Interest Rate Swap Valuation: Bond Portfolio & FRA Methods

In the previous chapter, we introduced the mechanics of interest rate swaps: the exchange of fixed-rate payments for floating-rate payments between two counterparties. You learned how these instruments work, what drives their use, and the basic terminology that market participants employ. Now we turn to the critical question: how do we determine the value of a swap?

Swap valuation connects present-value calculations to quoting, hedging and synthetic cash-flow construction. This chapter develops the bond and FRA approaches in a stated single-curve model, calibrates a curve to hypothetical par quotes, and applies the results to matched borrowing hedges, synthetic coupons and asset-liability management.

The key insight is that a swap can be decomposed into more fundamental instruments we've already studied. We can view it either as a portfolio of bonds or as a portfolio of forward rate agreements. The bond view groups cash flows by leg; the FRA view groups them by payment period. Under the assumptions below, the two constructions give the same value.

The examples use one curve for both projecting floating payments and discounting them, with no credit adjustment or floating spread. The reset-date examples assume that the current floating fixing matches the forward rate from that curve. Under these assumptions, the bond and FRA valuations agree. Later, we discuss why market pricing may require separate projection and discount curves.

The most intuitive approach to swap valuation treats each leg of the swap as a bond. This perspective builds on our existing knowledge of bond pricing and allows us to value swaps using familiar present value techniques. Consider a plain vanilla interest rate swap from your perspective if you are receiving fixed and paying floating. This position is economically equivalent to:

• Being long a fixed-rate bond (receiving fixed coupon payments)
• Being short a floating-rate bond (making floating-rate payments)

The value of the swap is simply the difference between these two bond values. This decomposition works because the cash flows of the swap exactly replicate the combined cash flows of holding a fixed-rate bond while having borrowed at a floating rate. Understanding this equivalence turns swap valuation from an abstract exercise into a straightforward application of bond mathematics.

The fixed leg of a swap generates a stream of known cash flows, which makes it the more straightforward component to value. Unlike the floating leg, where future payments depend on interest rates that have not yet been determined, the fixed leg's payments are contractually specified at inception. This certainty allows us to apply standard present value techniques directly.

If the swap has a notional principal $N$, a fixed rate $K$, and payment dates at times $t_1, t_2, \ldots, t_n$, we can calculate the present value of the fixed leg by discounting each cash flow back to today. For the bond-portfolio representation, add a hypothetical principal repayment at maturity. The corresponding fixed-rate bond value is:

where:

• $V_{\text{fixed}}$: corresponding fixed-rate bond value, including hypothetical principal
• $K$: fixed interest rate
• $\delta_i$: day count fraction for period $i$
• $N$: notional principal amount
• $Z(0, t_i)$: discount factor from today to time $t_i$
• $t_i$: payment date for period $i$
• $n$: total number of payment periods
• $\sum_{i=1}^{n} K \cdot \delta_i \cdot N \cdot Z(0, t_i)$: present value of the coupon payments
• $N \cdot Z(0, t_n)$: present value of the notional principal repayment

The final term represents the notional principal "repayment" at maturity. Even though no principal exchanges hands in a swap, we include it for the bond equivalence to hold. This might look like an accounting trick, but it's essential: by adding and subtracting the notional principal on both legs, we maintain the mathematical equivalence between the swap and the bond portfolio. The notional terms cancel when we compute the net swap value, but including them allows us to value each leg independently using standard bond pricing formulas.

Recall from our discussion of bond pricing in Part II, Chapter 2 that the discount factor $Z(0, t)$ represents the present value of receiving one dollar at time $t$. These discount factors are derived from the term structure of interest rates and encode all the information we need about the time value of money across different horizons.

The floating leg presents an interesting challenge: we don't know the future floating rates. Future floating coupons are uncertain, so direct cash-flow projection is less straightforward. Replication values them without predicting the realized rates. However, a useful property simplifies the calculation and clarifies how floating-rate instruments behave.

Just after a floating-rate reset, a floating-rate bond trades at par because each future payment will be set to the prevailing market rate. This property is key to understanding floating-rate instruments.

To understand why, consider what happens at a reset date. The floating rate for the upcoming period is set to the current market rate, which by definition represents fair compensation for lending money over that period. At the next reset, the same thing happens: the rate adjusts to whatever the market rate is at that time. Since each coupon payment reflects the market rate at the time it was set, the bond always offers a fair market return. Consequently, investors are willing to pay exactly face value for it, and the bond's value equals its face value at each reset date.

