Long Dated FX products Dr. Sebastián del Baño Rollin Global Head FX and Equity Quantitative Research
Overview 1. Long dated FX products 2. The Power Reverse Dual Currency Note 3. Modelling of long dated FX products 4. The impact of the volatility smile 5. Some market considerations 2
Long Dated FX products Recent years have witnessed a significant increase in the demand for long dated FX products Corporates with substantial FX exposures typically will consider FX swaps (a strip of forwards). They will also often add extra features to the contract: Cancellability clauses held by either the bank or the corporate Other exotic features to cheapen the structure Investors wishing to place capital in high yield currencies Emerging markets Yen investors (USD or AUD) 3
The Power Reverse Dual Currency Note (PRDC) Designed as a yield enhancement instrument for Yen investors Investor swaps Yen LIBOR by Dollar LIBOR paid on a Yen notional This is offset by some exposure to USDJPY risk Typically maturities around 30Y Very popular product in the past. On lower USD rates market is now shifting towards AUD 4
The Power Reverse Dual Currency Note (PRDC) Examples: 1. Investor receives string of forwards with maturities 1Y, 2Y,, 30Y 2. Investor receives string of USD call / JPY Put options pays string of JPY LIBOR payments 3. Trigger PRDC. Yield can be enhanced with a substantial first coupon (typically around 4%). This is offset by a discrete USDJPY knock out clause. 4. Callable PRDC. Yield can be enhanced with a substantial first coupon (typically around 4%). This is offset by a callability clause on the Bank. Investor hopes a PRDC will be called/triggered in 1Y to collect a substantial return on a JPY investment. 5
The Power Reverse Dual Currency Note (PRDC) USDJPY 1Y 2Y 3Y 4Y Time 6
The Power Reverse Dual Currency Note (PRDC) USDJPY 1Y 2Y 3Y 4Y Time Customer receives 4% coupon Bank can decide to cancel deal 7
The Power Reverse Dual Currency Note (PRDC) USDJPY 1Y 2Y 3Y 4Y Time K 1 Customer receives payout of USD Call/ JPY Put Bank can decide to cancel deal 8
The Power Reverse Dual Currency Note (PRDC) USDJPY 1Y 2Y 3Y 4Y Time K 1 K 2 Customer receives payout of USD Call/ JPY Put Bank can decide to cancel deal 9
Modelling of long dated FX products A fundamental observation Vega = S T N( d1) e r f T α T Rho d = KTN( d 2) e r d T βt Thus, intuitively, vol risk is relevant for the shorter maturities and interest rate risk for longer maturities 10
Modelling of long dated FX products To value and hedge long dated FX trades we need to consider the impact of stochastic interest rates Example: Amin Jarrow (1991) price a vanilla option in a Black Scholes model enriched with HJM dynamics for the interest rates Main result is that implied vol is the volatility of a string of forwards to the maturity of the option This forward volatility will include the volatility of spot, volatilities of interest rates and correlations between spot/domestic rate/foreign rate. 11
Modelling of long dated FX products The Amin Jarrow model can be used to value PRDC s. Important aspects of the implementation: Choice of a particular HJM rate model: Hull-White, Vasiceck, BGM, Estimation of correlations: spot rate/domestic rate/foreign rate. How does one manage the correlation risk (correlation will also move with time ) Effects of the volatility smile 12
The impact of the volatility smile Ideally one would want a stochastic volatility model coupled with stochastic interest rate models to be able to value and hedge the impact of the smile This is unrealistic: too many parameters, calibration problems, speed issues, In practice one often analyses the Vega profile of the PRDC to see where in strike space is our vol exposure 13
The impact of the volatility smile USDJPY 1Y 2Y 3Y 4Y Time Bank will cancel deal if spot is above a certain level K 1 Bank is short this strike 14
The impact of the volatility smile USDJPY 1Y 2Y 3Y 4Y L 1 Bank is long this strike Time K 1 Bank is short this strike 15
The impact of the volatility smile USDJPY 1Y 2Y 3Y 4Y L 1 Bank is long this strike Time K 1 Bank is short this strike This is a Risk Reversal position: Bank is long high side vol and short low side vol 16
The impact of the volatility smile A risk reversal is typically a zero cost structure under the Black Scholes model assumptions. If we value this risk reversal under the smile we ll obtain the smile value corresponding to the second year leg of the PRDC 17
Some market considerations Why is the PRDC marketable USD/JPY interest rate differential is (was) very negative. Forward is very low. We can offer very profitable strike schedule. USDJPY was not perceived to be following the forward. Difference between risk neutral measure and real world measure means a structure can look very profitable with a high likelihood (with risk) whereas the value of the hedged position be flat (without risk) Limitations of mathematical modelling The PRDC market is one sided. All banks are hedging the same long dated vol positions. Supply/demand effects determine the shape of the long dated USDJPY smile. This does not respond to USDJPY rate dynamics and poses difficult problems to the mathematical modelling of spot. 18
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