**Introduction – What is an Interest Rate Swap?**

Imagine you have a loan with a fixed interest rate, meaning you pay the same interest amount every year. Your friend, on the other hand, has a loan with a variable interest rate that changes each year based on market conditions. An interest rate swap is like an agreement where you and your friend decide to swap your interest payments. You agree to pay your friend’s variable interest, and your friend agrees to pay your fixed interest.

Why would you do this? Maybe you believe that variable rates will go down and save you money, while your friend prefers the certainty of fixed payments and avoid any downside risk. This is also the case with companies.

**Vanilla Bond and Interest Rate Swaps**

Now, consider a vanilla bond. This is a simple bond that pays a fixed coupon (interest payment) every period (e.g., year) and returns the principal amount at the end of its term. It does not contain any special provisions or exotic features. Borrowers might use an interest rate swap on this bond to manage their interest rate risk. For example, if they pay variable payment from the bond but think that fixed rates will be more advantageous, they can swap their variable payments for fixed ones.

**The Binomial Pricing Model**

To determine the fair value of such swaps, binomial pricing model can be used. Let’s break down this model into simple terms.

**Two Possible Outcomes**: At each time step (say, each year), the interest rate can either go up or down. This creates a “binomial” tree of possible future rates.**Tree Structure**: Imagine a tree where each branch splits into two more branches, one for the rate going up and one for it going down. Over several years, this tree will have many possible paths the interest rate could take.**Calculating Values**: Starting from the final year and working backward, we calculate the value of the swap for each possible interest rate at each node of the tree. This is done by considering the possible up and down movements and their probabilities.**Discounting Back**: At each node, we take the average of the possible future values and discount it back to the present value using the current interest rate. This process continues until we reach the present day.**Fair value of a swap**: By the time we finish, we have a fair value for the swap today. This helps both parties know what is a fair exchange of payments given the uncertainty of future interest rates. Using Excel’s Solver, we can also modify swap fixed interest rates so that it equals zero value for both buyer and seller at the inception date.

**Practical Tool for Accountants**

Attached is a template designed for the quick calculation of vanilla bond interest rate swap valuation. It contains the following inputs:

- Hedged principal amount
- Swap fixed interest rate (annual)
- Expiration (years)
- Payments settlement date (years; 0 – present period, 1 – present period + 1, etc.); in the template, we assume payment takes place one year in arrears, after the actual interest rates are known. If delay beyond 1 year is expected, then the template would require reworking of formulas with respect to discounting
- Current market interest rate
- Floating rate – up and down movements – the expectation set by the user here should already take into account the actual probabilities.

Probabilities of outcomes in the rows 32:37 are included as 50% for each of the two base movements, but an be adjusted manually as needed. “Floating rate – up and down movements” are already supposed to take into account the actual probabilities.

**Conclusion**

Using the binomial pricing model, borrowers and investors alike can make more informed decisions about engaging in interest rate swaps to manage their risks and potentially save money. For example, if the model shows that variable rates are likely to rise, a fixed-rate payer might benefit from a swap, as they could end up paying less compared to sticking with their fixed payments. Conversely, if variable rates are expected to fall, a fixed-rate receiver (or a variable-rate payer) might benefit from the swap. In summary, an interest rate swap on a vanilla bond allows two parties to exchange interest payments to suit their preferences and risk outlooks. The binomial pricing model helps them determine a fair value for this exchange by considering the many possible future interest rate scenarios. The attached template serves as a resource for quick check on the valuation.