spot while the one of Listed options is FX future. Nevertheless, their analytics are very similar.

Currency options are one of the most common ways for corporations, individuals or financial institutions to hedge against adverse movements in exchange rates. Corporations primarily use FX options to hedge uncertain future cash flows in a foreign currency. The general rule is to hedge certain foreign currency cash flows with forwards, and uncertain foreign cash flows with options.

Options give market participants many opportunities to limit risk and increase profit. Investors buy calls when they think the FX rate will rise or sell a call if they think it will fall. Selling an option is also referred to as ”writing” an option. On the other hand, they buy puts if they think the FX rate will fall, or sell one if they think it will rise.

One of the most common reasons for using FX options is for short-term hedges of spot FX or foreign market positions. Unlike a FX forward contract that locks in the FX rate for a future transaction, FX options allow the investors to benefit from favorable FX rate movements. Currency market fluctuations can have a lasting impact on cash flow whether it is buying a property, paying salaries, making an investment or settling invoices. By utilizing FX Options, business can protect themselves against adverse movements in exchange rates.

FX Options are also useful tools which can be easily combined with Spot and currency Forward contracts to create bespoke hedging strategies. There are many bullish, bearish and even neutral strategies that can be implemented with options contracts. Spread strategies that are used in equity options can also be used with FX options, including vertical spreads, straddles, condors and butterflies.

2. Forex Market Convention

One of the biggest sources of confusion for those new to the FX market is the market convention. We need to make clear the meaning of the following terms in the forex market first.

  • FX quotation: The quotation EUR/USD 1.25 means that one Euro is exchanged for 1.25 USD. Here EUR (nominator) is the base or primary currency and USD (denominator) is the quote currency. One can convert any amount of base currency to quote currency byQuoteCurrencyAmount = FxRate * BaseCurrencyAmount
  • Spot Date: The spot date or value date is the day the two parties actually exchange the two currencies. In other words, a currency pair requires a specification of the number of days between the quotation date (trade date) and the Spot Date on which the exchange is to take place at that quote. Spot days can be different for each currency pair, although typically it is two business days.
  • Holidays: Each currency pair has a set of holidays associated with it. The holidays of a currency pair is the union of the holidays of the two currencies.
  • FX curves: The observed curves in the FX market are FX forward points/spreads that cannot be used to price a FX trade directly. One needs to bootstrap FX forward points into FX yield curves in order to conduct valuation. Note that FX yield curves are quite different from LIBOR yield curves or government yield curves. Find more details about FX curves.
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3. Currency Option Payoffs

The payoff of a European call option

FX call option payoff in FinPricing

The payoff diagram of a European call option

FX call option payoff diagram in FinPricing

The payoff of a European put option

FX put option payoff in FinPricing

The payoff diagram of a European put option

FX put option payoff diagram FinPricing
4. Valuation

European FX Option

The present value of a European call option is given by

Pricing currency call opltion in FinPricing

Here we want to emphasize that the interest rates of base currency and quote currency are derived from currency yield curves rather than LIBOR or treasury curves. This is another distinguished feature in the FX market.

The present value of a European put option is given by

Valuing Forex put option in FinPricing

where all notations are the same as (1)

American FX Option

FinPricing is using the Odd-Even Cox Ross Binomial model to compute prices and risk sensitivities for American-style FX OTC options.

The Odd-Even Binomial model is an extension of the Cox Ross Binomial model. Compared to Cox Ross Binomial model, the Odd-Even Binomial model provides better price accuracy. It was implemented by creating two tress, one with even number n of iterations and another with n+1 number of iterations, then taking the average of the two results. This method also helps to reduce the number of oscillations that can be observed with traditional Binomial models, where the option value depends quite heavily on the number of periods. .

Practical Notes

  • Please note the time differences in (1) and (2), which is an important factor in order to apply the Black formula to the FX market. Usually the delivery date is different from the expiry date.
  • You first need to construct FX implied yield curves for both base and quote currencies. The FX curve construction in FX world is different from the one in interest rate world. FinPricing provides useful tools to construct  various curves and volatility surfaces.
  • Then you need to construct an arbitrage-free FX implied volatility surface. FinPricing is using Vanna Volga model to build FX implied volatility surface.
  • After that, you can use formula (1) or (2) to calculate the fair value and risk sensitivities.
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6. More Details

Click the following links for more details.