SOPHIE Daddy Quant Blog - Stock & Options Analysis

1. Foundational Intuition

The fundamental transfer of credit risk: Deconstructing the insurance-derivative hybrid.

The Bilateral Payout Mechanism

A Credit Default Swap (CDS) is a derivative that separates credit risk from a loan or bond. It involves two parties: the Protection Buyer (who pays a spread) and the Protection Seller (who assumes the risk).

Reference Entity

The corporation or sovereign whose credit is being tracked. Note the Entity is the name, while the Obligation is the specific bond used to determine seniority.

Insurable Interest

Unlike insurance, CDS do not require the buyer to suffer a "loss." This allows for Long/Short Credit strategies, where a trader can profit from a company's demise without owning their debt.

ISDA Credit Events

Bankruptcy

Entity becomes insolvent or liquidates.

Failure to Pay

Entity misses a payment after grace periods.

Restructuring

Terms changed (interest, principal, maturity).

Obligation Default

Another debt triggers a default clause.

Repudiation

Sovereign denies the validity of debt.

Acceleration

Debt becomes due immediately.

2. Pricing and Valuation

The mathematical architecture: Solving the 'Credit Triangle' through hazard rates.

The Hazard Rate and Survival

CDS valuation relies on modeling Hazard Rates (\lambda), the instantaneous probability of default given survival. This allows us to construct the Survival Probability curve (P(t)).

P(t) = e^{-\int_0^t \lambda(u) du}

Market spreads are "bootstrapped" to find the sequence of hazard rates that satisfy the zero-NPV condition.

The Premium Leg

The PV of periodic spread payments, conditional on survival.

PV_{Prem} = s \sum \Delta t_i D(t_i) P(t_i)

The Protection Leg

The PV of the contingent payout (1-R) upon default.

PV_{Prot} = (1-R) \int_0^T D(t) dP(t)

The Credit Triangle Simplification

For "napkin math," traders use the Credit Triangle relationship. For a flat curve and low default probability, the fair spread (s) simplifies to:

s \approx \lambda \times (1 - R)

Spread

Hazard Rate

Loss Given Default

Institutional Note: The Z-spread on a cash bond should theoretically equal the CDS spread. The difference between them is the Basis.

Basis = CDS \, Spread - Cash \, Z\text{-}Spread

3. The Big Bang Protocol

Evolution of the market: From bespoke contracts to standardized clearing and auction logic.

Standardization & Upfronts

Before 2009, CDS traded with "Par Spreads" (coupons that made NPV=0). Post-Big Bang, coupons are fixed at 100bps or 500bps to facilitate Trade Compression and Central Clearing.

Settlement Logic (Post-2009)

The Cash Gap:

PUF \approx (s_{mkt} - Coupon) \times RD

The difference is paid as a cash lump sum at inception, called Points Upfront.

Settlement Direction:

If mkt spread > couponBuyer Pays

If mkt spread < couponSeller Pays

Credit Event Auctions

To handle massive volumes of CDS during a default (like Lehman Brothers), ISDA introduced the Auction mechanism. Market participants submit bond bids to find a "Final Price." The CDS payout is simply 100 - Final \, Price, avoiding the physical delivery of scarce bonds.

4. Risk Sensitivities (CS01)

Mastering the Greeks: Quantifying spread risk, term structure, and the convexity of default.

CS01 & Risky Duration

CS01 (Credit Spread 01) is the dollar change in NPV for a 1bp shift in the credit spread. It is fundamentally linked to Risky Duration (RD), which is the sensitivity of the Premium Leg to the spread.

CS01 = \frac{PV(s + 1bp) - PV(s - 1bp)}{2}

For safe entities (Low Spreads), RD is high (e.g., 4.8 for 5Y maturity).

For distressed entities (High Spreads), RD collapses because the contract is likely to end early.

Bucketed Credit Exposure

Bucket1Y

Bucket3Y

Bucket5Y

Bucket7Y

Bucket10Y

By bumping individual tenors, traders manage Curve Risk (steepening/flattening) rather than just parallel shifts.

Credit Convexity (Negative Gamma)

CDS are non-linear. Credit Gamma measures the change in CS01 as spreads move.

\Gamma = \frac{\partial^2 NPV}{\partial s^2}

For a protection seller, the contract displays Negative Gamma. As spreads widen, your losses accelerate, but as they approach infinity, the loss per basis point (CS01) actually shrinks as the payout becomes certain.

CRITICAL: This means that a linear CS01 model will under-estimate losses in the initial stage of widening and over-estimate them as the name approaches default.

5. Precise Estimation

The professional's toolkit: Estimating P&L and risk profiles on the fly.

Manual Risk Estimation

Calculating CS01 without a pricing engine requires estimating the Risky Duration (RD), which is the sensitivity of the annuity to the spread.

Risky Duration Estimate

RD ≈ 4.7 (for 5Y IG)

CS01 Valuation

CS01 = N \times RD \times 10^{-4}

Where $10^{-4}$ represents 1bp (0.01%).

Recovery ($R$) Sensitivity

Recovery defaults to 40%. Changing it affects the Hazard Rate bootstrapped from the spread.

Low Recovery ⇒ High Hazard Rate ⇒ Short RD ⇒ Low CS01
High Recovery ⇒ Low Hazard Rate ⇒ Long RD ⇒ High CS01

6. Stress Testing Logic

Tail-risk quantification: Evaluating the portfolio's breaking points.

Tiered Stress Testing

Professional desks use three tiers of stress testing to ensure they can survive a systemic or idiosyncratic credit crash.

Tier 1: Linear Stress (Parallel)

A "Systemic Widening" shock (e.g., +200bps). This is a 1st order estimate used for daily risk reporting.

Linear Logic

Loss \approx CS01 \times \Delta s

Convexity Effect

Note: This over-estimates losses for sellers in extreme shocks because it ignores the payout cap.

Tier 2: Jump-to-Default

Assumes an instantaneous credit event. This removes all probability modeling and calculates the actual cash payout.

JTD = N(1 - R) - MTM

Ultimate Worst-Case Loss

Tier 3: Recovery Shock

In a crisis, Wrong-Way Risk occurs: spreads widen and Recovery rates drop simultaneously (e.g., 40% → 15%).

This "Double Whammy" stress captures the systemic nature of credit cycles where assets and recovery values correlate to the downside.

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