Part 2

1. CTD refers to the cheapest security delivered in a futures contract to a long position to satisfy the contract specifications. If a particular grade was not specified, the seller who holds the short position can identify which instrument will be the cheapest to deliver.

2. Allows to maximize the gain in a Cash & Carry Arbitrage Strategy involving bond futures

3. Is the bond within the deliverable list which has the lowest market price

1. Optimize financial conditions of debt

2. Convert financial conditions of debt

3. Create new synthetic assets

4. Hedge bond or other against any change of the yield curve

Compute:

100 - P = ex: 0,3% < 0,4% (Euribor future < forward bid rate)

Then:

1. borrow for 90 days

2. lend for 180 days

3. sell expensive 3M Euribor Future contract with delivery in 90 days

The implied repo rate refers to the rate of return that can be earned by simultaniously selling a bond future contract & then buying that actual bond of equal amount in the cash market using debt.

Computation:

If financing rate < implied repo rate = Cash & Carry Arbitrage Opportunity

Actions:

1. t0: buy CTD (cheapest to deliver) bond in the cash market & sell future contract (eurobond), finance through repo market

2. tT: settle future position by delivering bonds & settle the financing

1. No-arbitrage models are calibrated to fit the observed term structure of interest rates (TSIR), using the yield curve as an input.

2. Equilibrium models derive the short-term interest rate based on economic assumptions, then generate the yield curve as an output.

A Forward Rate Agreement (FRA) that:

• Starts in 3 months

• Ends in 6 months

• Covers a 3-month interest period (months 3–6)

• Used to lock in a future interest rate

X

X

1. Tick Size: 0.005 (or 0.005%)

2. Tick Value: €12.50 per contract

1. Tick Size: 0.01 (or 1 basis point)

2. Tick Value: €10 per contract

3. Contract Size (Notional): €100,000

1. Transform floating-rate debt into fixed-rate debt

2. Hedge a portfolio of fixed coupon bonds

3. Benefit from rising interest rates

Implied Rate = 100.00 - Futures Price

Implied Rate = 100.00 - 100.25 = –0.25%

✅ The correct implied rate is –0.25%

1. The current 3-year swap rate is 3% (matches the flat term structure).

2. The swap has positive value to you because you're paying 2.5% (below the current market rate) and receiving floating.

3. The value of the swap:

   -> (Market Rate – Contract Rate) × Notional = X

   -> X / (1+Y) + X/(1+Y)^2 etc.

Allows to increase the macaulay duration of a bond portfolio

1. Investor holds the option to sell (put) the bond back to the issuer at a set price before maturity.

2. Provides downside protection if interest rates rise or the issuer’s credit worsens.

3. Higher price than an equivalent option-free bond due to added value of the put option.

4. Lower yield compared to similar option-free bonds (investors pay for the added flexibility).

5. Less interest rate sensitivity (lower duration) because the price floor reduces downside risk.

Futures Price × Conversion Factor × Notional x #contracts

1. A floor contract is a portfolio of put options on a reference interest rate.

2. It provides a minimum interest rate (the "floor") for the holder.

3. Often used by holders of floating rate assets (e.g., FRNs) to hedge against falling interest rates.

1. A cap contract is a portfolio of call options on a reference interest rate.

2. It sets a maximum interest rate (the "cap") the holder will pay.

3. Often used by borrowers with floating rate debt to hedge against rising interest rates.

1. A payer swaption gives the right to enter a swap paying fixed and receiving floating.

2. Its value is positively related to interest rates — it becomes more valuable as rates rise.

3. It is often used to hedge against rising interest rates, especially by floating-rate borrowers.

1. The value of a CDS increases when the default probability rises.

2. This is because the expected payoff increases, and buyers are willing to pay more for protection.

1. Euro Bund futures are based on 10-year German government bonds

2. Bond prices and yields move in opposite directions

3. Going long Euro Bund futures = you expect interest rates to fall (bond prices to rise)

4. Going short Euro Bund futures = you expect interest rates to rise (bond prices to fall)

False.

Explanation:

In Treasury bond futures contracts (e.g., U.S. Treasury futures), the conversion factor is a number used to adjust the invoice price for different deliverable bonds so that they are fairly compared to a hypothetical 6% coupon bond.

• Conversion factors can be lower than, equal to, or greater than 1, depending on the coupon rate and maturity of the deliverable bond relative to the 6% notional benchmark.

  • If the bond’s coupon is below 6%, the conversion factor is less than 1.

  • If the bond’s coupon is exactly 6%, the conversion factor is 1.

  • If the bond’s coupon is above 6%, the conversion factor is greater than 1

1. 3 months rate for a 90 day euro term deposits of 100.000€

2. Quoted as 100 - implied rate

3. Tick size: 0,005% / Tick value: 12,5€

4. Settled with cash

1. Underlying: 100.000€ Notional of a government bond with 10 years of maturity & 6% coupon rate

2. Quoted in %: Tick size: 0,01% / Tick value: 10€

3. Physical settlement

Structural Models

• Default happens when firm value < debt.

• Based on firm’s balance sheet.

• Default is predictable.

• Strong economic intuition (e.g., Merton model).

Reduced-Form Models

• Default is a random event with a hazard rate.

• Based on market data.

• Default is unpredictable.

• Easier to calibrate (e.g., Jarrow-Turnbull).

Both are arbitrage free interest rate models

• Ho-Lee: dr(t) = θ(t)·dt + σ·dW(t)

• BDT: dr(t) = r(t) · [ θ(t)·dt + σ(t)·dW(t) ]

1. Exposure at default

2. Probability of default

3. Loss given default

1. is positively related with the interest rates

2. may be used to hedge against increases in interest rates

3. A payer swapation may be used as an hedge instrument against the rise of interest rate

1. Is negatively related with the interest rates

2. May be used to hedge against declines in interest rates

3. A receiver swaption may be used as a hedge instrument against the fall of interest rates

allows to transform a floating rate debt into a fixed rate debt

 allows to hedge a portfolio of fixed coupon bonds

Puttable -> higher price

Callable -> lower