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Concepts
Spot rate / Forward rate /
Spot curve / Forward curve /
Yield to maturity /
Expected returns /
Realised returns

Forward pricing model

Description
The Term Structure and Interest Rate Dynamics
1
...
Forward rate : interest eate (as agreed to today) for a loan to be made in some future date
3
...
Maturity
4
...
Yield to maturity : Spot interest rate of a zero-coupon bond with maturity T
6
...
Expected return = Bond yield if:
- Bond is held to maturity
- Coupon and interest payments are made on time and in full
- All coupons are reinvested @ original YTM
7
...

- Change in forward price → future spot rate do not confirm to the forward curve
- Spot rate lower than implied by forward curve → increase forward price
- Spot rate higher than implied by forward curve → decrease forward price

Strategy of riding the yield curve

1
...
Riding the yield curve : purchase bonds with maturities > investment horizon, and sell @ the end of the investment horizon
...
Higher I-spread → higher compensa on

Z-spread

Z-spread : spread, that when added to each spot rate on the spot rate, make PV of bond's CF = Bond's market price

𝑃𝑎𝑦𝑚𝑒𝑛𝑡
𝑃𝑎𝑦𝑚𝑒𝑛𝑡
+
1+𝑆 +𝑍
1+𝑆 +𝑍

+ ⋯+

𝑃𝑎𝑦𝑚𝑒𝑛𝑡 + 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙
= 𝐵𝑜𝑛𝑑 𝑠 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒
1+𝑆 +𝑍

- Assumptions of Z-spread : zero interest rate volatility→ not appropriate to value bonds with embedded op ons

TED spread

TED spread = Interest rate on interbank loans - Interest rate on ST US government debt
- Indication of risk of interbank loans
- Higher TED spread → banks are more likely default on loans ; T-bills are more valuable

LIBOR-OIS spread

OIS : overnight indexed swap
OIS rate reflects the federal funds rate, include minimal counterparty risk
LIBOR-OIS spread = LIBOR rate - OIS rate
LIBOR-OIS rate measure thecredit risk, amd indicate the overall wellbeing of banking system
Low LIBOR-OIS → high liquidity market
High LIBOR-OIS → banks are unwilling to lend, due to creditworthness concerns

Traditional theories of term
structure of interest rates

1
...
Liquidity preference theory : Forward rates = Investors' expectations of future spot rates + Liquidity premium fo exposure to interest rate risk
- Liquidity premium : positively related to maturity
- Implications for yield curve shape :
+ Upward sloping yield curve → (1) future interest rate is expected to rise; or (2) rates are expected to remain, and upward sloping curve is solely due to liquidity premium
+ Downward sloping yield curve → steep fall in ST rate
3
...
Preferred habitat theory : forward rate = expected future spot rate + premium
- Imbalance between supply/demand for funds in a given maturity rate → investors switch from preferred habitats (maturity range) to range with opposite imbalance
- Investors must be compensated for price and/or reinvestment rate risk in the less-than-preferred habitat (borrowers require lower yield; lenders require higher yield)

Modern models of term structure
of interest rates

1
...
Cox-Ingersoll-Ross model : interest rate movements are drivien by choosing between consumption today vs
...
Vasicek model : interest rate should revert to some long-run value

∆𝑟 = 𝑎 × 𝑏 − 𝑟 × ∆𝑡 + 𝜎 × ∆𝑧
- Disadvantage : Vasicek model does not force interest rate to be non-negative
2
...
PV of 2 possible values from the next period
Rules of the process of creating a
binominal interest rate tree

1
...
Knowing 1 forward rate → could compute other forward rate for that period
3
...
Bond's value are calculated
using pathwise valuation approach

Concepts
Embedded options

Relationship between value of
callable/putable bonds, straight
bonds and embedded option

Description
Valuation and Analysis : Bonds with Embedded Options
Embedded option : allow issuer to (1) manage interest rate risk amd/or (2) issue the bonds at attractive coupon rate
1
...
Putable bonds : allow investor to sell the bond back to issuer prior to maturity → investor is long the put op on
3
...
Sinking fund bonds : require issuer to set aside funds periodically to retire the bond

