PRDC Coupon Optionality and Callable FX–Interest Rate Risk

# What are typical payoffs of PRDCs?


# What are typical payoffs of PRDCs?












I understand that in PRDCs (Power Reverse Dual-Currency note), client is long call spreads coupons on e.g. USDJPY (the FX carry pair). The PRDC is also callable by the issuer. I'd expect the call spreads to make dealers short skew / long vanna (although dampened by the callable option?)

However I also heard that PRDCs typically make dealers longer backend vega when spot is down. That is dealer long skew / short vanna dynamic. So I must be missing something in the payoff. What is it?

## Answer by user35980 (score 4, accepted)

https://quant.stackexchange.com/a/83545

I think this question warrants a brief recap of PRDCs and their risks. Brace yourself.

##### PRDCs: a general description

From an investor's perspective, PRDCs (in the context you describe) are leveraged bets against the FX forward curve in an effort to avail positive carry. This is why they work best with currency pairs with wide rate differentials (like USDJPY). Historically, these products were invented to cater to mainly Japanese investors who wanted more enhanced returns for their JPY over their vanilla dual/reverse dual currency note counterparts in the early 2000s.

##### PRDC payoff coupon

To get this coupon enhancement the gurus came up with a coupon payoff which (in its simplest form) looked something like $$coupon_t=\max\left[\frac{S_t}{S_0}X_$ - X_¥,0\right]\tag{1}$$ paid on long dated structures, where (sticking with the USDJPY context) $S_0$ is USDJPY FX spot fixed at inception, $S_t$ is FX at the $t$th coupon and $X_{$}, X_¥$ are the USD and JPY coupon rates (also set at the note inception) - the ratio of these coupon rates dictate how much leverage the note pertains (the "power" in PRDC).

##### A series of call options

Formula (1) shows why the PRDC note investor is long a series of OTM USD call JPY put options - she makes money when JPY depreciates and gets stuck with zero coupon duration (hence why these notes need to be long dated to work) if the forwards are realized i.e. USDJPY strengthens. Explicitly, rewrite (1) as $$coupon_t=\frac{X_$}{S_0}\max\left[S_t - K,0\right]$$ where $$K=S_0\frac{X_¥}{X_$}.$$

##### Non-callable case: variations and risks

The yield in (1) can be enhanced further in several ways, one of which is by capping the FX call options the investor is long. This can be done by making these options call spreads (what the questioner is alluding to) or adding a strip of knock-in barrier options (which kick in when USDJPY depreciates beyond a certain level). In either case the investor is selling back optionality in this modification. The FX risks for such structures are fairly straightforward, and mainly depend on the term structure of the FX forwards as well as the USDJPY smile/skew. Simultaneously the interest rate risks are hedged in pretty standard fashion as well. However, it must be stressed that the structured note nature and lengthy durations involved make the FX optionality even in this non-callable case anything but vanilla - there is effective path dependence and FX/IR correlation at play (but nowhere near the extent of the callable case - see below).

##### Callable case: more complicated

Finally, another way to enhance the yield on this product is to make the entire structure callable. This means the investor is selling rate vol as well. It is this variation that both makes PRDCs complex to value and notoriously toxic products. The idea with these callable structures was for the investor is to make a chunky first coupon and then for the note to be redeemed by the issuer (taking care of the lengthy duration problem), assuming the market moved the investor's way

##### Callable case: more risks

However, the callability convolutes the interest rate and FX risks of the structure due to the inherent correlation in these markets, which introduces a short cross-gamma position for the issuer (who is also the only one who hedges - investors are usually not part of the secondary market). Explicitly: the issuer is selling a bond hence they are borrowed and receive rates on the hedge. Let's say the market moves the investor's way (USDPY weakens) and also that the USDJPY/USD rate correlation is positive. This means the coupon value goes up and the issuer will want to call the note. This reduces the duration of the note meaning the issuer is now less borrowed than when they hedged - so now they will need to reduce the hedge by paying rates. But they will do this at a time when rates have gone up (via the positive correlation). On the other hand, when the market moves against the investor (USDJPY strengthens, rates move lower), the call will be less likely i.e. the note duration will increase. Now the original hedge is insufficient and the issuer will need to receive more when rates are down.

The above is just the dynamics taking place in the linear space - similar issues arise in the non-linear space (where the FX vol and rate vol come into play), not to mention the fact that the FX options embedded in these structures are very long dated which essentially makes them more rate vol products rather than FX vol products. And all of this is taking place in copious proportions in a one way market - not an ideal situation for hedgers.

##### Conclusion

So, in conclusion, the risks of (callable) PRDCs extend well beyond standard FX vanna/vega measures the original question seems to have been looking to. Their primary risk drivers are the unhedgable FX/IR correlation intrinsically present in their construction.

## Answer by Socrates231 (score 1)

https://quant.stackexchange.com/a/83543

The Vanna profile of a call-spread seller looks like this

A dealer starts long Vanna but gets into a short Vanna position as the underlying gets closer to the strikes