This logic extends to any future reset date as well. Looking forward from today, we know that at each future reset, the bond will be worth par. This recursive property dramatically simplifies our valuation task.

Between reset dates, the corresponding floating-rate bond is worth the present value of the known next coupon plus its par continuation value:

where:

• $V_{\text{float}}$: corresponding floating-rate bond value between resets, including hypothetical principal
• $L_k$: floating rate set for the current period
• $\delta_k$: day count fraction for the current period
• $N$: notional principal
• $Z(0, t_k)$: discount factor to the next payment date $t_k$
• $t_k$: next payment date
• $L_k \cdot \delta_k \cdot N$: the fixed coupon payment for the current period
• $L_k \cdot \delta_k \cdot N + N$: known next coupon plus par continuation value immediately after payment (or principal repayment at final maturity)

The intuition here is straightforward: between reset dates, we know exactly what the next coupon payment will be because the rate has already been fixed. We also know that immediately after that payment, the bond will be worth par because a new rate will be set. Therefore, the current value is simply the present value of the known coupon plus the present value of receiving par at the next reset.

At inception or immediately after a reset, this simplifies to:

where:

• $V_{\text{float}}$: corresponding floating-rate bond value immediately after coupon payment and a matching reset
• $N$: notional principal amount

The floating-rate bond is worth exactly par. This result means that at reset dates, we do not need to forecast any future interest rates to value the floating leg. We simply know it equals the notional amount.

Combining these results, the value of a receive-fixed, pay-floating swap is:

where:

• $V_{\text{swap}}$: total value of the swap
• $V_{\text{fixed}}$: corresponding fixed-rate bond value including hypothetical principal
• $V_{\text{float}}$: corresponding floating-rate bond value including hypothetical principal

At a matching reset in this model, K above the current par swap rate for the same remaining schedule makes the corresponding fixed-rate bond worth more than par and the receive-fixed swap positive. If K is below that matching par rate, the fixed bond is below par and the receive-fixed swap is negative. Do not compare K directly with an arbitrary zero yield.

For a par swap entered without an upfront value premium, choose the fixed rate $K$ so that $V_{\text{swap}}=0$. At that rate, the fixed and floating coupon present values are equal. An off-market coupon can instead have nonzero initial value and an offsetting upfront payment.

Let's implement this valuation approach.

The positive swap value indicates that the fixed rate of 5% is favorable compared to current market rates. The receive-fixed party holds a valuable position because they are locked into receiving a higher rate than what the market currently offers for new swaps.

The key parameters for swap valuation using the bond portfolio approach are fundamental inputs that determine the swap's cash flows and their present values:

• N: Notional principal amount. Used to scale the cash flows, though it is not exchanged in a standard swap. This amount determines the size of each interest payment and is the reference for calculating percentage-based coupon payments.
• K: Fixed interest rate. The rate received by you in the receive-fixed position, contractually determined at inception and remaining constant throughout the swap's life.
• r: Risk-free interest rate. Derived from the discount factors used to value the cash flows. In practice, this comes from the term structure observed in the market.
• $δ_i$: Accrual year fraction for payment period i; the regular semiannual example uses 0.5. Contractual day-count conventions determine coupon amounts, while payment dates determine discounting times. Payments per year is a separate frequency, equal to 2 for regular semiannual dates.

An alternative and equally valid approach views a swap as a series of forward rate agreements. Rather than thinking of the swap as two bonds, we can decompose it into individual exchanges of fixed for floating payments at each payment date. Each payment exchange in the swap can be treated as a separate FRA. This perspective connects swap pricing directly to forward rates, which we discussed in the context of the term structure in Part II, Chapter 3.

The FRA approach offers different insights than the bond approach. While the bond view emphasizes the swap's relationship to fixed income securities, the FRA view highlights how each payment period contributes to the swap's total value. This decomposition is especially useful for analyzing where swap value comes from along the yield curve.

Before applying this to swaps, let's review forward rate agreements and their valuation. A forward rate agreement is a contract to exchange a fixed interest payment for a floating payment at a future date, based on a rate determined at an earlier fixing date. The contract specifies a notional amount, a forward period, and a contracted rate against which the realized floating rate will be compared.

The payoff of a receive-fixed FRA settling at time $T+\delta$ for a period of length $\delta$ starting at $T$ is:

where:

• $\delta$: accrual period length
• $N$: notional principal
• $K$: contracted forward rate
• $L_T$: realized floating rate at time $T$

The payoff is positive when the contracted rate exceeds the realized floating rate, meaning you receive the difference. Conversely, the payoff is negative when the floating rate exceeds the contracted rate.

To determine the present value before settlement, we use the simple-accrual forward rate implied by today's curve. In this single-curve model, $F(0,T,T+\delta)=[Z(0,T)/Z(0,T+\delta)-1]/\delta$. Its expectation interpretation uses the payment-date forward measure, associated with the bond maturing at $T+\delta$, rather than an unqualified physical forecast. For the stated end-of-period payoff, the present value is:

where:

• $V_{\text{FRA}}$: present value of the FRA
• $F(0, T, T+\delta)$: simple-accrual forward rate observed today for the period starting at $T$, with the same accrual fraction as the payoff
• $Z(0, T+\delta)$: discount factor to the payment date
• $T$: start date of the forward period
• $\delta$: accrual period length
• $N$: notional principal
• $K$: contracted forward rate

This formula tells us that the FRA has positive value when the contracted rate $K$ exceeds the market forward rate $F$, and negative value when the market forward rate exceeds the contracted rate.

With the FRA valuation framework established, we can now view the entire swap as a portfolio of these individual contracts. A swap with $n$ payment dates can be decomposed into $n$ forward rate agreements, each corresponding to one payment exchange. The value of the entire swap is the sum of these FRA values:

where:

• $V_{\text{swap}}$: total value of the swap
• $n$: total number of payment dates
• $\delta_i$: day count fraction for period $i$
• $N$: notional principal
• $K$: fixed rate
• $F_i$: forward rate for period $i$ ($F(0, t_{i-1}, t_i)$)
• $Z(0, t_i)$: discount factor for payment at time $t_i$

For a par swap entered without an upfront premium, choose K so that the initial swap value is zero; an off-market coupon can instead require an upfront value adjustment. By setting the swap value to zero and solving for the fixed rate, we can derive the par swap rate. The derivation proceeds as follows:

Solving for $K$:

where:

• $K$: par swap rate
• $n$: number of payment periods
• $F_i$: forward rate for period $i$
• $\delta_i$: day count fraction
• $Z(0, t_i)$: discount factor
• $\sum_{i=1}^{n} \delta_i \cdot F_i \cdot Z(0, t_i)$: present value of the expected floating leg payments per unit of notional
• $\sum_{i=1}^{n} \delta_i \cdot Z(0, t_i)$: annuity factor for payments of $\delta_i$ per unit notional, corresponding to a fixed annual rate of 1

The par swap rate is a weighted average of simple forward rates, with normalized weights proportional to $\delta_i Z(0,t_i)$. For equal accrual fractions and declining discount factors, later periods receive lower weights. Neither that ordering nor a forecast of physical expected short-term rates follows without additional assumptions. In this single-curve model, the floating payments telescope because $\delta_i F_i Z(0,t_i)=Z(0,t_{i-1})-Z(0,t_i)$, with $Z(0,0)=1$.

The example below takes each accrual fraction to equal the difference between its maturity times in years, so the semiannual schedule uses $\delta_i=0.5$. For a contractual day-count convention, use that convention's accrual fraction in the simple-forward conversion and payment calculation; it need not equal the zero curve's time difference.

Both approaches yield the same swap value, confirming their equivalence. The FRA approach provides additional insight by breaking down the swap's value across individual payment periods. This decomposition reveals which parts of the yield curve contribute most to the swap's value and helps you understand the term structure exposure embedded in your positions.

The key parameters for the FRA valuation approach connect swap pricing directly to the forward rate curve and the term structure of interest rates:

• $F_i$: Simple-accrual forward rate for period $i$, implied by the ratio of the endpoint discount factors. Its expectation interpretation depends on the pricing measure; it is not automatically a physical forecast.
• $K$: Fixed rate of the swap. Compared against the forward rate to determine the value of each period. The difference between $K$ and $F_i$ drives each FRA's contribution to the swap value.
• $\delta_i$: Contractual accrual year fraction (day-count fraction). Use the same fraction when annualizing the simple forward and calculating its coupon amount.
• $Z(0, t)$: Discount factor. Used to bring the future FRA payoff back to present value. These factors encode the time value of money embedded in the current term structure.

