FX Asian
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Four user interfaces:
- Data API.
- Excel Add-ins.
- Model Analytic API.
- GUI APP.
FX Asian Option Valuation
FinPricing provides valuation tools for the following FX products:
- FX Asian Option
- FX Asian Basket Option
- FX Aisn Lookback Option
- Asian Quanto Option
- Equity Asian Option
- Equity Asian Basket Option
- Equity Asian Lookback Option
- Check FinPricing valuation models
| 1. FX Asian Option Introduction |
Asian FX options allow the buyer to purchase or sell the underlying foreign exchange rate at the average rate
instead of the spot rate. FX Asian options are commonly seen FX options over the OTC
markets. Average rate options are less expensive than regular curreny options and are
arguably more appropriate than regular FX options for meeting some of investment needs.
Average can be calculated in a number of ways (daily, weekly, monthly, etc.).
One advantage of FX Asian options is that they reduce the risk of market manipulation of the underlying instrument
at maturity. Another advantage of FX Asian options involves the relative cost of Asian options compared to
FX European options or FX American options. Because of the
averaging feature, Asian options reduce the volatility inherent in the option; therefore, FX Asian options are
typically cheaper than FX European option or FX American options.
Asian options have relatively low volatility due to the averaging mechanism. They are used by traders who are
exposed to the underlying asset over a period of time. The arithmetic average rate options are generally used to
smooth out the impact from high volatility periods or prevent rate manipulation near the maturity date, which makes
the options less expensive.
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 FX forwards, and uncertain foreign
cash flows with FX options.
FX Options give market participants many opportunities to limit risk and increase profit.
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 Asian Options, business can
protect themselves against adverse movements in exchange rates.
| 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 by QuoteCurrencyAmount = 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.
| 3. Valuation |
The payoff of an average rate call is max(0, Xavg – K) and that of an average price put is max(0, K - Xavg),
where Xavg is the average rate of the underlying asset calculated over a predetermined averaging period.
If the underlying exchange rate, X, is assumed to be lognormally distributed and Xavg is a geometric average of
the X’s, analytic formulas are available for valuing European average rate options. This is because the geometric
average of a set of lognormally distributed variables is also lognormal.
When, as is nearly always the case, Asian options are defined in terms of arithmetic averages, exact analytic
pricing formulas are not available. This is because the distribution of the arithmetic average of a set of lognormal
distributions does not have analytically tractable properties.
However, the distribution of arithmetic average can be approximated to be lognormal by moment matching technical, which leads to a good analytic approximation for valuing average price options. One calculates the first three moments, shown below, of the probability distribution of the arithmetic average in a risk-neutral world exactly and then fit a lognormal distribution to the moments.
The sifted lognormal parameters are
By assuming that the average asset price is lognormal, you can use Black’s model to price an FX Asian option. The present value of an Asian call option is given by
The present value of an Asian put option is given by
Practical Notes
- You first need to construct FX forward 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 the formulas to calculate the fair value and risk sensitivities.
| 4. Related Topics |