How TARF Profit Caps and Knockouts Accumulate

# TARF - cumulative profit and knocking out


# TARF - cumulative profit and knocking out












Was reading a blog post on using a dupire local vol model to price TARFs. It's not a product i'm familar with, so i've been trying to work some examples for fun to understand how they work.

They key feature, as I understand it, is that the TARF comes with an "off-market" strike, but is subject to a "profit cap", and knocks out when reached.

It all seems fairly straightforward at first glance but there is one basic question which I'm genuinely not sure i've understood correctly.

When the cash flows are determined on the various settlement days, is it only the sum of positive pay-offs that are compared to the knock out cap? or is it the sum of all payments? Put differently, if the TARF is close to knocking out, but then on the next settlement a large loss is registered, is the TARF now less likely to knock out on the next settlement, or is it stuck at it's previous "high watermark"?

Many Thanks

## Answer by AKdemy (score 6, accepted)

https://quant.stackexchange.com/a/80605

Target redemption forwards (TARFs) are a widely used instrument in the FX market, but their variations often make their payoffs complex and not easily understood.

Key Concept:

In the most common TARFs, only positive payoffs contribute towards reaching the target. This can be seen in the Bloomberg screenshot, where I manually entered fixings and a strike rate for simple mental calculation. The tooltip for the field labeled `Accum. ITM` highlights that only Cash accumulated from fixings higher than the Rate counts. The field name itself implies that only in-the-money (ITM) positions are considered. In this case, the accumulated profit of 4 million arises from the two instances where the fixing is 102 and the strike is 100, with 1 million notional value.

If you have access to Bloomberg (with an anywhere license / own fingerprint login), you can access DLIB. It is a great (educational) tool for structured products in general, particularly the BLAN templates, because these show the code for the payoffs. As you can see below, it only accumulates if the value is positive (hence ITM).

```
let tarf (acc, (obs, pay)) = 
    let previous_amount_accum, target_counter, all_flows = acc in
    let spot_fixing = fix(obs, ccy_pair) in
    
    let cond_option = if is_call then spot_fixing - strike else strike - spot_fixing in 
    let this_accumulation = max(cond_option, 0) in  
    let new_amount_accum  = previous_amount_accum + this_accumulation in
```

General Description from a Term Sheet:

A typical term sheet might describe the knockout event like this:

> The Knockout event is triggered when the cumulative in-the-money (ITM) value of the current and previous strips equals the target profit. The ITM value is the difference between the prevailing FX rate and the strike, floored at zero. Once the target is reached, future settlements are canceled, the gains are locked, and you are no longer hedged.

Common Payoff Variations After Target is Hit:







A Broader Understanding of TARFs:

A TARF in general is a lot more than that. I do not think it has been asked frequently here, but TARF payoffs are definitely a common source of confusion with new employees / traders at the places I worked at. Therefore, I think a more detailed explanation might help some.

Fundamentally, a forward contract can be replicated with put and call options, as shown in the chart below. More details are available in this answer.

The core idea of a TARF is to provide a "better" forward rate (strike). To achieve this, the downside is usually leveraged (higher notional).

So far, this was only a one period consideration. A TARF is really a strip of options which ceases to exist (knock out) once a cumulative Target profit is reached. This target caps the upside. If you keep the "unlimited" leveraged downside, you get even cheaper product (more "favourable" strike).

Knock-in TARF

That leveraged downside is obviously a big risk not everyone is willing to take (some are not fully aware of it to be honest). Therefore, it is common to place an EKI (European Knock-in), meaning the OTM leverage side has to knock-in before it is "live. If the product has not reached the accumulation cap at the fixing:

- If fixing > rate, then the buyer of the TARF buys the ITM notional at the rate.

- If barrier < fixing < rate, there is not settlement.

- If fixing < barrier, then the buyer of the TARF buys the OTM notional at the rate

Dual Strike Tarf

Instead of a EKI, you can have separate ITM and OTM strikes. If the product has not reached the accumulation cap at the fixing:

- If fixing > upper rate, then the buyer of the TARF buys the ITM notional at the upper rate.