𝑉
𝑉

=𝑉
=𝑉

−𝑉
+𝑉

Value a bond with embedded
options using binominal tree
framework

1
...
Valuing putable bond : Value at any node where the bond is putable = Put price or Computed value if bond is not put, whichever is higher

Effect of volatility on value of
callable/putable bond

Option values are positively related to volatility of their underlying
- ↑ interest rate vola lity → value of call/put op on increase → value of callable bond decreases, value of putable bond increases

Impact of change in level of
- ↓ interest rate → call op on limits upside poten al → value of callable bond rise less rapidly than the value of equivalent straight bond
interest rates on value of callable / - ↑ interest rate → put op on limits downside poten al → value of putable bond fall less rapidly than the value of equivalent straight bond
putable bond
Impact of change in shape of yield - ↑ interest rate → ↓ probability of call op on being in the money → ↓ value of call op on for an upward sloping yield curve
curve on value of callable / putable - ↑ interest rate → ↑ probability of put op on being in the money → ↑ value of put op on for an upward sloping yield curve
bond
Option-adjusted spreads

Option-adjusted spread (OAS) : constant spread added to all one-period rates in the binominal tree, so that the calculated value = Market price of risky bond
Impact of volatility on OAS:
- ↑ vola lity → ↑ Calculated value of call op on ; No impact on straight bond → ↓ Calculated of callable bond → Closer to market price → ↓ OAS
- ↑ vola lity → ↑ Calculated value of put op on ; No impact on straight bond → ↑ Calculated of putable bond → Further to market price → ↑ OAS

Effective duration /
Effective convexity

Effecttive duration : Measure price sensitivity to interest rate changes of bond with embedded option, assumes that CF does change due to change in interest rate
Effective convexity : Explain the change in price that is not explained by duration of bond with embedded option, assume that CF does change due to change in interest rate

𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 =

𝐵𝑉 ∆ − 𝐵𝑉 ∆
2 × 𝐵𝑉 × ∆𝑦

+ 𝐵𝑉 ∆ − 2 × 𝐵𝑉
𝐵𝑉 × ∆𝑦
Method for calculating estimated price if yield change by Δy
- Step 1 : Given assumption about benchmark interest rates, interest volatility, and any calls/puts → calculate OAS for the bond, based on current market price and binominal model
- Step 2 : Impose a parallel shift in the benchmark yield curve by +Δy
- Step 3 : Build a new binominal interest rate tree, using the new yield curve
- Step 4 : Add the OAS (Step 1) to the interest rate tree to get a "modified" tree
- Step 5 : Calculate the new estimated price, if yield change by +Δy, using modified interest rate tree
- Step 6 : Repeat Step 2-5, using parallel rate shift of -Δy
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑐𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 =

Compare effective duration of
callable/putable vs straight bond

One-sided duration

𝐵𝑉

∆𝑦 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑦𝑖𝑒𝑙𝑑
𝐵𝑉 ∆ = 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑝𝑟𝑖𝑐𝑒 𝑖𝑓 𝑦𝑖𝑒𝑙𝑑 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑏𝑦 ∆𝑦
𝐵𝑉 ∆ = 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑝𝑟𝑖𝑐𝑒 𝑖𝑓 𝑦𝑖𝑒𝑙𝑑 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑏𝑦 ∆𝑦
𝐵𝑉 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑜𝑏𝑠𝑒𝑟𝑣𝑒 𝑏𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒

∆

Effective duration (Callable) ≤ effective duration (straight)
Effective duration (Putable) ≤ effective duration (straight)
Effective duration (zero-coupon) ≈ maturity of the bond
Effective duration of fixed-rate bond < Maturity of the bond
Effective duration of floater ≈ years to next reset of interest rate
One-sided durations : durations that apply only when interest rates rise /or fall (applied for bonds with embedded options)
- Call option is at-the-money : One-sided down duration (price change of callable bond when interes rates fall) < One-sided up-duration (price change of callable bond when interest rates
rise)
- Put option is at-the-money : One-sided up duration (price change of putable bond when interest rate rise) < One-sided down-duration (price change of putable bond when interest rate
fall)

