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CFA Level II 2020 COPY (552) > Derivatives > Flashcards

Derivatives Flashcards

1
Q

Forward Contracts

A

Long forward position - party that agrees to buy

Short forward - agrees to sell

Typically no money is exchanged upfront

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2
Q

Cash and Carry Arbitrage

Reverse Cash and Carry Arbitrage

A

Cash and Carry: If a forward/future is overpriced you:

sell forward –> borrow money –> buy spot asset

Reverse Cash and Carry: If a forward/future is underprice you:

buy forward –> borrow asset –> sell spot asset –> lend money

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3
Q

Forward Rate agreement (FRA)

A

Purpose: agreement to borrow (long) or lend (short) at a fixed rate in the future

  1. Based on Libor
  2. Being Long = Pay fixed and receive floating
  3. Being Short = Pay floating and received fixed
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4
Q

Credit Risk in Forward Contracts

A
  1. The winner is exposed to the credit risk
  2. Marking-to-market will reduce credit risk (paying up multiple times)
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5
Q

Futures are different from Forward….

A
  1. Futures are marked to market at the end of each day
  2. Futures are traded on exchanges (forwards are private contracts)
  3. Futures are standard, forwards are customized
  4. Futures use a clearing house as the counterparty
  5. Futures contracts are regulated
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6
Q

Futures Contracts Notes

A
  1. Zero sum game. Settle up every day
  2. Futures price will converge to spot price each day
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7
Q

Value of a futures contract

A

current futures price - previous mark-to market price

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8
Q

How Interest Rates affect Forward and Futures

A

If Interest rates and assets are positively correlated

  1. Higher prices for futures (people want futures)
  2. Higher reinvestment rates for gains
  3. Lower borrow costs to fund losses

If interest rates and assets are negatively correlated

  1. Higher price for forwards (people want forwards)
  2. Avoid mark-to-market cash flows

Note: For bonds the short can deliver any treasury bond over 15 years

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9
Q

Net Costs (NC)

A

storage costs - convenience yield

It makes the FP = S0 x (1 + Rf)^T + FV(NC)

FV (NC) = the future costs of holding the asset

This also will make contango occur

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10
Q

Net Benefits (NB)

A

It makes the FP = S0 x (1 + Rf)^T - FV(NB)

FV (NB) = the future benefits of holding the asset

This also will make backwardation occur

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11
Q

Eurodollar Deposits vs T-Bills

A

Eurodollar: U.S. dollar-denominated deposits outside the US

  1. Priced off LIBOR, uses 360 days
  2. Cannot be priced using no arbitrage models (cost and carry)

Eurodollars use ADD-ON interest (borrow $1M then pay back $1M plus interest)

T-Bills are discount instruments (only would borrow 980K)

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12
Q

Types of Options

A

Call: the right to buy an asset

Formula: Max (0, S - X)

Put: the right to sell an asset

Formula: Max (0, X - S)

European option: Can only be exercised at expiration

American option: can be exercised at any time prior to expiration

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13
Q

European Put-Call Parity

A

Formula: C0 + PV(X) = P0 + S0

Left side = fiduciary call

PV(X): zero coupon bond

Right side = protective put

Remember: PV of bond is X / (1 + R)^T

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14
Q

Synthetic call

A

Formula: C0 = P0 + S0 - PV(X)

Breakdown: Long put, long stock, short bond

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15
Q

Synthetic Stock

A

S0 = C0 - P0 + PV(X)

Long call, short put, long bond

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16
Q

Synthetic Put

A

P0 = C0 - S0 + PV(X)

Long call, short stock, long bond

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17
Q

Synthetic Bond

A

PV(X) = P0 - C0 + S0

Long put, short call, long stock

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18
Q

Binomial Model: Calls and Puts

A

Propability of up-move = 1 + Rf - D / U - D

D and U are opposites of each other. Up move of 1.15 means 1/1.15 is a down move of 0.87.

