Termination of FX Contracts

CHAPTER 3: FOREIGN EXCHANGE

Extension, Early Take Up and Termination of Forward Contract

An early take up is a situation where the delivery of the foreign currency is brought to an earlier date the the contracted delivery date. The situation arises when the expected cash inflow or outflow is occurring earlier than forward rate contract delivery date. An extension, on the other hand is a situation where the delivery of the foreign currency is extended to a later date, possibily due to extension of payment/receipt date. Termination of a fx contract is simply a cancellation or nullification the previous contract.

In any of the above situation, either party may have to be compensated for any losses arising from such action.

Table 3-8

For the remaining of this chapter, rates in Table 2-2 are used with the assumption that the rates are for value spot (assuming June 17, 2020 is the spot date). The information have been merged to produce Table 3-8 which includes USD rates.

In previous discussion, Table 3-1 assumed that the MYR lending is at the implied MYR rate of 2.34154%, which is the MYR offshore rate. Unfortunately, direct borrowing and lending at the MYR offshore rate is not possible due to regulations imposed by BNM. Lending and borrowing at the offshore rate is only possible through FX swaps and cross currency swaps which will be discussed in Chapter 6.

Locally, the MYR can be lent for one month at 2.65% p.a. (Table 3-8). Instead of lending at the implied rate, the bank can arbitrage and lend at KLIBOR of 2.65%. User can run a simulation using Table 3-1 by changing 'MYR Rate (%)' to see the profitability of the transactions in Table 3-2.

Early Take Up

Table 3-9

Example 3-3

On May 15, 2020, a bank transacted a deal with an importer to sell USD1 million for MYR at the rate of 4.2200 for delivery on Aug 17, 2020. The foreign exchange exposure was covered via a spot deal (value date May 19, 2020) at 4.2000 and the cash fow was managed via a swap transaction at 195 point. Unfortunately, the importer needs to make payment earlier than scheduled and the new date is July 17, 2020. The bank’s original cash flows after eliminating the forward exposure via a FX spot and swap transaction is in Table 3-9.

As an illustration, the swap market prices remains as per Table 3-4. USD/MYR spot rate however, is current trading at 4.1000. How is the new forward rate priced to the importer? Tabled 3-10 is the new cash flow after client requested the change of date. The bank has yet to price the request or manage the cash flow. Cleary, there are cash flow mismatches which have to be resolved and price accordingly. Bear in mind that the original transaction has a profit of MYR500 that falls on Aug 17, 2020. For now, we will ignore the present value of the amount. Let's first manage the cash flows.

Table 3-10

  1. Unwind the forward cash flow from the original swap through a 2M sell-buy swap at 126. Click 'Toggle 1st Step' in the table to see the impact on the cash flow. The USD cash flow on Aug 17 is now gone. But wait!. The MYR 500 cash flow is now gone and replaced by a negative cash flow of 106,900. We will look at that later. Lets look at the next step.
  2. The cash flow occuring on June 17, has to be shifted to match client requirement on July 17. The bank would have to do a 1M sell buy swap at 64, for the purpose. Click 'Toggle 2nd Step' in the table to see the impact on the cash flow.
  3. USD cash flow on July 17 are matched and netted out to be zero. But MYR? The bank has yet to agree on the forward rate to charge the client hence the '??'. But the MYR amount the client needed to pay is the sum of MYR cash flow on July 17 and Aug 17. The total sum will be 4,106,400 + 106,900 = 4,213,300. This will match the cash flow on July 17, hence the bank can charge 4.2133 as the new forward rate.

    We are forgetting two things here:

    1. We forgot that originally the bank was making MYR500, and the amount needed to be included in the calculation.
    2. We didnt do any present value exercise on the MYR106,900 and it has to be extended to the MYR 500 as well.

  4. Total amount owed by the client for the cash flow on Aug 17 is MYR107,400 = 106,900 + 500. Client has to pay the present value of the amount either upfront or incorporate the amount into the forward rate. Lets do this step by step again:
    1. Upfront
      1. Find the present value of 106,900 at 2.70% (2M rate as per table 3-8) and. Lend the amount for 2 months at the same rate. This should nullified remaining cash flow on Aug 17.
      2. Find the present value of 500 at 2.70%. The total sum of (i) and (ii) is the amount that the client should pay upfront.
      3. The new rate for the client can now be 4.1064 (4,106,400/1,000,000) assuming no additional cost is added to the pricing.
    2. Incorporate Into New Forward Rate
      1. Find the one month value of upfront payment in (a) using the 1M rate in Table 3-8. Borrow the amount for one month. This will nullify cash flow on June 17 and add new amount to July 17 MYR cash flows.
      2. The net cash flow on July 17 will be -4,213,550.43. The new forward rate for the client will be 4.2136 (rounded to four decimals)

Lets try to put the above exercise in formula form and see whether the process can be simplified. After a lapse of one month, the client requested an earlier delivery and asking for a new rate. Lets denote time as a subscript as the actual time from current spot. The original contracted fx rate is then denoted by \(f_{2}\) and the new rate will be denoted as \(f_1\) and the spot rate as \(f_0\).

