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Valuing FX Quanto Basket Options with FINCAD

To view FINCAD's quanto basket calculator and the underlying FINCAD quanto function, contact a FINCAD Representative to download the latest trial version of FINCAD Analytics.

The Instrument

A quanto (quantity-adjusting) option is a cash-settled cross-currency derivative where the underlying asset is denominated in a different currency from the one in which the option is settled. Settled OTC at a fixed exchange rate, a quanto option provides protection from exchange rate fluctuations. If an investor believes that a foreign asset will do well but fears that the foreign currency will not, buying a quarto option on the foreign asset will keep the payout in the domestic currency. It will also allow the holder to capture the foreign asset's returns while being protected from foreign exchange risk. In the case of a quanto Basket option, the underlying is a basket of assets that can be denominated in various currencies from the one in which the option is settled. This structure allows investor to participate in the returns from an international sector while being protected from the exchange rate risk from which the underlying basket's assets are denominated. Hence, this simplifies the hedging procedures for such risk as well as the costs associated. In the case of a FX quanto basket, the underlying assets are simply currencies denominated in a given reference currency and where the payout currency can be specified in another domestic currency. This allows the capturing of the exchange rate returns/losses from a basket of currencies vis-à-vis a reference currency while having the payout in a different currency.

How can FINCAD help?

The FINCAD library offers a variety of functions to value quanto options and quanto basket options. These functions are designed to value generic quanto options and quanto basket options. In the following we will show, through an example, how to use this function to value a basket FX quanto option, by properly arranging the inputs.

Before jumping into the details of the example we give a little background of the function aaQuanto_basket_MC. The valuation methodology behind this function is based on the Black -Sholes lognormal model. More specifically, all of the underlyings in the basket are assumed to follow a lognormal process. It is well known that a basket of log normally distributed assets, in general, no longer follow a lognormal distribution and hence closed-form solutions are not available for a quanto basket option. In the implementation of aaQuanto_basket_MC a Monte Carlo method is used.

The following is the formula of the payoff of a basket quanto options at maturity:

where n is the number of assets in the basket, K is the option's strike price in units of the payout currency, is the price at maturity T of asset j denominated in the original currency and wj is the weight of asset j in the basket.

  • For further modeling references see the FINCAD Math Reference for quanto options and basket options.
  • For full details of the function inputs, their restrictions and special notes see the aaQuanto_basket_MC function reference.
  • For ready-to-use solutions see FINCAD Quanto and Quanto basket Workbooks through: FINCAD menu → Workbooks (user data) → Options - Exotic

Example: Valuing FX Quanto Basket Options with FINCAD

Deal description of a newly issued FX quanto basket:

  • A FX Quanto Basket call option.
  • USD as the reference currency and CAD as the payout currency.
  • The basket is composed of the following 5 currencies ; CAD, MXN, EUR, JPY and CNY denominated in USD. In more detail, in the above option's payoff formula , j = 1,2,…,5 are the FX rates of the five currencies, respectively. For example, is the FX rate USD/CAD, which is the number of USD units per one unit of CAD.
  • Strike is $500 (CAD)
  • The weights for each of the currencies in the basket : CAD: 121.9416, MXN: 1153.8, EUR: 78.14203252, JPY: 10582.1025 and CNY: 827.65. Note that these weights are chosen to make each currency in the basket have a weight of $100 USD approximately at the issue date.
  • The spot FX rates of the currencies are 0.82, 0.08667, 1.279721, 0.00945, and 0.12082, respectively.
  • Value (also the issue) date is March 14th, 2006 and Expiry date is March 18th, 2008

To value the above quanto FX basket option we can treat the FX rates as assets denominated in USD. This way the problem is reduced to valuing a single currency basket quanto option: a quanto option on a basket of USD assets. The payout currency is CAD.

Steps in FINCAD XL: (see screen shot below)

  1. Paste an example of aaQuanto_basket_MC
  2. Set the Asset and option info table as follow:
    • Currency code : 1 = Payout currency (CAD), 2= Reference currency (USD) . In this setup, all the FX rates in the basket are treated as assets denominated in USD.
    • FX rates: expressed in units of USD per one unit of the currencies CAD/MXN/EUR/JPY/CNY, respectively.
    • Weights: given as above
    • Foreign risk free rates: quoted on an annually compounded, Act / 365 ( fixed) basis. See aaConvert_cmpd2 for converting a rate to a different accrual method.
    • FX volatility
  3. Set the rate and FX volatility table as follow:
    • Currency code: 1 = Payout currency (CAD), 2= Reference currency (USD)
    • rate - annual - Actual/365: domestic risk free rate for the Payout currency (CAD) and the reference currency (USD)
    • FX volatility
  4. Set the correlation matrix: a correlation matrix is the instant correlation matrix of the variables (YCAD, YCAD / USD, S1, S2, S3, S4, S5, where YCAD =1), representing the FX rate of the payout currency per one unit of itself, and YCAD / USD, which equals 1/S1, is the FX rate CAD/USD, which is the number of CAD units per one unit of USD.
  5. Specify the exercise price, value (settlement) date, expiry date and option type according to the specifications above.
  6. Set the number of random trials for the Monte-Carlo simulation. If the number of trials is not entered as an integer then the Monte Carlo simulation will use a fixed seed to initialize its internal random number generator otherwise a random seed will be used.

The function output the fair value of the quanto basket option. its accuracy and the deltas for each of the underlying currencies.

Disclaimer

Your use of the information in this article is at your own risk. The information in this article is provided on an "as is" basis and without any representation, obligation, or warranty from FINCAD of any kind, whether express or implied. We hope that such information will assist you, but it should not be used or relied upon as a substitute for your own independent research.

For more information or a customized demonstration of the software, contact a FINCAD Representative.