Pricing of vanilla Power Reverse Dual Currency (PRDC) Swaps
August 17, 2006
Since early 2004 Power Reverse Dual Currency (PRDC) swaps have become very popular with the Japanese investors, especially in the Dollar-Yen market. Despite the ominous sounding name, PRDCs are essentially long dated FX options and PRDCs are a great way to get an exposure to long term volatility in the FX market. Besides, most PRDCs are structured in such a way that the upfront coupon (the initial payment) is sometimes pretty high, a gimmick to lure the investors.
Callable Dollar-Yen PRDCs have been one of the most popular types of callable structured notes in the last couple of years. Most of these notes are principal protected and pay a high initial coupon - generally a single upfront payment - and then the investors are exposed to long periods of, between 15 to 30 years, of low coupon, sometimes very close to 0% if the Japanese Yen appreciates against the US Dollar. Of course, a lot of PRDCs get called very soon by the issuer.
A generalized vanilla PRDC has a coupon payoff like this:
In its simplest form a vanilla PRDC coupon payoff, as can be seen from the above formula, is simply a series of call options on the FX rate. In a more generalized form a PRDC coupon can be represented as:
If the floor is zero and the cap is positive infinity and let us say that Dollar-Yen is at 110 and the Dollar coupon rate (interest rate) is 20% and Yen coupon rate is 15% the PRDC coupon payoff function will be:
The option notional in the above is very low and this could result in lowering of the amount of coupon payment. The above is a series of deep in the money call options (Yen Call/Dollar put) on Dollar-Yen. The pricing of the above vanilla PRDC is pretty trivial.
Generally the callable feature of the Callable PRDC notes is embedded as a Bermudan structured whereby the note can be called at each coupon date. In that case a tree could be used to value the Bermudan calls.
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