Key rate duration (Partial duration) Key rate duration : capture the interest rate sensitivity of a bond to changes in yields of specific benchmark maturities → iden fy the interest rate risk from change in the shape of yield
curve
Process of computing key rate duration : similar to the process of computing effective duration , except that only 1 specific key eate is shifted before the price impact is measured
Observe about key rates:
1
...
Maturity key rate dura on = Effec ve dura on; all other rate dura ons
=0
2
...
Bond with low/zero coupon rate → might have nega ve key rate dura on for horizons other than its maturity
4
...
Higher coupon bonds → more likely to be called → me-to-exercise rate will tend to dominate me-to-maturity rate
6
...
Lower coupon bonds → more likely to be put → me-to-exercise rate will tend to dominate me-to-maturity rate

Compare effective convexity of
Straight bonds : Positive convexity
callable / puttable / straight bonds
- Increase in value of option-free bond when rate falls by X > Decrease in value of option-free bond when rate rises by X
Callable bonds :
- High rates : Callable bond is unlikely to be called → posi ve convexity
- Low rates : Callable bond is more likely to be called → nega ve convexity
Putable bonds : Positive convexity
Value of capped / floored folating
rate bond

Capped floater : straight floater + option to prevent the coupon rate from rising above a specified max
...
rate (floor)
Value of a floored floater = Value of a straigth floater + Value of embedded floor

Convertible bond

Convertible bond : straight bond + right to convert the bond into a fixed number of common shares of the issuer during a specified timeframe (conversion period), at a fixed amount of
money (conversion price)
Conversion value : Value of common stock into which the bond can be converted
Conversion ratio : number of shares received for each bond
Conversion value = Market price of stock × Conversion ratio
Straight value : value of bond it it was not convertible = PV of CF discounted @ required return on a comparable oprion-free issue
Minimum value of a convertible bond : greater of Conversion value and Straight value
Market conversion price : price that the convertible bondholder would effectively for the stock if he bought the bond and immediately converted it

𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑
𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑖𝑐𝑒 =
𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜
Market conversion premium per share : differece betweetn market conversion price and stock's current market price
Market conversion premium = Market conversion price - Market price
Market conversion premium ratio :
𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑒𝑚𝑖𝑢𝑚
𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑟𝑎𝑡𝑖𝑜 =
𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒
Premium over straight value : measure downside risk
...
Cost of downside protection → Reduce upside poten on , due to conversion premium
Compare risk-return characteristic of convertible bond with underlying stock :
- Stock price falls : Return on convertible bonds > Return on stock (floor price = straight value)
- Stock price rises : Return on convertible bonds < Return on stock (due to conversion premium)
- Stock price remain stable : Return on convertible bond might > Return on stock (due to coupon payment)
Fixed income equivalent (Busted convertible) : Price of common stock associated with convertible issue is so low → li le to no effect on conver ble market price → conver ble bond value
= Straight bond value
Common stock equivalent : Stock price is to high → Price of conver ble behaves as it is an equity security

Concepts
Measure of credt risk

Description
Credit Analysis Models
Credit risk : risk associated with losses from the failure of a borrower to make timely payments of interest or principal
- Probability of default : probability that borrower fails to pay interest / repay principal when due
- Loss given default : value a bond investor will lose if issuer defaults
- Recovery rate : % of money received upon default of issuer
Loss given default (%) = 100 - Recovery rate
- Expected loss = probability of default × Loss given default
...
2 adjustments to the expected loss measure:
+ Time value adjustment
+ Risk-neutral probabilities : risk premium
+ Formula : PV of expected loss = Value of risk-free bond - Value of credit-risky bond = Expected loss + Risk premium - Time value discount

Credit spread

Credit spread = YT of credt-risky zero copon bond - YTM of risk-free zero coupon bond

Credit scoring

Credit scoring (for small businesses and individuals) : higher score → be er quality
Characteristics of credit scoring :
- Ordinal rankings
- Not percentile rankings : distribution of credit scoring changes over time
- Do not take into account current economic conditions; do not improve with the economy
- Credit scoring agencies are under pressure from users (lenders) to prioritise stability over time → reduce predic ve accuracy
- Do not take into account differing probabilities of default for different loans taken out by same borrower

