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## Editorial

Financial product innovation in FX markets has slowed down enormously in the second decade. The big innovation for treasurers in the first decade was the target redemption forward, which has now become a standard range of products trading on bank platforms. The main product innovation in the recent years is a tender-linked FX forward or FX contingent forward ordeal-contingent forward. It serves as a deal-contingent FX hedge. And even that isn’t actually a novelty. Our team at MathFinance has gathered some thoughts and information about this type of product, which I would like to share today.

An example could look like this: the sell-side enters a forward contract at zero cost maturing at time T. We are looking for the forward rate. The buy-side has the right at time t≤T to exit the forward contract at zero cost, if the M&A transaction specified contractually is disapproved by the cartel authority, which statistically happens with a probability p of about 5%. The key idea is that the client can establish an FX hedge for a future foreign exchange transaction, which he can call off, if he doesn’t need it anymore if he proves that the underlying business will not take place (tender is lost). If a client trades a standard FX forward, then she would have to exchange currencies at time T no matter what happens.

Midland Bank offered this many years ago, and called it “tender to contract”. I don’t think the valuation was anything more than a scribble on paper, which doesn’t help answer your question. Obviously you need to build a portfolio of these deals for it to work for the bank.

We will now try to analyze the value of such a contract and assume the product works as follows: Assuming the contractual forward rate is f’ in the currency pair FOR/DOM. At time T the bank pays f’ units of DOM to the client in exchange for 1 unit of FOR.

At some time t an event − non-market-linked loss of tender − can occur with a probability of 5%. In case of this event, the client has the right at time t to cancel the forward contract described above. We need to determine f’ so that the contract has an initial value of zero.

For now let us assume, that the time t is fixed in the contract, i.e., the cartel authority will publish its decision at a known time t.

Let us also consider first the case, where the probability is one. The client has the right to cancel the forward at time t. The product can be structured as a portfolio comprising

• a forward Fwd(f’, T) with pre-agreed exchange rat f’ and delivery in T and
• a Put(f’, t, T) with strike f’, maturity t, and deferred physical delivery in T.

In case the client exercises the option, the payoff of the put will cancel the cash-flows from the forward. The forward rate f’ can be found by solving PV( Fwd(f’, T) ) + PV( Put(f’, t, T) ) == 0 for f’, where PV is the present value at deal inception.

Now the event is said to occur with probability 5%. If we consider a lottery or pure betting scenario, one can think about determining f’ such that the expected value PV( Fwd(f’ ,T) ) + PV( I_{TenderLost} × Put(f’, t, T) ) is zero, where I_{TenderLost} denotes the indicator of the event of the lost tender, which takes the value 1 if the tender is lost and zero otherwise. Assuming the loss of the tender is independent of the FX rate, one could solve for f’ in PV( Fwd(f’, T) ) + 5%× PV( Put(f’, t, T) ) == 0. This approach would work if the bank takes an insurance-risk approach to the problem, i.e. trades many similar tender-linked deals and banks on the law of large numbers with a P&L distribution centered at zero.

But within a traditional hedging and risk-neutral pricing set up, of if tender-linked forwards trade rarely, the bank still has to be hedged as in the case of the probability being 100%. The event can occur, the bank has no way to hedge this risk, and then the client can cancel the forward.

Of course, in this case the contract with a f’ determined by solving PV( Fwd(f’, T) ) + 100% × PV( Put(f’, t, T)  == 0 is likely to look unattractive for the client. One could propose the following improvement for the client: In case that the tender is not lost, the client receives a rebate, which is the Put(f’, t, T).

More generally, in case that the decision time t is not known in advance, but is within some interval [t1, t2] one could make a worst case consideration, as one would do for time options/flexi forwards.

A detailed analysis can be found in a paper by Liede. There is also an example in my book on FX Options and Structured Products.

Let’s conclude with an example of a deal that could have happened in September 2018:

1. On 01 October 2018, a US-based company is told that he is the winning bidder on an asset in Canada.
1. Winning bid price is 500M CAD.
2. The company is in the US, have US funding and therefore has a long USD/CAD position
2. The deal will not reach financial closing until 01 Feb 2019.
1. There is a high probability that the deal will close – approximately 98% certain
3. The company wants to hedge his FX exposure.
1. It wants to lock in its exposure now (on 01 Oct 2018), it does not want any risk, and it is comfortable giving away upside in order to protect its downside.
2. On the rare chance (2%) that the deal falls apart, the company cannot under any circumstance have any costs, i.e. if there is no deal, the treasurer of the company has no place to put his expenses of unwinding a potentially underwater FX hedge.
4. A tender-linked forward as a hedge would assure:
1. The company fixes its USD/CAD rate f’ now (01 Oct 2018) for settlement on 01 Feb 2019.
2. If the deal happens, then this rate is assured.
3. If the deal falls apart, the company has no exposure – the hedge is ripped up and thrown away.

Your job for the weekend: determine the forward rate f’ that you think the banks offered. Obviously the answer will depend on you assumptions about the USD/CAD spot reference and how you handle the non-complete market situation: worst-case assumption vs. insurance-type risk. The good news is that the tender-linked forward appears to be a product a treasurer can actually use, and both Q- and P-quants could have a go at this.

Feedback and more hints on literature you can find is most appreciated, as there are not many publications for this product.

Uwe Wystup

Managing Director of MathFinance

Literature:

Jari Liede: Hedging contingent foreign currency exposures. Helsinki University of Technology, Systems Analysis Laboratory.

Uwe Wystup: FX Options and Structured Forwards, 2ndEdition. Wiley 2017.

## Upcoming Events

FX EXOTIC OPTIONS IN FRANKFURT 2018
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Lecturer: Prof. Dr. Uwe Wystup

This advanced practical three-day course covers the pricing, hedging and application of FX exotics for use in trading, risk management, financial engineering and structured products.

FX exotics are becoming increasingly commonplace in today’s capital markets. The objective of this workshop is to develop a solid understanding of the current exotic currency derivatives used in international treasury management. This will give participants the mathematical and practical background necessary to deal with all the products on the market.

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The special topics are Rough volatility and Long term investments. Minicourses will be delivered by Paolo Guasoni (Dublin City University) and Jim Gatheral (The City University of New York). Special invited lectures by René Aïd (Université Paris-Dauphine), Jean-Philippe Bouchaud (Capital Fund Management and Académie des Sciences) and Stéphane Crépey (Université d’Évry). Four short lectures complete the programme.