Credit curve and market observables

What you will be able to do

After this lesson, you should be able to:

• classify each quantity in a standard CDS valuation as market-observed, contractual, conventional, or model-solved;
• explain why the traded upfront alone is enough to determine the pricing hazard rate, and why that is a consequence of risk-neutral pricing rather than an extra assumption;
• read a credit curve as tenor marks together with the survival curve fitted to them, and tell a change of quotation from a curve fit;
• calculate the survival probability implied by fitted hazard segments and check that a tenor reprices to its mark.

A traded price is an expectation

The risk-neutral lesson established that, in an arbitrage-free model with the cash account as numeraire, a claim’s present-value is the expectation under the risk-neutral-probability-measure $\explain{risk-neutral-probability-measure}{\mathbb{Q}}$ of its discounted payoff; see (1.7.2). Shreve states the general discounted-payoff formula [1].

A CDS is such a claim. Let the local cds-buyer-discounted-cash-flows $\explain{cds-buyer-discounted-cash-flows}{\Pi^{\mathrm{buyer}}}$ be the random sum of the protection buyer’s discounted signed cash flows over the life of the contract, before any upfront amount. It is the protection received at the modeled default time minus the scheduled and accrued premium paid. Each cash flow is discounted from its own payment time to valuation-time $0$. The present value of the CDS is the risk-neutral expectation of this sum:

$$\explain{present-value}{PV_0} =\explain{expectation}{\mathbb{E}}^{\explain{risk-neutral-probability-measure}{\mathbb{Q}}}\!\left[\explain{cds-buyer-discounted-cash-flows}{\Pi^{\mathrm{buyer}}}\right]$$

(7.3.1)

Now add the one fact that the market gives. A new standard contract is traded at its market upfront amount: the buyer pays the cds-upfront-amount $\explain{cds-upfront-amount}{U_0}$ at time zero and receives the claim valued by (7.3.1). A trade at the market level has zero present value at inception. So the upfront amount equals the present value:

$$\explain{cds-upfront-amount}{U_0} =\explain{expectation}{\mathbb{E}}^{\explain{risk-neutral-probability-measure}{\mathbb{Q}}}\!\left[\explain{cds-buyer-discounted-cash-flows}{\Pi^{\mathrm{buyer}}}\right] =\explain{cds-protection-leg-present-value}{PV_0^{\mathrm{prot}}} -\explain{cds-premium-leg-present-value}{PV_0^{\mathrm{prem}}}$$

(7.3.2)

The second equality follows from the linearity of expectation: the expectations of the protection cash flows and of the premium cash flows are calculated separately. They are the two positive leg present values of the preceding lessons. Equation (7.3.2) is the same identity as (7.2.2), read in the other direction. In the preceding lesson, the model parameters were inputs and the upfront was the output. Here, the upfront is observed, and the equation constrains the model.

Why one equality is enough. The standard contract has no cash flow at inception other than the upfront amount. So the trade gives exactly one number. In the model of this course, discounting and recovery are deterministic, and both legs are linear expectations over the default time. So the only unknown in (7.3.2) is the timing of default under the pricing measure: the survival-probability curve. Setting the expected values of the two legs equal, with the upfront amount on the premium side, is therefore not a modeling choice added to risk-neutral pricing. It is what risk-neutral pricing says about a contract that has just been traded at the market level. Tuckman and Serrat describe the market convention in these steps. First, find the hazard rate that makes the expected discounted fee leg and contingent leg (in this course, the premium leg and the protection leg) equal. Then value the standard coupon at that hazard rate [2].

One number determines one unknown. With a single flat Constant hazard rate $\explain{hazard-rate}{\lambda}$ per contract, as in the preceding lesson, one traded price is exactly enough. With a term structure of hazard rates, one traded price per tenor is exactly enough only if the curve has one free parameter per tenor. The piecewise-constant curve below has this property. With fewer prices than parameters, the curve is under-determined, and a convention must fix the remaining parameters. With more prices than parameters, the curve can in general only fit the prices approximately (a best fit).