The first step was to reverse the cash flows of \(-f_2\) via a two month swap. The transactions can represented by two transactions \(f_0 \textrm{ and } (p_2 + f_0)\), which represent the first and second leg of the swap, respectively where \(p_2\) is the swap point for the two month period. We now have cash flows on two dates - spot (\(-f_0)\) and forward (\(-f_2 + (p_2 + f_0) \))

The second step was to match client's cash flow requirement and the cash flows has to be brought to the one month period via another swap creating two cash flows - spot (\(f_0\)) and forward \(-(p_1+f_0)\). This nullifies all cash flows on spot date as it netted out the \(-f_0\) MYR flows in step 1

The third step is to discount the cash flow occuring on the second month, including the original profit to the spot date:

\( \begin{align} PV_0 &= \dfrac{[-f_2 + (p_2 + f_0)]FV - 500}{1 + r_2\frac{t_2}{365}}\\ \textrm{where } PV &= \textrm{ present value of the cash flow} \\ FV &= \textrm{the USD amount} \\ r_2 &= \textrm{2M rate} \\ t_2 &= \textrm{number of days} \\ p_2 = \textrm{2M swap point} \end{align} \)

Replacing the formula with values:

\( \begin{align} PV_0 &= \dfrac{[-4.2195 + (0.0126 + 4.10)]\textrm{1,000,000} - 500}{1 + 0.027\frac{61}{365}}\\ &=-106,917.55 \end{align} \)

The amount as the same when we click the 'Toggle Step 3a' button in Table 3-10.

The next step is to bring the calculated \(PV_0\) to the one month cash flow via borrowing at 2.65.

\( \begin{align} PV_1 &= -106,917.55\left(1 + r_1 \frac{t_1}{365}\right)\\ &= -106,917.55\left(1 + 0.0265 \frac{30}{365}\right)\\ &= -107,150.43 \end{align} \)

This is the exact cash flow from clicking 'Toggle Step 3b'. The full formula therefore becomes:

\( \begin{align} f_1 &= (FV(p_1+f_0) + PV_1)/FV \\ &= (p_1+f_0) + \frac{PV_0}{FV} \left(1 + r_1 \frac{t_1}{365}\right) \\ &= (p_1+f_0) + \dfrac{\left(-f_2 + (p_2 + f_0)\right) + \frac{500}{FV}}{1 + r_2\frac{t_2}{365}} \left(1 + r_1 \frac{t_1}{365}\right) \\ \end{align} \)

When the contract is done at a breakeven rate, the formula is simplified slightly to:

\( \begin{align} f_1 &= (p_1+f_0) + \dfrac{\left(-f_2 + (p_2 + f_0)\right) }{1 + r_2\frac{t_2}{365}} \left(1 + r_1 \frac{t_1}{365}\right) \\ &= (p_1+f_0) + \dfrac{-f_2 + (p_2 + f_0) }{1 + r_2\frac{t_2}{365}} \left(1 + r_1 \frac{t_1}{365}\right) \end{align} \)

The formula may not look friendy, but perhaps a bit of description on the formula will clear up the air.

\( \begin{align} p_1+f_0 &= \textrm{1M forward rate}\\ f_2 &= \textrm{original forward rate with client}\\ p_2 + f_0 &= \textrm{2M forward rate}\\ \frac{1}{1 + r_2\frac{t_2}{365}} &= \textrm{discount factor to present value the cash flow to spot date} \\ 1 + r_1\frac{t_1}{365} &= \textrm{factor used to calculate the future value of the cash flow } \end{align} \)

At this juncture it is best to note that the \(f\) can also be seen as the MYR cash flow per USD, which make it easier to use the above formula as exchange rate as well as MYR cash flow for foreign exchange contract. The breakeven general formulation is as below:

\( \begin{align} f_n &= f_{tm} + \dfrac{-f_o + f_{to}}{1 + r_{to}\frac{t_o}{365}} \left(1 + r_{tn} \frac{t_n}{365}\right)\\ \textrm{ where } f_n &= \textrm{ new forward contract rate}\\ f_{tm} &= \textrm{market forward rate for new delivery date}\\ f_{o} &= \textrm{old contracted forward rate}\\ r_{to} &= \textrm{rate from spot date to old contract delivery date}\\ t_{o} &= \textrm{tenor from spot date to old contract delivery date}\\ r_{tn} &= \textrm{rate from spot date to new contract delivery date}\\ t_{n} &= \textrm{tenor from spot date to new contract delivery date}\\ \end{align} \)

Equation 3-3

An extension of a contract follows the same process.

Termination

Termination of a forward contract is simpler. Using the example above:

  1. Follow step 1 in the above example
  2. Sell back the USD at market rate. For simplicity, we are assuming that the spot foregn exchange rate does not change and the same as the rate used for the first leg of the swap i.e. 4.1000. This will clear the cash flows on spot date.
  3. The last step is as per step 3.a above. It is the upfront amount the client has to pay the bank for terminating the contract.