Let's now dive into the technical details of FX swaps to analyze how they react to changes, in FX spot rates and interest rates of the two currencies involved. The best way to do this is by building a simple FX swap valuation model, and we are using the following data and assumptions. A euro US dollar spot rate of 1.095.

A USD six month interest rate of 5.395%.

A euro six month interest rate of 3.754932%.

A forward period of 182 days, a notional of 100 million US dollars, and we assume the trader buys and sells US dollars and an agreed forward rate of 1.10391. Furthermore, we assume actual 360 day count conventions in both currencies. Ignore bid office spreads for simplicity and do not include a phenomenon called the FX basis at this point. We'll build this model step by step. As we know, an FX swap consists of two parts. First, a spot transaction where in our case, USD is bought and euro is sold. And second, a forward transaction where in our case, the same amount of USD is sold and euro is bought back at a predetermined forward rate. Let's begin by calculating the USD cash flows. Since the trader buys 100 million US dollars at spot, the spot cash flow in USD is simply 100 million US dollars. For the forward leg the trader will sell back 100 million US dollars in six months at the agreed forward rate of 1.10391. The undiscounted value of this forward cash flow is 100 million US dollars, meaning the full notional amount is exchanged. However, since the cash flows we want to look at occur at different times, we need to bring them on a consistent basis. And in finance, we usually do this by calculating the present value. And to do this, we need to discount the forward cash flow using the six month USD interest rate of 5.395% over 182 days. To calculate this present value, we divide the forward cash flow by one plus the six month USD interest rate multiplied by the forward days divided by 360.

This results in a present value of approximately 97.34 million US dollars. So the net US dollar cashflow is the spot inflow of 100 million US dollars minus the present value of the forward outflow, which gives us a net result of 2.66 million US dollars. Now let's move on to calculating the euro cash flows.

To buy 100 million US dollars at the spot rate of 1.095, the trader needs to sell 100 million divided by 1.095, which is approximately 91.32 million euro. This is a negative cashflow in euro because euro is being sold. For the forward leg, the trader will receive euro by selling 100 million US dollars at a forward rate of 1.10391. The amount of euro received is 100 million divided by the forward rate of 1.10391, which is approximately 90.59 million euro.

Now we discount this cashflow using the six month euro interest rate of 3.754932% over 182 days. As again, we want to look at everything from a PV perspective. To do so, we divide the forward cash flow by one plus the euro interest rates multiplied by 182 days divided by 360.

This gives us a present value of approximately 88.9 million euro. The net euro cashflow is the spot outflow of 91.32 million, plus the present value of the forward inflow of 88.9 million, which results in a net euro cash flow of negative 2.42 million euro. So that we can calculate the net present value of the entire FX swap in a single unit. We need to express all cash flows in a common currency, and let's use US dollars in our case. This is common practice in financial markets when evaluating cross currency transactions as it simplifies comparisons and decision making by using a single base currency. To convert the net euro cashflow into US dollars, we multiply the net euro amount by the spot rate of 1.095. Which gives us a result of approximately negative 2.66 million US dollars. With both the net US dollar cashflow and the net euro cashflow expressed in US dollars, we can now sum them up.

Since they perfectly offset each other the net present value of the FX swap is zero. This makes sense because we are using market rates and nothing has changed since trade inception. Spot rate forward rate and interest rates remain unchanged. Therefore, at trade inception, the FX swap has an NPV of zero, assuming no bid ask spreads, and no other transaction costs.

Let's now examine how changes in key variables affect the NPV of the FX swap. We'll look at three scenarios, changes in the spot rate, changes in USD interest rates, and changes in euro interest rates.

First, suppose the euro US dollar spot rate increases by one pip to 1.0951 while keeping all other variables constant.

This doesn't affect the USD cash flows or the euro cash flows. Since all these cash flows have already been agreed. However, it does impact the conversion of the net euro cashflow into US dollars. As this now happens at a different rate, this results in a small negative impact of approximately negative 242 US dollars on the swaps NPV. Why does a US dollar weakening cause a negative P&L in this case? At the start of the FX swap, the trader bought US dollars at spot and agreed to sell US dollars forward, effectively creating a small net long position in US dollars. Since the US dollar weakened slightly as indicated by the higher euro US dollar spot rate, the value of this long US dollar position decreased slightly leading to a small loss in the swaps in NPV. This is consistent with the idea that when you buy a currency at spot and sell it forward, any weakening of that currency results in a negative impact.

Next, let's increase the USD six month interest rate by one basis, point to 5.405% while keeping the euro rate and spot rate unchanged.

This leads to a positive impact of approximately 4,791 US dollars on the FX swaps NPV. Why does this happen? The forward leg of the FX swap involve selling US dollars in the future, and we calculate the present value of this cashflow by discounting it using the USD interest rate. When the USD interest rate increases, the discount factor becomes larger, which means the present value of the US dollar cashflow decreases slightly. Since the trader already received 100 million US dollars at spot, the reduction in the present value of the forward US dollar payment results in a higher net US dollar cash flow. This ultimately improves the NPV of the FX swap.

Lastly, let's increase the Euro six month interest rate by one basis, point to 3.764932%, keeping other variables unchanged. This leads to a negative impact of approximately negative 4,829 US dollars on the NPV of the swap. Why does this happen? The forward leg of the FX swap also involves receiving euro in the future, and we calculate the present value of this cash flow by discounting it using the euro interest rate. When the euro interest rate increases, the discount factor becomes larger, which means the present value of the euro cashflow decreases slightly. Since the trader originally sold 91.32 million euro at spot and the present value of what they're receiving in euro is now slightly lower, the net euro cashflow decreases this reduction in the euro cashflow when converted back into US dollars results in a loss, hence the negative NPV impact. To summarize, in the case of buying and selling US dollars in a six month euro US dollar FX swap a weakening of USD, so a higher euro US dollar spot rate leads to a small negative in NPV impact. Because the trader holds a small net long position in US dollars and a short position in Euro and a weaker US dollar reduces the value of that long position. An increase in USD interest rates results in a positive NPV impact because it reduces the present value of the future US dollar payments. Improving the Trader's net position. An increase in euro interest rates results in a negative NPV impact because it reduces the present value of future Euro receipts. Worsening the trader's net position when converted back into US dollars.