A par swap curve shows fixed rates for zero-initial-value swaps across maturities under specified contract conventions. Swap quotes are used to calibrate projection and discount curves for valuing interest-rate products. The resulting curves are valuation inputs; par quotes are not zero-coupon discount factors and do not by themselves specify every derivative's risks.

Government bond yields can be affected by supply-demand imbalances, tax considerations, and liquidity preferences. Swap rates also contain more than expectations: their interpretation depends on the projection and discount curves, risk premia, and contract terms. For example, investor demand or central-bank purchases can make particular government bonds trade rich or cheap relative to comparable maturities; above-par or below-par price alone does not establish that effect. The swap curve is particularly important because:

• It provides swap-rate quotes across maturities, often out to 30 years or more; a fitted curve connects those quotes without uniquely identifying expected future short-term rates.
• Swap quotes are inputs to curve calibration. The resulting discount factors, together with appropriate floating-rate projection curves and risk-model inputs, support derivative valuation. A par swap quote is not itself a zero-coupon discount factor, and option valuation also needs assumptions about future rate variability.
• Historically, unsecured IBOR-based swap curves reflected an interbank funding benchmark, including bank credit and liquidity components. RFR-based overnight index swap (OIS) curves instead reference overnight near-risk-free rates and do not generally measure banks' unsecured term borrowing costs (BIS, Beyond LIBOR).
• Liquidity and quote freshness vary by market and tenor. A fitted curve may use interpolation or indicative inputs, so a displayed curve point is not necessarily a fresh executable quote.

Bootstrapping is the process of extracting discount factors from market swap rates. The term "bootstrapping" refers to the iterative nature of the procedure: we use information derived from shorter maturities to solve for discount factors at longer maturities. The technique works iteratively, starting from the shortest maturity and working outward.

For a par swap with maturity $T$ and swap rate $S_T$, the no-arbitrage condition requires that the value of the fixed leg equals the value of the floating leg. In the matching-reset single-curve model, the corresponding floating-rate bond including hypothetical principal is worth 1 per unit notional. A par swap therefore has a corresponding fixed-rate bond worth 1 as well:

where:

• $S_T$: par swap rate for maturity $T$
• $n$: number of payment periods up to maturity $T$
• $\delta_i$: day count fraction for period $i$
• $Z(0, t_i)$: discount factor at coupon date $t_i$. For the explicit last-factor solve, factors with $i<n$ must already be known or fixed by a stated interpolation rule; $t_n=T$ is the new endpoint.
• $Z(0, T)$: discount factor for the final maturity $T$ (the unknown variable)

On a coupon-complete grid, earlier coupon-date discount factors are available from previous steps. Sparse quotes leave unquoted coupon dates: a 5-year annual-pay swap still pays at year 4 even if no 4-year swap is quoted. We therefore specify an interpolation rule and include those dates in the calibration. If their discounts depend on the new endpoint, we solve the full coupon equation for that endpoint.

We can rearrange the no-arbitrage condition to solve explicitly for the unknown discount factor $Z(0, T)$ by separating the final term and isolating $Z(0, T)$:

where:

• $Z(0, T)$: discount factor for maturity $T$
• $S_T$: par swap rate for maturity $T$
• $n$: number of payment periods
• $\delta_i$: day count fraction for period $i$
• $Z(0, t_i)$: known discount factor for time $t_i$
• $\delta_n$: day count fraction for the final period
• $1 - \sum_{i=1}^{n-1} S_T \cdot \delta_i \cdot Z(0, t_i)$: remaining value to be covered by the final payment
• $1 + S_T \cdot \delta_n$: final coupon plus hypothetical principal per unit notional, the coefficient multiplying the final discount factor

The explicit quotient requires $1+S_T\delta_n\ne0$ and a positive solved discount factor. It applies when the earlier coupon factors are fixed inputs. For this sparse-quote example, we instead interpolate continuously compounded zero rates linearly between quoted nodes, keep the first zero rate flat before the first node, and solve each full coupon equation with the trial endpoint included. Integer payment indices generate every regular coupon date. The resulting curve must reprice every input quote using those same conventions. This specifies a model curve; finite quotes do not uniquely determine its values at all other dates.