What the market shows, the model assumes, and the model solves

If every quantity is called an input, it is not clear which quantities the market can contradict. Table 7.3.1 classifies the quantities of a standard contract at one tenor.

Table 7.3.1Observed, contractual, convention, and solved quantities. Each quantity of a standard contract at one tenor: whether the market shows it, the contract fixes it, a convention assumes it, or the model solves it, and where it comes from.

Quantity	Status	Where it comes from
Signed upfront $\explain{cds-upfront-amount}{U_0}$, or the cds-market-standard-quote it stands for	Observed	Dealer bid and offer for the standard contract; a mid is taken as the mark. [3]
Risk-free discount-factor $\explain{discount-factor}{D(0,t)}$	Observed in another market, then an input	Built from the rates market, not from the CDS; the converter takes it as a discount input. [4]
cds-standard-coupon $\explain{cds-standard-coupon}{c_{\mathrm{std}}}$, cds-notional $\explain{cds-notional}{N}$, maturity, credit events, reference obligations	Contractual	Written into the standard contract; the coupon is 100 or 500 basis points and maturities fall on standard dates. [5] [6]
recovery-rate $\explain{recovery-rate}{R}$ and hence loss-given-default $\explain{loss-given-default}{\mathrm{LGD}}$	Convention	Assumed by the converter, commonly 40% but 20% or 25% for some contract types. It is not observed in the quote. [7]
Shape of the hazard rate between and beyond tenors, accrual treatment	Convention	The converter’s single flat hazard rate, or this lesson’s piecewise-constant curve. [8]
Constant hazard rate $\explain{hazard-rate}{\lambda}$, the survival curve, the cds-par-spread $\explain{cds-par-spread}{s^{\star}}$, the other quotation	Solved	Root of (7.3.2) given everything above. [9]

The risk-neutral interpretation has two consequences.

• The solved probabilities are pricing weights. Hull describes implying default probabilities from CDS quotes as the analogue of implying volatilities from option prices. Hull states that CDS valuation needs risk-neutral, not real-world, default probabilities [10]. A survival curve fitted to quotes is a statement about prices, not a forecast of default frequencies. Tuckman and Serrat make the same point for the price-implied hazard rate [11].
• Recovery must be assumed because one price cannot identify two unknowns. The protection payoff is proportional to $\explain{loss-given-default}{\mathrm{LGD}}$, and the implied hazard rate is approximately proportional to $1/\explain{loss-given-default}{\mathrm{LGD}}$. So a contract valued with the same recovery rate that implied its hazard rate is not very sensitive to the choice of recovery rate. A binary CDS, whose payoff does not depend on recovery, would add the second equation needed to separate the two [12].

The credit curve is two objects

A discount curve is a set of dated discount factors in one currency and on one funding basis; it is not one yield (see the rates lesson). A credit curve is the same idea for one reference entity. But a credit curve has two layers, and this course keeps them separate.

The marked curve. Use the local cds-tenor-index $\explain{cds-tenor-index}{k}$ across the cds-tenor-count $\explain{cds-tenor-count}{K}$ quoted tenors with maturities $\explain{cds-tenor-maturity}{T_1}<\cdots<\explain{cds-tenor-maturity}{T_{\explain{cds-tenor-count}{K}}}$. At each tenor, the market shows the price of the standard contract. A mark is the recorded price at one tenor. If the trading desk records the price as a conventional spread, the mark is the local cds-tenor-quote $\explain{cds-tenor-quote}{s_{\explain{cds-tenor-index}{k}}}$. If the desk records the traded price itself, the mark is the local cds-tenor-upfront-fraction $\explain{cds-tenor-upfront-fraction}{u_{\explain{cds-tenor-index}{k}}}$. This course calls a curve whose marks are market-standard quotes an MSQ-marked curve, and one whose marks are upfront fractions an upfront-marked curve. Both labels are local to this course (NEEDS_SOURCE: the desk vocabulary for marking conventions is not documented in the registered sources). Tuckman and Serrat tabulate five-year spreads for several reference entities. They also plot the term structure of spreads across tenors: its slope is normally upward, but it is inverted in periods of stress [13]. Hull lists the tenors that commonly trade; the five-year tenor is the most liquid [14].

