# Power reverse dual currency note

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Power reverse dual currency note

A "dual currency note" (DC) pays coupons in the investors' domestic currency with the notional in the issuers’ domestic currency. A "reverse dual currency note" (RDC) is the reverse. A "power reverse dual currency note" (PRDN) or "power reverse dual currency bond" (PRDB) is an exotic financial structured product where an investor is seeking a better return and a borrower a lower rate by taking advantage of the interest rate differential between two countries. The power component of the name denotes higher initial coupons and the fact that coupons rises as the domestic/foreign exchange rate depreciates. The power feature comes with a higher risk for the investor. Cash flows may have a digital cap feature where the rate gets locked once it reaches a certain threshold. Other add-on features are barriers such as knockouts and cancel provision for the issuer.

Market

The majority of investors are Japanese with a 9 billion USD worth of notes issued 2003. Major actors in the market are (in order of market share) Mizuho, Nomura, Citigroup, Daiwa SMBC, JP Morgan, Bank of Tokyo Mitsubishi, Credit Lyonais, Goldman Sachs and Shinkin.

Payoff and cashflows

The investor pays a coupon times a fixed rate in currency c1 and receives a coupon times a fixed rate in currency c2 times current FX rate divided by the FX rate at the inception of the deal. However, the cash flows are always guaranteed to be positive for the investor. The investor, therefore, has the option to receive cash flows making the payoff similar to a Bermudian style FX option. The swap house is, thus, selling a series of Currency options with a floating rate as a premium; the rate is usually subtracted with a spread.

$sum_\left\{t=1\right\}^\left\{n\right\} MAX\left(N frac \left\{FX_t\right\} \left\{FX_0\right\} r1_t - r2_t\left(N-1\right),0\right)$

where:: $N = ext \left\{notional\right\}$:: $t = ext \left\{time of a cash flow\right\}$:: $0 = ext \left\{time at the start of the deal\right\}$:: $r1 = ext \left\{fixed rate at t of currency1. A set of rates for every t are fixed at time 0. \right\}$:: $r2 = ext \left\{fixed rate at t of currency2. A set of rates for every t are fixed at time 0. \right\}$:: $FX = ext \left\{exchange rate between currency1 and currency2\right\}$:: $t = ext \left\{time of a cash flow\right\}$

Model

Pricing of PRDCs is usually solved by 3-factor Heath-Jarrow-Morton , LIBOR Market models where one factor represents the movement of the interest rates in currency1; the second factor the movement of the interest rate in currency2; and the third factor the movement in the FX rate between currency1 and currency2.

Inputs

* Grid parameters to determine the granularity of the grid
* Time step parameters for each factor and exercise nodes
* Mean reversion constants
* Correlation constants between each factor. Those correlation parameters are usually estimated historically.
* FX volatility calibrated based on fx options and user inputs
* IRS volatilities of each currency calibrated based on IRS Swaptions and yield curves
* Yield curve of money market rate1 based on deposit rates, futures yields and swap rates
* Yield curve of money market rate2 based on deposit rates, futures yields and swap rates
* Basis spread curve between rates.
* Spot FX rate

Computation

Unless PRDCs are broken down in separate parts and valued by replication (see: portfolio replication theories); values, such as the present value, may take several minutes to produce.

Hedging

A plain vanilla PRDC is exposed to volatility, interest, fx, correlation, and basis risks. Those exposures are hedged with interest rate swaps in each currency to reduce interest rate risk, interest rate swaptions in each currency to reduce interest rate volatility exposures, Currency Options to reduce fx volatility exposures and Basis swaps to reduce basis risk. It is not possible to reduce the impact of changes in correlation.

References

* [http://www.ose.or.jp/futures/report/0406.pdf#search='PRDC' Market value theory of PRDC ]
* [http://giddy.org/sf/articles/structured_notes.pdf Structured note markets]

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