The key parameters for bootstrapping the swap curve are the inputs and outputs of the iterative procedure that builds the discount function from market data:

• $S_T$: Par swap rate. The market rate observed for a specific maturity, representing the fixed rate at which a new swap would have zero value.
• $Z(0, t)$: Discount factor. The unknown variable being solved for iteratively at each maturity point. These factors encode the present value of future cash flows.
• Maturities: The tenor points of the input swap curve (e.g., 1y, 2y, 5y). Market data is typically available at standard tenors, and interpolation may be needed for intermediate points.
• Zero Rate: The continuously compounded spot rate implied by the discount factor. Calculated as $r = -\ln(Z(0,t))/t$, and gives an alternative representation of the same information contained in the discount factors.

To calculate a par quote for a new swap, find the fixed coupon that makes its initial model value zero under the specified payment, floating-index and discounting conventions. A client can also request an off-market coupon, in which case a nonzero initial value may be offset by an upfront payment. The calculation below uses discount factors to obtain the par coupon in the chapter's single-curve model.

For a par swap at inception, fixed and floating coupon PVs are equal. Equivalently, after adding equal hypothetical principal repayments, the corresponding fixed- and floating-rate bonds both have value N under the matching single-curve reset assumptions.

The calculated rates reprice the hypothetical input quotes using the full annual coupon schedule and the same interpolation policy as calibration. Remaining numerical differences reflect solver and floating-point tolerance. Different contractual schedules require their own payment dates and accrual fractions; changing frequency is a separate calculation, not an explanation for roundoff.

The key parameters for calculating the par swap rate connect the discount function to the fair fixed rate for a new swap:

• $Z(0,t)$: Payment-date discount factors used for the fixed coupon annuity and hypothetical principal in the bond representation; the plain interest-rate swap does not exchange that principal.
• $δ_i$: Contractual accrual year fraction for period i. The example uses a common annual accrual of 1.0, not a payments-per-year parameter.
• $S_{par}$: Fixed coupon rate that equalizes fixed and floating coupon PVs. Equivalently, the corresponding bonds including hypothetical principal are at par, giving zero initial net swap value.

Once a swap is traded, its value can change as interest rates move. A par swap's initial zero value can become positive or negative, but some cash-flow states or curve moves leave it unchanged. Mark-to-market (MTM) valuation calculates the current model value of an existing position. Its applications include:

• Regulatory capital calculations for banks within the applicable framework, which distinguish current counterparty exposure from measures of potential future exposure
• Collateral management under Credit Support Annexes (CSAs), where parties exchange margin based on the current value of their positions
• Profit and loss attribution, where you need to understand how rate movements have affected portfolio value
• Risk management and hedging, where understanding current exposure is essential for making informed decisions about position adjustments

Consider a 5-year receive-fixed swap entered at a rate of 5.5%. After rates change, we need to revalue the swap using current market discount factors. The mechanics are identical to initial valuation: we calculate the present value of the fixed leg and subtract the floating leg value.

In this annual receive-fixed example, a small parallel decline in the current continuous zero rates increases model MTM under the stated fixing convention. This is a model mark, not an executable takeover or unwind quote; actual amounts can differ because of bid-offer spreads, fees and contractual close-out terms.

The key parameters for mark-to-market valuation distinguish between the original contract terms and current market conditions:

• $K_{old}$: The original fixed rate on the swap. This rate was set at inception and remains constant throughout the swap's life, regardless of how market rates move.
• $N$: Notional principal amount. The reference amount used to calculate payment sizes, unchanged from inception.
• $Z_{new}(0, t)$: Current market discount factors. These reflect the new interest rate environment and are used to present-value the remaining cash flows.
• $T_{remaining}$: Remaining time to maturity. Only remaining cash flows are valued; past payments have no effect on current mark-to-market value.

Understanding how swap values respond to rate changes matters for risk management. You need to know how much money could be gained or lost as interest rates fluctuate. The key measures are DV01 (dollar value of a basis point) and swap duration, both of which quantify interest rate sensitivity.