Example: S0 = $30, up factor is 1.15 and Rf = 7%, strike is $30

Step one: Up move is 30 * 1.15 = 34.5
Step two: Down move is 30 * .87 = 26.1
Step three: A call option would be worth $4.50 in the up state and $0 in the down
Step four: Probability of up state = 1.07 - .87 / 1.15 - .87 = 0.0.7143
Step five: C0 = (4.5 * .715) + ($0 * 0.285) = $3.00

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19
Q

Black-Scholes-Mertan Model

A

Only works for European options

Assumptions

  1. Rf and volatility are constant
  2. Markets are frictionless
  3. Underlying asset has no cash flow and is normally distributed

Limitations

  1. Cannot price options on bonds or interest rates
  2. Less useful with taxes and transaction costs
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20
Q

Delta

A

Definition: change in the price of an option for a 1-unit change in the price of the underlying stock (speed)

Call Range from 0-1

Out-of-the-money is closer to 0

In-the-money is closer to 1

Put Range is from -1 to 0

Out-of-the-money is closer to 0

In-the-money is closer to -1

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21
Q

Gamma

A

Definition: rate of change in delta as stock price changes (acceleration)

  1. Largest when option is at-the money and close to expiration
  2. Small for deep in-the-money and deep out-of-the-money options not close to expiration
  3. Low gamma would reduce trading cost
22
Q

Swaps

A
  1. zero at initiation

Swap value: difference in the value of the fixed payments and floating payments

23
Q

Replicating Swaps: Fixed-Rate Side

A

Replicated by:

  1. Issuing fixed rate bonds (match maturity and payment dates)
  2. Using proceeds to purchase floating rate notes at LIBOR
  3. Vpayer = Vfloating - Vfixed

Important:

  1. Bonds have principal payments, swaps DO NOT
24
Q

Replicating Swaps: Off-market FRAs

A
  1. Swap rate is constant
  2. Off-market FRAs have forward rates that do not yield a zero value at initiation
25
Q

How to Replicate an FRA with Options

A

An FRA can be replicated with two options

Long interest rate call + short interest rate put

If rates increase, the call wins. Rates fall the put loses

26
Q

Replicating Swaps: Floating-Rate Side

A

On each settlement date, the value of a floating rate note will always reset to par

Floating coupons are paid in arrears (based on LIBOR at the start)

Example: $100 par value, 3-year annual-pay FRN, and 12-month (forward) LIBOR of 4%, 5%, and 3%

PV = 104 / 1.04 + 105 / 1.05 + 103 / 1.03

27
Q

C Formula

A

C = (1 - Z4) / Z1 + Z2 + Z3 + Z4

Pay attention to the time frame: monthly, quarterly, semi-annually, etc.

28
Q

Z discount factor formula

PV of Payment

A

Each Z is a discount factor

Discount factor: 1 / [1 + ( r * days/360)]

PV of payment: r * (days/360) then Par / (1 + x)

Example: Find the PV of a $100 payment, 180 days away. 5% LIBOR

Step one: .05 * 180/360 = .025

Step two: PV = 100 / (1 + 0.025) = 97.561

29
Q

Valuing a Currency Swap

A

Principal amounts are exchanged at initiation

PV (Euro fixed “bond”) - PV($ fixed “bond”)

Use yield curve for each currency

30
Q

Equity Swaps

A

Equity return payer

Pays any positive return on equity

Receive fixed rate payment plus any negative equity

Fixed-rate payer

Pays fixed rate plus negative equity return

Receives positive equity return

31
Q

Payer Swaption

Receiver Swaption

A

Payer swaption: right to enter swap as fixed-rate payer (wins if rates increase)

Receiver swaption: Right to enter swap as fixed-rate receiver (wins if rates fall)

32
Q

Swaption Uses

A
  1. Hedge anticipated floating rate exposure in the future
  2. Speculate on interest rate changes
  3. Terminate existing swap
33
Q

Swaption Credit Risk

A
  1. Current credit risk: payment due
  2. Potential credit risk: future obligations
  3. Highest in the middle of the life of a swap

Reduce by:

  1. Marking-to-market
  2. Payment netting
34
Q

Caps and Floors

Similar too…..

A

Buyer of cap: benefits when interest rates rise (similar to a call on LIBOR or long put on a bond)

Buyer of a floor: benefits when interest rates decrease (similar to a put on LIBOR or call on a bond)

35
Q

Cap Payoff

A
36
Q

Floor Payoff

A
37
Q

Interest rate collar

Zero-cost collar

A
  1. Interest rate collar: buy a cap and floor over the same time period

Type 1: purchase a cap and sell a floor (makes the cap cheaper)

Type 2: purchase a floor and sell a cap (makes the floor cheaper)

  1. Zero-cost collar: cost of cap purchased = cost of floor sold
38
Q

How Changes in Interest Rates affect Options

A
39
Q

Credit Default Swaps (CDS)

A

Purpose: Insurance contract

If an event occurs the buyer (short credit risk) gets compensated from the seller (long credit risk)

Note: CDS spread: the premium paid

40
Q

Single-Name CDS Payoff for Bonds

A

Formula: Payoff = notional - (% of par * notional)

Payoff on a single-name CDS is based on the cheapest-to-deliver obligation

THINK: Bascially they give back the partial bond for a full one

41
Q

Index CDS

A

Covers multiple issuers and is equally weighted

Formula: Payoff: (notional / # of entities) - (par * share of notional)

Credit correlation is important factor in pricing

42
Q

CDS coupon

A
  1. CDS coupon does not = CDS spread
  2. ISDA standard: 1% investment grade, 5% high yield
  3. Can settle by physical or cash
43
Q

Physical vs Cash CDS Settlement

A

Physical: Swap buyer delivers the asset, swap seller gives cash at par value

Cash: Swap seller gives cash at par value less current value

Example: value is now 20 and par is 100. Swap seller pays 80

44
Q

Loss Given Default

Expected Loss

A

Loss given default (LGD): 1 - recovery rate

expected loss = hazard rate * loss given default

45
Q

Upfront Payment for CDS

A

Upfront payment: (CDS spread - CDS coupon) * duration

Protection leg is the expected cash flows paid by seller

Premium leg is the expected cash flow payments from the buyer

46
Q

CDS Profit Formula

A

Profit = change in spread * duration * notional

47
Q

Types of CDS

A
  1. Naked CDS: Betting on default (doesn’t hold underlying)
  2. Long/short trade: buy protection for one and sell on another (betting difference in spreads)
  3. Curve trade: a long/short trade on the same position with different maturities (expects the YC to flatten)
  4. Curve-steepening trade: going short l/t and long s/t on the same entity (expects the YC to steepen)
48
Q

Calculate Swap Rate and Fixed Payment

A

Example: Calculate the swap rate and the fixed payment on a 1-year, quarterly settlement swap with a notional principal of $10MM

Maturity Annalized Rate Discount Factor

90 day 4.5% 0.98888
180 day 5.0% 0.97561
270 day 5.5% ?
360 day 6.0% 0.94340

270 day = 100 / 1 + (0.055 X 270/360)

Now the Z formula:

1 - 0.94340 / 0.98888 + 0.97561 + 0.96038 + 0.94340

= 0.0146 (Remember this is QUARTERLY for this question. Need to annualize.

1.46% x (360 / 90) = 5.84%

Value of payment would be $10M x 0.0146

49
Q

Delta Neutral Hedging

A

of calls for delta hedge = # shares of stocks / delta of call option

  1. Only works for very small changes
  2. Must be frequently rebalanced
50
Q

Options on Futures

A
  1. Benefit to early excercise of deep-in-the-money options
  2. American options are more valuable than European

3.

51
Q

Greek Risk (BSM Model) and Relation to Calls/Puts

A

Input Calls Puts

Delta Asset Price Positive Negative

Vega Volatility Positive Positive

Rho Rf Positive Negative

Theta Time to exp Value moves to zero closer to maturity

Price Exercise Price Negative Positive

CFA Level II 2020 COPY (552) (13 decks)

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