The fitted curve. The legs lesson allows a deterministic time-varying hazard rate. It shows that the survival probability is the exponential of minus the integral of the hazard rate. The fitted credit curve is the special case in which the hazard rate is constant on each segment between consecutive tenors: the local cds-segment-hazard-rate $\explain{cds-segment-hazard-rate}{\lambda_{\explain{cds-tenor-index}{k}}}$ on $(\explain{cds-tenor-maturity}{T_{\explain{cds-tenor-index}{k}-1}},\explain{cds-tenor-maturity}{T_k}]$, with $\explain{cds-tenor-maturity}{T_0}=0$. The survival probability is then a product with one factor per segment:

$$\explain{survival-probability}{S^{\explain{risk-neutral-probability-measure}{\mathbb{Q}}}(0,\explain{cds-tenor-maturity}{T_k})} =\explain{survival-probability}{S^{\explain{risk-neutral-probability-measure}{\mathbb{Q}}}(0,T_{\explain{cds-tenor-index}{k}-1})} \exp\!\left(-\explain{cds-segment-hazard-rate}{\lambda_k} \left(\explain{cds-tenor-maturity}{T_k}-\explain{cds-tenor-maturity}{T_{\explain{cds-tenor-index}{k}-1}}\right)\right), \qquad \explain{survival-probability}{S^{\explain{risk-neutral-probability-measure}{\mathbb{Q}}}(0,0)}=1$$

(7.3.3)

Inside a segment, the survival probability decreases at the constant hazard rate of that segment, as in the constant-hazard lesson. Hull notes that when spreads for different maturities are available, the hazard rate is calculated as a step function [15].

The marked curve is data. The fitted curve is a model object, chosen so that the model reprices the data. The next distinction depends on keeping the two layers separate.

Transforming marks is not fitting the curve

Curve transformation changes the quotation of each mark and does not build a term structure. For each tenor separately, the standard converter takes $\explain{cds-tenor-quote}{s_{\explain{cds-tenor-index}{k}}}$ and solves for a flat hazard rate for that tenor alone. This course writes this rate as the local cds-flat-tenor-hazard-rate $\explain{cds-flat-tenor-hazard-rate}{\lambda^{\mathrm{flat}}_{\explain{cds-tenor-index}{k}}}$. The converter then values the fixed coupon at that rate and returns $\explain{cds-tenor-upfront-fraction}{u_{\explain{cds-tenor-index}{k}}}$. The converter can also do the same steps in the reverse direction. This is the conversion of the preceding lesson, applied once per tenor [16]. The flat hazard rates of different tenors are solutions of separate equations. They are not one survival curve, and the official converter itself distinguishes its single flat hazard rate from a term structure [17]. The same tenor-by-tenor conversion also gives a third quotation: the par spread of a hypothetical zero-upfront contract. The name curve transformation belongs to this course (NEEDS_SOURCE for the phrase itself).

Fitting the curve finds one term structure that reprices every mark at once. With the marks written as upfront fractions, the fit condition at tenor $\explain{cds-tenor-index}{k}$ is the buyer-value identity (7.3.2), evaluated with the segment hazard rates up to $\explain{cds-tenor-index}{k}$:

$$\explain{cds-protection-leg-present-value}{PV_0^{\mathrm{prot}}} \!\left(\explain{cds-tenor-maturity}{T_k}; \explain{cds-segment-hazard-rate}{\explain{hazard-rate}{\lambda}_1},\ldots, \explain{cds-segment-hazard-rate}{\lambda_k}\right) -\explain{cds-standard-coupon}{c_{\mathrm{std}}} \explain{cds-notional}{N} \explain{cds-premium-annuity}{A_0^{\mathrm{prem}}} \!\left(\explain{cds-tenor-maturity}{T_k}; \explain{cds-segment-hazard-rate}{\explain{hazard-rate}{\lambda}_1},\ldots, \explain{cds-segment-hazard-rate}{\lambda_k}\right) =\explain{cds-tenor-upfront-fraction}{u_k}\, \explain{cds-notional}{N}$$

