Interest Rate Swap Valuation and Applications › Worked Example: Existing Swap Value and Rate Risk

# Swap parameters
swap_details = {
    "notional": 200_000_000,
    "original_rate": 0.050,
    "original_tenor": 10,
    "years_elapsed": 3,
    "remaining_tenor": 7,
}

# Hypothetical continuous-zero curve for the remaining annual schedule
current_curve = {
    "maturities": np.array([1, 2, 3, 4, 5, 6, 7]),
    "zero_rates": np.array([0.038, 0.040, 0.042, 0.044, 0.046, 0.047, 0.048]),
}

# Current annual-pay par rate, computed from the same current zero curve.
current_discounts = np.exp(-current_curve["zero_rates"] * current_curve["maturities"])
current_7y_swap_rate = calculate_par_swap_rate(
    current_discounts, current_curve["maturities"], payment_freq=1.0
)

# Step 1: Value the existing swap
def comprehensive_swap_valuation(swap, curve):
    """
    Complete swap valuation with breakdown.
    """
    N = swap["notional"]
    K = swap["original_rate"]
    remaining = swap["remaining_tenor"]

    maturities = curve["maturities"][:remaining]
    zero_rates = curve["zero_rates"][:remaining]
    discount_factors = np.exp(-zero_rates * maturities)

    # Fixed leg components
    fixed_payments = N * K * np.ones(remaining)  # Annual payments
    pv_fixed_payments = fixed_payments * discount_factors
    pv_notional = N * discount_factors[-1]
    fixed_leg_pv = np.sum(pv_fixed_payments) + pv_notional

    # Floating leg (at par since we're at a reset date)
    floating_leg_pv = N

    # Swap value
    swap_value = fixed_leg_pv - floating_leg_pv

    return {
        "fixed_leg_pv": fixed_leg_pv,
        "floating_leg_pv": floating_leg_pv,
        "swap_value": swap_value,
        "fixed_payments": fixed_payments,
        "discount_factors": discount_factors,
        "pv_fixed_payments": pv_fixed_payments,
    }


valuation = comprehensive_swap_valuation(swap_details, current_curve)

# Step 2: Calculate DV01
def swap_dv01_analysis(swap, curve, bump_size=0.0001):
    """Annual existing-swap risk immediately after the current fixing.

    Keep that observed fixing unchanged under every parallel zero shock.
    bump_size controls the central derivative, normalized back to one bp;
    the displayed +/-1bp and +/-10bp stress scenarios remain fixed.
    """
    N = swap["notional"]
    K = swap["original_rate"]
    remaining = swap["remaining_tenor"]
    if isinstance(remaining, bool) or not isinstance(remaining, int) or remaining <= 0:
        raise ValueError("Use a positive integer number of annual payments.")
    maturities = np.asarray(curve["maturities"], dtype=float)[:remaining]
    zero_rates = np.asarray(curve["zero_rates"], dtype=float)[:remaining]
    if len(maturities) != remaining or len(zero_rates) != remaining:
        raise ValueError("The curve must cover every remaining annual payment.")
    dv01, _, _, _ = calculate_swap_dv01(N, K, maturities, zero_rates, bump=bump_size)
    known_first_fixing = np.expm1(zero_rates[0] * maturities[0])
    scenarios = {}
    for name, shift in [
        ("down_10bp", -0.001),
        ("down_1bp", -0.0001),
        ("base", 0.0),
        ("up_1bp", 0.0001),
        ("up_10bp", 0.001),
    ]:
        discounts = np.exp(-(zero_rates + shift) * maturities)
        fixed_bond = N * (K * np.sum(discounts) + discounts[-1])
        floating_bond = N * (1 + known_first_fixing) * discounts[0]
        scenarios[name] = fixed_bond - floating_bond
    return dv01, scenarios


dv01, scenarios = swap_dv01_analysis(swap_details, current_curve)

# Step 3: Decision analysis
def analyze_unwind_decision(swap_value, dv01, current_rate, original_rate, view):
    """A qualitative receive-fixed risk prompt, not an optimal trading decision.

    No probabilities, holding horizon, carry/roll, execution costs or fund
    liabilities are modeled. Use a matching current par rate as comparator.
    """
    if view not in {"rates_rising", "rates_stable", "rates_falling"}:
        raise ValueError("Use rates_rising, rates_stable or rates_falling.")
    rate_advantage = original_rate - current_rate
    analysis = {
        "current_mtm": swap_value,
        "rate_advantage_bps": rate_advantage * 10000,
        "dv01": dv01,
    }
    if view == "rates_rising":
        analysis["recommendation"] = "DISCUSS REDUCING RATE EXPOSURE"
        analysis["reasoning"] = (
            f"An instantaneous local 1bp parallel rate rise reduces this "
            f"receive-fixed MTM by approximately ${dv01:,.0f}. "
            f"Current MTM is ${swap_value:,.0f}; this is not cumulative profit."
        )
    else:
        analysis["recommendation"] = "REVIEW CARRY, COSTS AND HEDGING OBJECTIVE"
        analysis["reasoning"] = (
            "Same-time flat or downward curve shocks do not imply a future "
            "holding-period return. Compare coupon cash flows, curve roll, "
            "costs and portfolio liabilities before choosing to hold or unwind. "
            f"The contracted fixed coupon is {rate_advantage * 10000:.1f}bp "
            "above the matching current par coupon, not a guaranteed net receipt."
        )
    return analysis


# Assume manager expects rates to rise
decision = analyze_unwind_decision(
    valuation["swap_value"],
    dv01,
    current_7y_swap_rate,
    swap_details["original_rate"],
    "rates_rising",
)