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Pricing Power Reverse Dual Currency Notes

Despite a recent decline in popularity, Power Reverse Dual Currency notes continue to exist on many books due to the strengthening of the JPY currency. Therefore accurate pricing of Power Reverse Dual Currency notes remains an important, yet challenging, endeavor for both issuers and investors worldwide. FINCAD Analytics Suite Excel and FINCAD Analytics Suite for Developers provides pricing and cash flow analysis for a wide range of Power Reverse Dual Currency notes.

Overview

During the mid 1990's, the Japanese interest rate market suffered a sharp decline in yields. For
instance, the 10y swap rate fell from a high of 6% to 1%. These movements caused Japanese
investors to start searching for structured products that gave higher yield than available domestically. They had to look elsewhere, in foreign interest rate markets where there was a significant interest rate differential. The first incarnation was a principal protected note, denominated in yen, but paying a coupon that referenced that foreign currency. These notes, whose coupons were typically floored at zero, were referred to as Reverse Dual Currency (RDC) notes and could effectively be thought of as a strip of foreign exchange coupons.

To download the latest trial version of FINCAD Analytics Suite for free, contact a FINCAD Representative.

Types of Data Used in Calibration

The instruments used in the calibration should be as similar as possible to the instrument being valued. In general you would want to have caps/floors or swaptions that mature or fall on the important dates (cashflow dates or call/put) of the underlying instrument that you are trying to value. For example, to value a Bermudan swaption that is exercisable beginning five years from today to nine years, into a swap with maturity ten years from today, you would use European swaptions with the following maturities: 5x5; 6x4; 7x3; 8x2; 9x1.

Another example would be an American exercise callable bond maturing in 10 years that can be exercised starting today. Some sample European swaptions to use would be: 1x9; 2x8; 3x7; 4x6; 5x5. Additional criteria that should be considered is that some of the instruments used for calibrating may not be actively traded instruments (stale quotes). For what constitutes good calibration, please see below.

FINCAD Analytics Suite supports the use of either market quoted ATM European swaptions or caps and floors. For calibration using caps and floors the inputs that are required are caplets and floorlets. Since data for caplets and floorlets is not likely to be available, the function aaVol_Crv2_Rcap_BL can be used to bootstrap the necessary data.

The Continuing Search For Yield

However, JPY interest rates continued to decline, the RDC notes stopped producing a significant yield enhancement for the JPY investors. The idea of leverage was introduced to the notes and the Power Reverse Dual Currency was born. The different methods of producing this leverage resulted in a wide variety in the types and characteristics of Power Reverse Dual Currency notes.

As a first measure to increase yield, the notes were given extremely long nominal tenor (25-30 years are common) from a desire to access the increasing yield further out in the curve. However, investors typically believed that the notes would be called back immediately following the non-call period.

An initial fixed coupon period of approximately 2-5 years is very typical, usually with a very high coupon, such as 5%-10%. This period is non-callable, however typically the notes are Bermudan callable, meaning that the issuer retains the right to call back the note at any cash flow date.

To further increase yield, an additional parameter was added to the coupon formula, the "FX base". This parameter scales the FX rate used in the coupon formula and is usually set to be equal to the FX forwards seen in the market at the time of issue. Mathematically, this changes the slope of the coupon payoff thereby adding leverage to the product. In practice this makes Power Reverse Dual Currency notes sensitive not only to the FX rate, but how the FX rate has moved relative to the FX forward curve. A increase of the FX rate above that predicted in the forward market (a weakening of the JPY currency) increases the coupon and a decrease of the FX rate (a strengthening of the JPY currency) decreases the coupon.

Initially, Power Reverse Dual Currency notes were linked to the JPY/USD exchange rate. However after a decline in the strength of the USD between 2001 and 2003, Power Reverse Dual Currency notes began being issued linked to the JPY/AUS exchange rate. More recently, the Power Reverse Dual Currency note has broken free from its JPY origins and can now be found to be linked to the USD/EUR exchange rate.

In today's climate of historically low interest rates, Power Reverse Dual Currency notes may yet experience a resurgence in popularity as investors again undertake the "search for yield". However, during the recent global credit crunch, all markets have seen a drastic increase in volatilty, including the FX and interest rate markets. This has caused an increase in the magnitude of the daily hedging of PRDC notes, most of which has been at a loss to the issuing institution.

