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.
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.
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.
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:
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:
An extension of a contract follows the same process.
Termination of a forward contract is simpler. Using the example above: