## FX Tarn

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*FinPricing provides valuation tools for the following FX products:*

- FX TARN
- FX Target Redemption Forward
- Check FinPricing valuation models

1. FX TARN Introduction |

The term of “TARN” represents “Target Accumulated Redemption Notes”. In general, a TARN is a (structured) coupon bond which will be compulsively terminated (or canceled) once the accumulated coupon reaches or exceeds a pre-determined barrier

If structured coupons in a TARN are functions of one or multiple currency exchange rates, then the TARN is called a foreign (currency) exchange (FX) rate TARN, or simply an FX TARN. Particularly, if structured coupons are functions of a given single exchange rate, it is then called a single-FX TARN. Or, if structured coupons are functions of given two exchange rates, it is thus called a double-FX TARN. The so-called FX Chooser TARN is a special case of double-FX TARN.

A so-called FX TARN swap is a structured swap contract with a regular funding leg and a structured leg in which coupons are defined as the same as in the corresponding FX TARN. Moreover, the swap has a mandatory termination once the accumulated structured coupon, which is exactly the same as in the FX TARN, reaches or exceeds a pre-determined barrier

The term of “PRDT” represents “Power Reverse Dual Currency Triggered” notes. The coupon structure of a PRDT notes is the same as the one of an FX TARN except that the notes will be terminated once a pre-determined FX-index breaches a given barrier.

Similarly, a so-called PRDT swap is a structured swap contract with a regular funding leg and a structured leg in which coupons are defined as the same as in the corresponding PRDT notes. Moreover, the swap has a mandatory termination once the FX-index, which is exactly the same as in the PRDT notes, breaches a pre-determined barrier.

2. Pricing FX TARN |

We consider FX TARN/PRDT swaps with following restrictions. (1) Structured coupons are linked to a single-FX rate or double-FX rates; (2) structured coupons are piece-wise affine-linear with respect to FX rates; and (3) the swap is not callable before its maturity.

The FX TARN/PRDT swap is a “special” cap-floor FX-swap which will be terminated immediately after either, for a TARN, an accumulated coupon (amount) reaches or exceeds a target or, for a PRDT, an FX-index rate breaches a barrier. The (TARN) target and the (PRDT) barrier are predetermined.

If we set a target or a barrier far enough, the swap becomes virtually a regular cap-floor FX-swap. A regular FX-swap is a swap contract in which coupon rates are linear functions of the FXindex rates. A regular cap-floor FX-swap is an FX-swap in which FX call/put options are embedded in coupon rates.

In fact the FX TARN swap can be decomposed to a regular cap-floor FX-swap and a so-called target redemption part. Similarly, the FX PRDT swap also consists of a regular cap-floor FXswap and a so-called cancelation part. Since the value of a regular cap-floor FX-swap can be calculated analytically, this has been applied to test the valuation approach embedded in the FX TARN/PRDT swap pricing model. Furthermore, we have examined the calculation of the target redemption and the cancelation in a path-wise granularity.

A three-factor and A five-factor hybrid FX log-normal and IR Gaussian HJM dynamic models are respectively used to price the non-callable single-FX TARN, PRDT or TARN/PRDT, and double-FX TARN/PRDT swaps, or more specifically, FX chooser TARN swaps.

The valuation method of Monte Carlo simulation is applied to the dynamic models. In the hybrid models, IR Gaussian HJM term structure sub-models are calibrated to IR swaption markets, while the FX log-normal sub-models are calibrated to FX option markets.

3. Related Topics |