This relationship between the spot FX rate, the price of a Power Reverse Dual Currency note and the expected duration is demonstrated using FINCAD Analytics Suite in figure 1. Note that FINCAD Analytics Suite uses Monte Carlo pricing to determine the fair value and optimum exercise date. The early exercise date is calculated using the Longstaff-Schwartz algorithm, and is expected to exhibit more variance than the fair value. This accounts for the observed scatter in the expected duration in figure 1.

History

From the above considerations, investors in Power Reverse Dual Currency notes can be thought of as taking a view on the forward FX market. The general economic thinking was that the JPY currency would not appreciate more than the FX forward market, however, if it did this would signal a rally in the JPY economy and it would cease to be a low yield environment.

Spot Foreign Exchange Rate

Up to 2006, the JPY currency essentially followed the forward. However, it began to appreciate against the USD in 2007 causing a decrease in Power Reverse Dual Currency coupons, meaning investors were left holding long dated extremely low-yielding instruments! Counter-intuitively, this was actually not entirely favourable to the issuers either - hedging such long dated structures is done in the long end of the FX forwards and options markets, which are very illiquid and therefore the hedges prove to be costly.

For these reasons, accurate pricing of Power Reverse Dual Currency notes using model sufficiently complex to incorporate the long dated FX options market data is invaluable for both investors and issuers.

Modeling and Calibration

Although the notes are primarily exposed to the foreign exchange rate, the arbitrage-free dynamics of the FX rate

indicate that the FX rate is, in turn, exposed to movements of both the domestic and foreign interest rate (rd and rf respectively). One could imagine a model where the dynamics of the interest rates are frozen being satisfactory for an FX-linked product of short duration, however this type of approximation will not be sufficient for Power Reverse Dual Currency notes due to their long tenor (that this is only a nominal tenor and not expected duration is not important, as issuers will always need to hedge FX options out to the longest maturity possible).

The FINCAD Analytics Suite pricing engine uses the three factor model described in [3], where the two interest rates are each modeled using a one factor Hull-White model

and the FX rate is modeled using a time-dependent CEV model described by the diffusion term

Equally as important as the choice of model, is the choice of model parameters. They must be chosen to reflect the current market data. With a relatively complicated model, this can become quite cumbersome. In order to mitigate this complication, FINCAD Analytics Suite offers a calibration function that will take in FX market data and output the best set of volatility σ(t) and CEV exponents β(t) to use in the above three factor IRFX model. The procedure used is outlined uses two novel techniques: Markovian projection and parameter averaging. These techniques are outlined in [3].

Instrument Coverage

The FINCAD Analytics Suite can price a wide range of Power Reverse Dual Currency notes. Most Power Reverse Dual Currency coupons can be described by the following formula

is sometimes referred to as a "vanilla" Power Reverse Dual Currency coupon. The parameters f and d are referred to as the foreign and domestic coupon respectively, the nomenclature arising from the fact that d is multiplied by the domestic notional, whereas f must first be multiplied by the prevailing FX rate prior to being multiplied by the domestic notional. The parameters a and b refer to the coupon floor (usually set to zero) and cap, respectively.

The second type of coupon structure handled by FINCAD Analytics Suite is the "digital" or "step-up" coupon, where the coupon structure is a piecewise constant function of the underlying FX rate - in other words the coupon is constant but experiences jumps to a different constant level when the FX rate reaches specific values. Mathematically

The other important feature of Power Reverse Dual Currency notes are their call feature. FINCAD covers all of the following call features:

  • Bermudan callable
  • Automatic Trigger/Knock-out
  • Targeted Automatic Redemption (TARN)

which can be used in any combination with the above coupon structures, thus allowing FINCAD Analytics Suite to price a high percentage of the different types of Power Reverse Dual Currency notes available.

Spot Foreign Exchange Rate - Vanilla and Digital Coupons

References

[1] Antonov, Alexandre and Misirpashaev, Timur (October 2006), Markovian Projection onto a
Displaced Diffusion: Generic Formulas with Applications, http://ssrn.com/abstract=937860.
[2] Jeffery, Christopher (2003), The problem with power-reverse duals, Risk Magazine, 16(10): pp. 20-22.
[3] Piterbarg, Vladmir (2006), Smiling Hybrids, Risk Magazine, 19(5): pp. 66-71.
[4] Sippel, Jason and Ohkoshi, Shoichi (2002), All power to the PRDC notes, Risk Magazine, 15(11): pp. S31-S33.

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.