(7.3.4)

Both legs are the exact default-time integrals of the legs lesson, with the piecewise-constant hazard rate substituted. Each premium period lies inside one segment. So each period is a one-period flat-hazard model that starts from the survival probability and the discount factor at the start of the period. Solve (7.3.4) in maturity order. The first tenor determines $\explain{hazard-rate}{\lambda}_1$. Then $\explain{hazard-rate}{\lambda}_1$ is held fixed, and the second tenor determines $\explain{hazard-rate}{\lambda}_2$, and so on. Each step is a one-dimensional root solve for $\explain{cds-segment-hazard-rate}{\lambda_{\explain{cds-tenor-index}{k}}}$. The buyer value of a contract increases with the hazard rate of any segment inside the life of the contract, so each step has at most one root. A zero-upfront par mark is the special case $\explain{cds-tenor-upfront-fraction}{u_{\explain{cds-tenor-index}{k}}}=0$, with the coupon set to the quoted par spread. The result is a curve under which every quoted tenor reprices exactly. The survival probabilities of this curve at all tenors are consistent with each other.

The same survival curve then prices every other contract on the same reference entity: a maturity between the quoted tenors, an existing contract with a different coupon, or a hypothetical zero-upfront contract. This is the purpose of a fitted curve. The fit has two limits. First, the fitted par spread at a tenor is in general not equal to the MSQ mark of that tenor. The reason is that the fitted premium annuity differs from the flat annuity of the converter, although both reprice the same traded upfront amount. This is the “par spread from another curve” point of the preceding lesson. Second, a solution need not exist. A later mark that is cheaper than the zero-hazard value implied by the earlier segments would need a negative $\explain{cds-segment-hazard-rate}{\lambda_{\explain{cds-tenor-index}{k}}}$. The model rejects a negative hazard rate, because a survival probability cannot increase with time.

Example 7.3.1 A credit curve from market marks

Open the set, then follow one MSQ-marked curve through transformation and fit.

Transform the marks

Take an MSQ-marked curve for one reference entity: standard contracts with quarterly premiums and a fixed coupon $\explain{cds-standard-coupon}{c_{\mathrm{std}}}=0.010$ per year (100 basis points per year), continuously compounded risk-free rate 2% per year, recovery $\explain{recovery-rate}{R}=0.40$, and marks $\explain{cds-tenor-quote}{s_1}=0.008$, $\explain{cds-tenor-quote}{s_2}=0.012$, $\explain{cds-tenor-quote}{s_3}=0.016$ at maturities $\explain{cds-tenor-maturity}{T_1}=1$, $\explain{cds-tenor-maturity}{T_2}=3$, $\explain{cds-tenor-maturity}{T_3}=5$ model-years. Notional is USD 10,000,000.

For each tenor separately, the flat converter of the preceding lesson gives:

Tenor $\explain{cds-tenor-index}{k}$	$\explain{cds-tenor-quote}{s_k}\ \text{(bp/yr)}$	$\explain{cds-flat-tenor-hazard-rate}{\lambda^{\mathrm{flat}}_k}$, per yr	Flat $\explain{cds-premium-annuity}{A_0^{\mathrm{prem}}}$, model-yrs	$\explain{cds-tenor-upfront-fraction}{u_k}$	$\explain{cds-upfront-amount}{U_0}$, USD	Flat $\explain{survival-probability}{S(0,\explain{cds-tenor-maturity}{T_k})}$
1	80	0.013300046	0.981077842	−0.001962156	−19,621.56	0.986788009
2	120	0.019950083	2.820140305	0.005640281	56,402.81	0.941905574
3	160	0.026600129	4.449093452	0.026694561	266,945.61	0.875464525

Each row is the conversion of the preceding lesson. For example, at five years, $\explain{cds-tenor-upfront-fraction}{u}_3=4.449093452\times(0.016-0.010)=0.026694561$. The one-year mark is below the coupon, so the buyer receives the upfront amount. The three flat hazard rates are solutions of three separate equations. The last column is not one survival curve: for example, it does not define the survival probability at two years.