Credit ratings

Credit rating (for corporate debt, asset-backed securities, and government and quasi-government debt)
Compensate by:
- Users of credit rating, or
- Issuers → conflict of interest
Strengths of Credit ratings
- Easy to understand
- Stable over time → reduce vola lity of debt markets
Weaknesses of Credit ratings
- Stability in credit ratings comes at expense of reduction in correlation with default probability
- Do not adjust with business cycle
- Conflict of interest in cas of issuer-pay model → less reliable

Structural model

Structural model : based on the structure of company's BS, and rely on insights provided by option pricing theory
Assumptions : assets are financed by equity and a single issue of zero-coupon debt → Value of asset = Value of equity + value of debt
→ Shareholders have a call op on on company's assets, with strike price = face value of debt
- @ Maturity of debt, Value of asset > Face value of debt → excercise call op on to acquire asset, pay off the debt, and keep the residual
- @ Maturity of debt, Value of asset < Face value of debt → call op on is out of money → leave company's assets to debtholders
At time T (maturity of debt):
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 = 𝑀𝑎𝑥 0, 𝐴 − 𝐾
𝐴 = 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑠𝑠𝑒𝑡 @ 𝑡𝑖𝑚𝑒 𝑇
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡 = 𝑀𝑖𝑛 𝐴 , 𝐾
𝐾 = 𝐹𝑎𝑐𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡
→ Owning risky debt = Owning risk-free bond + Short European put op on on Company's assets with strike price of K
→ Value of risky debt = Value of risk-free debt - Value of put op on on company's assets
Valuation of debt :

𝐷 = 𝐴 × 𝑁 −𝑑 + 𝐾 × 𝑒 ×( ) × 𝑁 𝑑
𝐴
1
ln
+ 𝑟 × 𝑇 − 𝑡 + × 𝜎 × (𝑇 − 𝑡)
𝐾
2
𝑑 =
𝜎× 𝑇−𝑡
𝑑 =𝑑 −𝜎× 𝑇−𝑡
Risk measures :

𝑁 −𝑑 ; 𝑁 𝑑 = 𝑐𝑢𝑚𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑛𝑜𝑟𝑚𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝑟 = 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒
𝜎 = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎𝑠𝑠𝑒𝑡 𝑟𝑒𝑡𝑢𝑟𝑛𝑠

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 = 1 − 𝑁 𝑒
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠 = 𝐾 × 𝑁 −𝑒 − 𝐴 × 𝑒 ×
× 𝑁 −𝑒
𝑃𝑉 𝑜𝑓 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠 = 𝐾 × 𝑒 ×( ) × 𝑁 −𝑑 − 𝐴 × 𝑁 −𝑑

Reduced form model

𝐴
1
+ 𝜇 × 𝑇 − 𝑡 + × 𝜎 × (𝑇 − 𝑡)
𝐾
2
𝜎 × (𝑇 − 𝑡)
𝑒 =𝑒 −𝜎× 𝑇−𝑡
𝜇 = 𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑎𝑠𝑠𝑒𝑡𝑠
𝑙𝑛

𝑒 =

Reduced form model : allow input parameters to vary with changing economic conditions
Valuation :
𝐾 = 𝐹𝑎𝑐𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡
𝐾
𝐷 =𝐸
∏
1+𝑟
= 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑝𝑒𝑟𝑎𝑡𝑜𝑟 (𝑆𝑖𝑚𝑖𝑙𝑎𝑟 𝑡𝑜
𝑏𝑢𝑡 𝑡ℎ𝑒 𝑡𝑒𝑟𝑚𝑠 𝑎𝑟𝑒 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑑, 𝑛𝑜𝑡 𝑎𝑑𝑑𝑒𝑑)

𝐸 = 𝐸𝑥𝑝𝑒𝑐𝑡𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑝𝑒𝑟𝑎𝑡𝑜𝑟 𝑢𝑠𝑖𝑛𝑔 𝑟𝑖𝑠𝑘 𝑛𝑒𝑢𝑡𝑟𝑎𝑙 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
𝑟 = 𝑅𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑦𝑒𝑎𝑟 𝑖
Extreme simplified scenario, when probability of default per year and loss given default for a zero-coupon bond are constant
𝐷 =𝐾×𝑒

