# How do banks hedge their FX TARF trades?

How do banks hedge their Target Redemption Forward trades?

• How effective are these hedges?
• How profitable are TARFs from the selling side ?

Hedging works similar to any other derivative.

That said, there exist a lot of variations (Pivot, Chooser, Dual / Triple currency, conditional, knock-in, ...) and pricing is quite intricate and usually done via a stochastic local vol model and mostly via Monte Carlo simulation.

Therefore, Greeks require a fair bit of attention to detail. While the logic is always the same (bump and reprice), what this actually means becomes less clear the more you think about it. The phrase “while holding all other variables constant” is clear in Black Scholes with the actual mathematical derivative but a lot more subtle in case of complex models.

Depending on the implementation, it will likely be based on a finite-difference solver of the PDE or Monte Carlo (MC) simulation of the SDE. However, calibration in these models frequently involve several steps.

One usually distinguishes between Model Greeks and Market Greeks. In terms of bump and reprice slang: Market Greeks are classic bump market and reprice methodology (usually requires recalibration but if you have complex calibrations, often only parts like the LV model and some steps in SV are recalibrated), while model Greeks are done via bump model parameters and reprice. If you have MC, you will have to regenerate the paths.

Bump size also matters. If you have recalibration, there will be errors. MC paths will add some more noise. In simple Black Scholes logic, you can bump and reprice in literally almost infinitesimally small steps to get arbitrarily close to the closed form Greeks. In reality, you have the tradeoff between having a bump that is too big and captures second order effects, or to small and is just influenced by noise.

These Greeks are usually aggregated, bucketed and some less obvious ones like Rega and Sega are often computed alongside. However, if the pricing engine works well and hedging is done properly, these hedges will be accurate and reliable.

In terms of profitability, I don't think anyone can answer that question for the sell side as a whole because there is no transparency for these OTC trades. However, thinking of a simple TARF, which knocks out once a certain profit level is reached, while having unlimited leveraged downside for the buyer, makes it clear that these setups usually favor the seller (in my experience most of the time the favourable forward is the reason to enter such a strategy, say buy EUR at 1.05 instead of the fair forward of 1.1).

• Wow thanks for the detailed answer. So the hedge is mainly calls / puts with different strikes ? What about these more complicated tarfs (with pivots/ dual strike/ Multi currency / stop loss ...) do you need more than vanillas to hedge those ? Commented May 27 at 23:33

Import TARFS are to first order a strip of up and out calls (with the barrier at the strike + target profit) funded by selling a strip of up and out puts (with the same barrier). So if you have a decent model and hedging strategy for simple barrier options you are most of the way there to pricing and hedging traditional TARFS. It also shows the risk for the buy-side, as you have limit upside profit potential funded by taken unlimited downside potential.

• Pretty much sums up what I wrote in a much more concise way. Commented May 27 at 20:05
• Thanks for your answer!! So the hedge is mainly calls / puts with different strikes ? What about these more complicated tarfs (with pivots/ dual strike/ Multi currency / stop loss ...) do you need more than vanillas and barriers as a hedge ? Commented May 27 at 23:34