Fit the curve

Now fit a piecewise-constant hazard curve to the three upfront fractions in maturity order.

Tenor $\explain{cds-tenor-index}{k}$	Segment, model-yrs	$\explain{cds-segment-hazard-rate}{\lambda_k}$, per yr	Fitted $\explain{survival-probability}{S(0,\explain{cds-tenor-maturity}{T_k})}$	Fitted $\explain{cds-premium-annuity}{A_0^{\mathrm{prem}}}$, model-yrs	Fitted $\explain{cds-protection-leg-present-value}{PV_0^{\mathrm{prot}}}/\explain{cds-notional}{N}$	Fitted $\explain{cds-par-spread}{s^{\star}}\ \text{(bp/yr)}$
1	(0, 1]	0.013300046	0.986788009	0.981077842	0.007848623	80.0000
2	(1, 3]	0.023463765	0.941550234	2.829254583	0.033932826	119.9356
3	(3, 5]	0.037572831	0.873389867	4.500220799	0.071696769	159.3183

Every tenor reprices. For example, at five years, $0.071696769-0.010\times4.500220799=0.026694561=\explain{cds-tenor-upfront-fraction}{u}_3$. In the tested implementation, the residuals at all three tenors are below $10^{-12}$.

Compare this table with the transformation. The hazard rate of the first segment equals the one-year flat rate, because a one-year contract depends only on the first segment. The hazard rates of the later segments are higher than the flat rates. The five-year flat rate, 0.026600, is an average over five years. The fitted hazard rate on the last two years is 0.037573, because the shorter tenors, with lower hazard rates, already price the earlier years. So the fitted five-year survival probability, 0.873390, is below the flat survival probability, 0.875465. The fitted par spreads at three and five years, 119.94 and 159.32 basis points, are not equal to the marks of 120 and 160 basis points. The reason is that the fitted curve reproduces the same traded upfront amounts with different premium annuities.

The fitted curve also defines the survival probability between tenors. By (7.3.3), the survival probability at two years is $0.986788009\exp(-0.023463765\times1)=0.963903771$, and at four years it is $0.941550234\exp(-0.037572831\times1)=0.906829881$.

The marks are prices of particular contracts

Now read the same three numbers, 80, 120, and 160 basis points, as zero-upfront par spreads, not as MSQ marks with a coupon of 100 basis points. So $\explain{cds-tenor-upfront-fraction}{u_{\explain{cds-tenor-index}{k}}}=0$, and the coupon of each tenor equals its quote. The fit then gives segment hazard rates of 0.013300046, 0.023480220, and 0.037863368 per year, and a five-year survival probability of 0.872853786 instead of 0.873389867.

The first segment is unchanged, because the converter also treats the one-year MSQ of 80 basis points as the par spread of a zero-upfront one-year contract. The later segments change. A standard contract with a coupon of 100 basis points and an upfront amount is a different stream of cash flows from a zero-upfront contract with a coupon of 120 basis points. The two prices are written with the same number, but they are prices of different contracts. A mark is the price of a particular contract, and the fit must know which contract.

When no curve fits

Suppose the one-year zero-upfront par mark is 300 basis points and the three-year mark is 100 basis points. The first segment prices the one-year contract. Then the three-year contract at 100 basis points is worth more to the seller than the first year alone implies, even with zero default risk after year one. So its mark is below the zero-hazard bound, and the fit reports that the mark would need a negative segment hazard rate. In the tested implementation, a three-year mark of 110 basis points has a solution, with a hazard rate of 0.001573 per year in the second segment.

Steeply inverted marks are not necessarily an arbitrage, but they indicate a problem. Either the marks are out of date or not at market levels, or the piecewise-constant shape and the deterministic recovery of the model cannot describe them.