- If lower rate < fixing < upper rate, then there is no settlement.

- If fixing < lower rate, then rthe buyer of the TARF buys the OTM notional at the lower rate

PIVOT Tarf:

A Pivot TARF acts like a standard TARF unless the pivot rate is breached. After this, the structure reverses. Therefore, there are three levels for this structure: lower rate, pivot rate, and upper rate (in ascending order).

If the product has not reached the accumulation cap at the fixing:

- If fixing < lower rate, then the buyer of the TARF buys the OTM notional at the lower rate.

- If lower rate < fixing < pivot rate, then the buyer of the TARF buys the ITM notional at the lower rate.

- If pivot rate < fixing < upper rate, then the buyer of the TARF sells the ITM notional at the upper rate.

- If fixing > upper rate, then the buyer of the TARF sells the OTM notional at the upper rate.

In a chart (somewhat sloppy, due to time constraints), this looks like as follows:

Looking at the DLIB Template, you can see that it is indeed 4 legs put together, and plenty of choices on top of the ones mentioned so far.

In essence, the PIVOT TARF accumulates towards the target when spot is between the upper and lower level: these gains, relative to the pivot rate, are cumulative towards "Targ. (Cash)." or Targ. (Big Fig). The latter is something that confuses most people who are not working with FX frequently. In the OVML example with USDJPY from above, you can see that 25 Mio JPY in Cash are just 25 Big fig. The DLIB deal is using a EURUSD with settlement in Cash DOM. The deal manually was set to reach the target immediately.

That is why the pricing engine states the Model is Deterministic (it was already hit and all payoffs are known). The Call strike is 0.8 and the fixing was set (manually) to 1, which means we breached the 0.1 target (1-0.8 = 0.2). We get a capped payment, meaning 0.1*ITM Notional = 40000. However, in USD that is 40000/K = 50.000, which is what is displayed in the Cashflows section of DLIB.

Variations of the (PIVOT) TARF:

As can be seen in the DLIB Template, there are lots of possible variations.

The regular barriers in the customized Payoff section are creating the PIVOT TARF payoff. You can set separate strikes for each leg, separate barriers (Up & Out, Down & Out, Up & In, Down & In), continuous vs discrete barriers, global barriers, barrier rebates, use several possible targets (Big figure, cash, counter etc), include the other leg(s) in the ITM (or OTM) target, collars, ...

Exotic TARFs

Since TARFs are not exotic enough (it seems), you can trade numerous types. Some are for example:

- Individual KO (one / several legs remain active if one / several others KO)

- Callable and Putable TARFs





- Dual (Triple) currency (Pivot) Chooser TARFs: For example, on each settlement date, if EURUSD performance < GBPUSD performance, client sells EURUSD at EURUSD strike, else client buys GBPUSD at GBPUSD strike where performance is frequently defined as `(EURUSD Strike - EURUSD Spot Fix)/EURUSD strike` or `GBPUSD Spot - GBPUSD Strike)/GBPUSD Strike.`



Side remark with regards to pricing. LV will not be a useful model for these type of options. As long as its a single underlying SLV should be fine, provided it is calibrated to barrier options. Once you try to price Chooser TARFs you will get quickly into the realm of a good tweet I stumbled upon some time ago. Many people tend to think if a tool gives a price it works (here Monte Carlo Local Vol). However, that is classic GIGO.

TARFs and Autocallables are so popular because they seem to offer great deals. However, there is no such thing as free money and the better it seems, the worse the potential downside will be.

Disclaimer: Parts of the definitions are taken from the help page of Bloomberg DLIB and OVML.

## Answer by Felix (score 2)

https://quant.stackexchange.com/a/80594

Practically, there are two types of the sum of positive gain,

1/ Full Gain, at the KO day, you could take all the positive gains;

2/ Capped Gain, at the KO day, you could only take the positive gain capped;

Per the positive gain pre-decided, you could be showed as big figures (pips) or real amount.

Apart from the sum of positive gain as target, we also have the count of positive gain occurrences as target, say 3 times positive gain will be KO, whatever the real amount of gain is.