Question

What is the value of a swap with two years to maturity where SOFR is received and 5% per annum is paid (with semi-annual compounding) every six months on a $1,000,000 notional principal. Assume the OIS rates are 4.1% for all maturities (with continuous compounding).

Answer 1

To calculate the value of the swap, we need to determine the cash flows associated with receiving SOFR and paying 5% per annum with semi-annual compounding. Then, we discount these cash flows using the OIS rates.

Here's the calculation:

1. Determine the semi-annual cash flows:

• Notional Principal: $1,000,000

• Interest Rate Received (SOFR): Variable rate based on market conditions (not provided)

• Interest Rate Paid: 5% per annum, compounded semi-annually

• Maturity: 2 years (4 semi-annual periods)

For each semi-annual period:

• Interest Received: (Notional Principal) x (Interest Rate Received)

• Interest Paid: (Notional Principal) x (Interest Rate Paid) / 2 (since it's semi-annual)

2. Discount the cash flows using the OIS rates:

• OIS Rate: 4.1% for all maturities, continuously compounded

To discount each cash flow, we can use the formula: Discounted Cash Flow = Cash Flow / (1 + OIS Rate)^(number of periods)

3. Calculate the present value of each cash flow and sum them to find the total value of the swap.

Please note that the specific SOFR rate is not provided, so we cannot calculate the exact value of the swap without that information. The calculation above assumes a variable SOFR rate, which would need to be determined based on market conditions.

If you provide the specific SOFR rate, I can assist you in calculating the value of the swap more accurately.