A note on jargon

The vocabulary of CDS trading desks mixes contract terms, quotation conventions, and risk measures. Table 7.3.2 gives this course’s reading of the most common phrases, with the registered source where one supports it. Entries marked NEEDS_SOURCE are recorded as usage this course adopts locally; a human should confirm or replace them before review.

Table 7.3.2CDS desk jargon. Common phrases of CDS trading desks with this course's reading of each and the registered source that supports it. Entries marked NEEDS_SOURCE are local usage for a human to confirm.

Phrase	Meaning in this course
Reference entity, credit event, notional	The named borrower, the contractually defined trigger, and the amount protected. [18] [19]
Buying protection, selling protection; short credit, long credit	A protection buyer pays premium and gains on default, like a short seller of the bond; a protection seller resembles a bond holder. [20]
Index buyer and seller	For index CDS the words are reversed: the index buyer receives premium and pays on default, like a portfolio holder. [21]
Spread, quoted spread, conventional spread, MSQ	The annualized premium of a hypothetical zero-upfront contract, used as the conventional quote; this course’s local label is market-standard quote. [22] [14]
Par spread	The running spread that makes the two legs equal with zero upfront under a stated curve; see the cds-par-spread card.
Standard coupon, points upfront, price	The fixed 100 or 500 basis point running coupon and the upfront that balances it; the upfront per 100 notional is quoted as points, or as a price of 100 minus points. [23] [24]
Risky annuity, risky duration, RPV01	The premium annuity: the present value of one unit of running spread per unit notional, survival-weighted; Hull calls it the duration of the CDS payments. The label RPV01 is NEEDS_SOURCE. [24]
Risky DV01, spread DV01, CS01	The change in a CDS value for a one basis point change in the CDS spread, found by re-solving the hazard rate and revaluing; the next lesson uses it. The label CS01 is NEEDS_SOURCE. [25]
Duration times spread, DTS	A spread-risk measure for bonds that scales spread duration by the spread level, motivated by spreads moving proportionally. [25]
On-the-run, off-the-run	The most liquid current standard contract of a tenor versus earlier contracts with older maturity dates. [26]
IMM dates, roll	Standard maturity dates on the twentieth of March, June, September, and December; contracts and index series move to new dates on a schedule. [23] [27]
Recovery convention	The assumed recovery in the converter: commonly 40%, with 20% or 25% for some contract types. [7]
Credit curve, spread curve, term structure of spreads	Marks across tenors and the survival curve fitted to them; upward-sloping in calm markets and inverted in stress. [21]
MSQ-marked curve, upfront-marked curve, curve transformation, curve fitting	Local labels defined in this lesson (NEEDS_SOURCE for desk usage).
Equivalent notional, equivalent ratio	The liquid-tenor notional whose quote sensitivity offsets a position, and its ratio to the position notional; defined in the next lesson (NEEDS_SOURCE for desk usage).
CDS-bond basis, negative basis trade	The CDS spread minus a bond spread measure; a negative basis trade buys the bond and buys protection. [28] [29]
CDS-equivalent bond spread, hazard-adjusted duration	The CDS spread corresponding to the hazard rate that reprices a bond, and a bond duration computed under the hazard model. [30]
Cheapest-to-deliver, auction, final price	The delivery option among reference obligations and the ISDA auction that sets the cash-settlement value. [31] [22]
Index, series, CDX and iTraxx	Standard portfolios of single-name CDS, re-formed twice a year into numbered series. [32] [33]
Binary CDS	A CDS paying a fixed amount on default, independent of recovery. [10]
Jump-to-default, JTD	The loss on an immediate default of the reference entity, as opposed to the loss from a spread move; the next lesson computes one. The label is NEEDS_SOURCE.
Clearing	Offsetting cleared trades cancel at the central counterparty; uncleared offsetting trades leave two contracts in force. [34] [35]

Check your understanding

The assessment separates the observed-versus-solved classification, the transformation-versus-fit distinction, and the survival and repricing arithmetic of a fitted curve. Each competency has direct and transfer evidence.