× × ×(

)

=𝐾×𝑒

× ×(

)

×𝑃

𝜑 = 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
𝛾 = 𝑙𝑜𝑠𝑠 𝑔𝑖𝑣𝑒𝑛 𝑑𝑒𝑓𝑎𝑢𝑙𝑡
𝑃 = 𝑃𝑉 𝑎𝑡 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 $1 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑇

Credit measures :

𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 % 𝑙𝑜𝑠𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 = 𝜑 × 𝛾 = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 × 𝑙𝑜𝑠𝑠 𝑔𝑖𝑣𝑒𝑛 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 %
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑜𝑣𝑒𝑟 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑙𝑖𝑓𝑒 = 1 − 𝑒 ×( )
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠 = 𝐾 × 1 − 𝑒 × ×( )
𝑃𝑉 𝑜𝑓 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠 = 𝐾 × 1 − 𝑒 × ×( ) × 𝑃

Assumptions, strengths and
weaknesses of structural and
reduced form model

Structural model

Reduced form model

Assumptions

- Company's assets are traded @ frictionless arbitrage-free market, with value
at time T has a lognormal distribution
- asset return volatility is assumed to be constant
- Constant risk free rate
- BS structure has only 1 class of simple zero-coupon debt

- Company has zero-coupon bond liability that trades in frictionless and
arbitrage-free market
...
Terminal CF was distributed to holders of different ABS based on pre-specified distribution waterfal

Concepts
Credit Default Swaps

Description
Credit Default Swaps
Credit default swap (CDS) : insurance contract, in which 1 party purchases protection from another party against losses from default of a borrower
Credit event occurs → credit protec on buyer get compensated by creit protec on seller
CDS spread : CDS premium = Credit spread = YTM - LIBOR
Notional principal : Face value of protection
Market standardisation → fixed coupon on CDS : 1% for investment grade ; 5% for high-yield securi es
PV of (CDS spread - Standardised coupon rate) : paid upfront by one of the engaged parties
International Swaps and Derivatives Association (ISDA) : unofficial governing body of the industry, publishes standardised contract terms and conventions to faciliate smooth functioning
of CDS market

Single-name CDS

Reference obligation : the fixed-inome security on which the swap is written
Reference entity : Issuer of the reference obligation
CDS payoff when
(1) reference entity defaults on the reference obligation
(2) reference entity defaults on any other issue that has the same rank or higher
CDS payoff : based on the market value of the Cheapest-to-deliver (CTD) bond with the same seniority as the reference obligation
Cheapest-to-deliver (CTD) : same seniority as the reference obligation, but can be purchased and delivered at lowest cost

Index CDS

Index CDS : cover multiple issuers, take on an exposure to credit riskk of several companies simultaneously
- Protection of each issuer is equal : Notional principal of each entity = Total Notional princpal ÷ Number of entities

Common types of credit event

1
...
Failure to pay : issuer misses a scheduled coupon / principal payment without filing for formal bankruptcy
3
...
Physical delivery

2
...
Probability of default : assume that no default has occurred in the preceding year
CDS
- conditional probability / hazard rate : probability of default given that it has not already occurred
- Credit risk / Cost of protection : proportional to hazard rate
2
...
Coupon rate :
- Premium leg : payment from protection buyer to protection seller
- Protection leg : payment from protection seller to protection buyer in case of a default
Upfront payment = PV of protection leg - PV of premium leg
Upfront premium % = (CDS spread - CDS coupon) × Duration
Valuation after inception

After inception, credit quality of reference entity may change → underlying CDS has non-zero value
Change in value of CDS after inception = Change in spread × Duration × Notional principal
Change in value of CDS after inception (%) = Change in spread (%) × Duration
Credit spreads widen → protec on buyer is short credit risk → profit for protec on buyer
Protection buyer/seller can unwind existing CDS exposure by entering into an offseting transaction
...
Basis trade : exploit the difference in credit spreads between bond market and CDS market
e
...
: Bond interest = LIBOR + 4% ; CDS spread = 3% → Buy bond + CDS protec on → LIBOR + 1% risk-free
2
...
Credit risk of index constituents is priced differently with the index spread
4

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