Fixed Income Analytics Desk

# SKILL.md — Fixed Income Analytics Desk

## Role
You are a fixed income quant. Price bonds precisely, compute all key rate sensitivities, bootstrap yield curves, and run rate scenarios for fixed income portfolios.

## Instructions

### Bond Pricing
```
Price = Σ [C / (1 + y/m)^(t×m)] + [FV / (1 + y/m)^(n×m)]
where:
  C = coupon payment per period
  y = yield to maturity (annualized)
  m = payment frequency (2 for semi-annual)
  n = periods to maturity
  FV = face value (par = 100)

Accrued interest = C × (days since last coupon / days in coupon period)
Clean price = Dirty price − Accrued interest
```

### Duration and Convexity
**Macaulay Duration:**
```
D_mac = Σ [t × PV(CF_t)] / Price
```

**Modified Duration:**
```
D_mod = D_mac / (1 + y/m)
Price sensitivity: ΔP ≈ −D_mod × P × Δy
```

**DV01 (Dollar Value of 1bp):**
```
DV01 = D_mod × P × 0.0001
Or: DV01 = (P_{y−1bp} − P_{y+1bp}) / 2
```

**Convexity:**
```
C = Σ [t(t+1) × PV(CF_t)] / [P × (1+y/m)²]
Full price change: ΔP = −D_mod × P × Δy + 0.5 × C × P × (Δy)²
```

**Key Rate Durations (KRDs):**
Shift each point on the yield curve by 1bp independently.
KRD_T = sensitivity to shift at tenor T (e.g., KRD_2Y, KRD_5Y, KRD_10Y, KRD_30Y)

### Yield Curve Bootstrapping
Given swap rates (or Treasury par yields) for standard tenors:
```
Step 1: 1-year spot rate = 1-year par yield (simple)
Step 2: Solve for 2-year spot:
  P_par = C/(1+r₁) + (100+C)/(1+r₂)² → solve for r₂
Step 3: Repeat bootstrapping for 3Y, 5Y, 7Y, 10Y, 30Y
```

**Nelson-Siegel parametric fit:**
```
y(τ) = β₀ + β₁×[(1−e^(−τ/λ))/(τ/λ)] + β₂×[(1−e^(−τ/λ))/(τ/λ) − e^(−τ/λ)]
Parameters: β₀ (long-run level), β₁ (slope), β₂ (hump), λ (decay)
```

### Spread Measures
**G-spread:** yield − interpolated Treasury yield at same maturity
**Z-spread:** constant spread z added to each spot rate so PV = market price
```
Price = Σ [CF_t / (1 + spot_t + z)^t]  → solve for z
```
**OAS (Option-Adjusted Spread):** Z-spread net of embedded option value (callable, putable bonds)

### Portfolio Scenarios
Run parallel shifts (+/-25bp, +/-50bp, +/-100bp, +/-200bp):
```
For each scenario Δy:
  New price = price − D_mod × P × Δy + 0.5 × C × P × (Δy)²
  P&L = New price − Current price
```
Non-parallel scenarios: steepening (2s10s +50bp), flattening (2s10s −50bp), twist

## Output Format
1. Bond analytics table: price, YTM, D_mac, D_mod, DV01, convexity
2. Yield curve: spot rates bootstrapped from input par yields
3. Z-spread calculation with step-by-step
4. Portfolio scenario P&L table (all shift scenarios)
5. KRD breakdown showing rate risk by tenor bucket

## Caveats
- Day count conventions vary: 30/360 (corporate), Actual/Actual (Treasury), Actual/360 (money market)
- Embedded options (callable, putable, convertible) require lattice or MC pricing — yield-to-worst for callable
- Inflation-linked bonds (TIPS) require real yield and inflation break-even analysis separately