Knowledge check 7.3.1 Credit curve and market observables

1. DirectQuestion 1Not answered

2. TransferQuestion 2Not answered

3. DirectQuestion 3Not answered

4. TransferQuestion 4Not answered

5. DirectQuestion 5Not answered

6. TransferQuestion 6Not answered

Model boundary and review note

This AI-assisted lesson and all cited locators remain draft pending human editorial and quantitative review. All input values are invented for teaching. The fitted curve is piecewise constant with knots at quoted tenors, extended flat, under one deterministic discount rate, one deterministic recovery rate, and exact default-time accrual on a regular model-year schedule. A production curve also handles calendar schedules, day counts, business-day rules, settlement timing, accrued premium at inception, an interpolation and extrapolation policy chosen by the trading desk, and a discount curve built from the rates market. The lesson does not model bid-offer, liquidity, dealer inventory, stochastic rates or intensity, recovery risk, counterparty risk, collateral, funding, or transaction costs, and it makes no claim that pricing-model survival probabilities forecast realized defaults.

References

1. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models (2004). Ch. 5 §5.2.4, printed pp. 218-219, eqs. 5.2.29-5.2.31. draft ↩
2. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.6, printed pp. 368-370. draft ↩
3. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.1, printed p. 549 (market-maker bid and offer in basis points per year). draft ↩
4. International Swaps and Derivatives Association, ISDA CDS Standard Model and Standard CDS Contract Converter Specification. Standard CDS Contract Converter Specification, version May 5, 2009, Functionality and Specification, printed p. 1. https://www.cdsmodel.com/documentation.html draft ↩
5. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.6, printed pp. 366-367 (standard maturity dates on the twentieth of March, June, September, and December; 100 or 500 basis point coupons with a market-determined upfront). draft ↩
6. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.4, printed p. 556 (a coupon and a recovery rate are specified for each underlying and maturity). draft ↩
7. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.6, printed p. 368, n. 15. draft ↩
8. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.6, printed p. 370 (the quote-to-upfront translation is a convention like price and yield; participants need not believe in constant hazard or a particular recovery, but all use the convention). draft ↩
9. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.4, printed pp. 556-557 (a hazard rate is implied from the quoted spread by iterative search). draft ↩
10. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.2, printed p. 554. draft ↩
11. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.7, printed p. 371. draft ↩
12. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.2, printed pp. 554-555. draft ↩
13. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.5, printed pp. 362-363, Table 14.9 and Figure 14.5. draft ↩
14. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.1, printed p. 549. draft ↩
15. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.2, printed p. 554, n. 6. draft ↩
16. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.4, printed pp. 556-557. draft ↩
17. International Swaps and Derivatives Association, ISDA CDS Standard Model and Standard CDS Contract Converter Specification. Standard CDS Examples, version October 26, 2012, printed p. 2 (the converter uses a single flat hazard rate rather than a term structure of flat spreads). https://www.cdsmodel.com/documentation.html draft ↩
18. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.1, printed pp. 548-549. draft ↩
19. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.5, printed p. 361. draft ↩
20. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.5, printed pp. 364-365. draft ↩
21. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.5, printed p. 363. draft ↩
22. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.5, printed p. 362. draft ↩
23. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.6, printed p. 366. draft ↩
24. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.4, printed p. 557. draft ↩
25. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.10, printed p. 379. draft ↩
26. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.6, printed pp. 366-367. draft ↩
27. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.3, printed pp. 555-556. draft ↩
28. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.8, printed pp. 374-375. draft ↩
29. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.1, printed pp. 550-551. draft ↩
30. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.7, printed p. 371; §14.9, printed p. 377. draft ↩
31. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.1, printed pp. 549 and 551. draft ↩
32. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.5, printed p. 363; §14.13, printed p. 387. draft ↩
33. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.3, printed p. 555. draft ↩
34. Tuckman & Serrat, Fixed Income Securities: Tools for Today's Markets (4th ed., 2022). Ch. 14 §14.6, printed p. 367, n. 14. draft ↩
35. Hull, Options, Futures, and Other Derivatives (8th ed., 2012). Ch. 24 §24.1, printed p. 550. draft ↩