DV01 is the signed local, first-order value sensitivity per one basis point (0.01%) parallel shift in the specified yield curve. It approximates a small value change; finite moves are repriced and can differ because of curvature. Comparisons across positions require the same shock, fixing convention and normalization, or explicit conversion to a common basis. The mathematical definition is:

where:

• $\text{DV01}$: dollar value of a basis point
• $V$: value of the swap
• $y$: yield curve level (interest rate)
• $0.0001$: one basis point scaling factor

The minus sign makes DV01 positive for a position that gains from a small decline in the specified curve. The five-year receive-fixed example below has positive DV01 under its stated curve and fixed-current-coupon convention. That is a property of its remaining cash-flow exposure, not of the receive-fixed label alone. Preserve any already observed floating fixing in rate scenarios.

For a counterexample, take one remaining annual payment with notional $N=100$, fixed rate $K=1\%$, known floating rate $L=5\%$, and discount factor $D=1/1.05$. The net cash flow is $N(K-L)=-4$, so its value is $V=-4D=-3.80952$. A lower continuous zero rate increases $D$ and makes this negative value more negative. With one year remaining, the signed local DV01 is $V\times0.0001=-0.000380952$ per 100 notional.

A par swap has zero net market value, so ordinary modified duration, $-\partial V/\partial y\,/V$, is undefined there. We use a different, explicit reference: notional-normalized rate sensitivity,

This has units of years and does not depend on the position's notional scale. Net dollar sensitivity is fixed-bond sensitivity minus floating-bond sensitivity. In this annual example, the current floating coupon is already fixed, so the corresponding floating bond retains exposure through its next payment. It is not held at par in every shocked scenario. A short time to the next reset can justify a small-floating-duration approximation, but that is a separate stated approximation.

The following examples show how swaps can change borrowing-rate exposure, construct synthetic fixed coupons and adjust a balance sheet's duration gap under stated matching and risk assumptions.

If you have floating-rate debt, you face uncertainty about future interest payments. When rates rise, borrowing costs increase, potentially squeezing profit margins or even threatening solvency. A pay-fixed, receive-floating swap allows you to convert your exposure to fixed-rate debt synthetically. You continue to make floating payments on your original loan but enter a swap to receive floating and pay fixed. The floating index received on the swap offsets the matching index paid on the loan, leaving the fixed swap payment plus the loan's original spread and any fees. This requires matching notionals, index conventions, payment dates and accrual fractions.

Swaps enable the creation of synthetic instruments that may not be available directly in the market. If you own a floating-rate note but desire fixed-rate exposure, you can use a swap to transform the economic characteristics of the asset. Rather than selling the floating-rate note and purchasing a fixed-rate bond, which might involve transaction costs and tax consequences, you can overlay a swap to achieve the desired exposure.

With equal notionals, matching SOFR observation, accrual, reset and payment dates, and both contracts performing, the combined coupon rate is 5.30%: the swap's fixed rate plus the note's spread. This establishes coupon income, not a yield-to-maturity, which also requires the package price and dated redemption cash flows. The issuer exposure remains, and the swap adds counterparty exposure; contractual basis risk can arise if the two contracts' floating-rate terms diverge.

Banks and insurance companies use swaps to manage mismatches between asset and liability duration. For a common parallel-rate shock, let $A$ and $L$ be asset and liability values and $D_A$ and $D_L$ their durations for that same shock. The first-order equity change is $\Delta E\approx-(A D_A-L D_L)\Delta y$. Equity falls for a small rate rise when $A D_A>L D_L$, equivalently when the asset-normalized gap $D_A-(L/A)D_L$ is positive ($A>0$). Raw duration ordering alone does not state this condition. The following example has long-duration mortgages funded by short-duration deposits.

A pay-fixed notional of $1.375 billion reduces the calculated duration gap from 4.93 years to the target of 1.00 year under the assumed 4-year sensitivity magnitude. The swap contributes negative dollar duration, reducing the balance sheet's first-order parallel-rate exposure. The nonzero target leaves residual rate risk; it is not complete immunization.

This worked example combines the bond-portfolio valuation, a matching current par comparator and signed rate-risk analysis for an existing swap. We then identify the additional inputs needed for a hold-or-unwind decision.

Suppose we entered a 10-year receive-fixed swap three years ago at a rate of 5.00%. The current curve's matching seven-year par coupon is below this 5.00% contracted coupon. We need to:

1. Value the existing swap position
2. Calculate the DV01 exposure
3. Discuss the position's conditional rate risk and the additional inputs needed for a hold-or-unwind decision