Power Reverse Dual Currency (PRDC) Structures - Are they Hybrids?
June 4, 2007
We ran an article on PRDCs earlier and discussed some of the salient features of the structure there. PRDCs are extremely popular with Japanese investors, or with investors in JPY exposures. In fact PRDCs give an investor long term exposure to JPY volatility. Of late, we have run into quite a few detailed discussions on PRDC pricing and hedging and we have been pricing a lot of PRDC term sheets as hybrids in our intermediate and advanced quantitative modeling training sessions with front office professionals. And the interest in these payoffs is quite high from both FX and IRD sales professionals across Asia .
Some of them are of the impression that a PRDC structure is simply an FX structure whereby the investor is buying long volatility through Dollar-Yen call options. That is only part of the story.
Actually, PRDCs are hybrid structures. They are as hybrid as they come. A typical PRDC payoff, in its most vanilla form, looks like this (refer to our earlier article on this):
In the above payoff the investor's (or the client's) profit and loss is in JPY and is the value of Dollar-Yen at initiation, which is know. In the above payoff formula, is the value of Dollar-Yen at maturity of the contract, is the short term USD interest rate and is the short term JPY interest rate.
If we assume a PRDC contract to be of very short term, say a three month or a six month maturity - which is not how they are structured in practice - then of course, you can take both the short term rates as constant and the payoff will collapse into a structured FX call option with a certain strike and a leverage factor.
But in practice PRDC contracts and structured products are long term products with maturities typically going on to 10 years or even 30 years. In that case both the short term rates in the above payoff - in dollar and yen - have to be treated as stochastic and need to be modeled. We normally use a one factor or two factor LIBOR market model or Vasicek's model to simulate the USD and JPY rates and also use the exponential (integral) stochastic equation to model and simulate the Dollar-Yen FX rate. All three of them are then put into a Principal Components Analysis (PCA) framework to simulate the correlated paths and then price the contract with around 20,000 simulation runs.
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