Derv

Question 1

3 types of CDS

Answer 1

1. Single name CDS: reference obligation is FI
2. Index CDS
3. Tranche CDS

Question 2

CDS pays when:

Answer 2

When the reference entity(issuer) defaults in ANY other issue ranked park passu or higher

Question 3

CDS payoff

Answer 3

Based on MV of cheapest to deliver bond with same seniority as reference obligation

CTD: Debt purchased at lowest cost but same seniority

Question 4

CDS:

Protection buyer/seller

Answer 4

Insurance contract; credit risk protection only

Protection buyer pays CDS spread
Protection seller longs credit risk
FV: notional; amt to be protected

Protection leg: contingent pmt seller makes to buyer
Premium leg: pmt buyer makes to seller

Question 5

Hazard Rate

Answer 5

Probability that an event will occur given that it hasn’t already occurred

Question 6

Credit curve

Answer 6

Credit spread for a range of maturities of company’s debt make up its credit curve

Question 7

IR Cap

Answer 7

Agreement which one party agrees to pay when benchmark IR > strike rate (cap rate); portfolio of call options on LIBOR (caplets)

Buyer: call on LIBOR

Question 8

IR Floor

Answer 8

Agreement which one party agrees to pay when benchmark IR

Question 9

For a call option on a FI:

Answer 9

When IR rises, price falls, call option value decreases

When IR falls, price rises, call option value rises

Question 10

For a put option on FI:

Answer 10

When IR rises, price falls, put option value rises

When IR falls, price rises, put option value falls

Question 11

Interest rate collar

Answer 11

Issuer: buys cap (protect from high IR) and sells a floor
Bond holder: buys floor (protect from low IR) and sells the cap.

The net prem paid by an ISSUER for a collar = (prem paid for cap) - (prem received for selling the floor). Issuer can set the exercise rates on the cap and floor such that the price received for floor = price paid for cap. Eliminates the upfront cost of buying interest rate call options, and result in a zero-cost collar for the issuer.

Question 12

2 types of collars

Answer 12

1. Buy cap, sell floor
   Investor has LIBOR liability, borrowing cost will stay within collar (floor-cap)
2. Buy floor, sell cap
   Investor has LIBOR asset, return will stay within collar (floor-cap)

Question 13

Fiduciary Call

Answer 13

(Call option on stock) + (zero coupon rf bond)

Question 14

Protective Put

Answer 14

(Put option on stock) + (share of stock)

Pay prem for limited downside
Unlimited upside

Question 15

Hedging (Covered Call)

Answer 15

Receive call premium

No upside potential

Question 16

Delta Hedging

Answer 16

Hedge needs to be continually rebalanced even if stock price doesn’t chg, b/c delta chgs as time passes and option approaches maturity

Question 17

1-period binomial model

Answer 17

U: size of up move
D: 1 - U
prob(u): prob of up move
prob(d): 1 - prob(u)

Question 18

Risk Neutral Probability

Answer 18

prob(u) = (1+ rf - D)/(U-D)
prob(d) = 1 - prob(u)

Question 19

Lower/Upper Bounds

call option

Answer 19

Lower: Max(0, So- (X/(1+rf)^t))

Question 20

Lower/Upper Bounds

put option

Answer 20

Lower:
European Put: Max(0, (X/(1+r)^t) - So)
American Put: Max(0,X-So)

Question 21

Price options on bonds

Answer 21

1) Price bond at each node using projected IR
2) Calculate intrinsic value of option at each node @ maturity of the options
3) Bring the terminal option values determined in step 2 back to today

Question 22

BSM assumptions

Answer 22

1) underlying price follows lognormal distribution
2) rf constant and known
3) vol of underlying is constant and known
4) mkts are frictionless
5) underlying has no CFs
6) European options only

Question 23

BSM inputs

Answer 23

1) Stock price
2) Exercise price
3) Stock volatility
4) Time to expiration
5) rf rate

Question 24

Vega

Answer 24

measures sensitivity of option price to chgs in volatility of So

Question 25

Rho

Answer 25

option price doesnt chg much with chgs in rf rate

Question 26

Theta

Answer 26

Time

Question 27

Delta Vega Rho Theta

Answer 27

``` Calls: Delta > 0 Vega > 0 Rho > 0 Value approaches $0 as option approaches maturity (Theta 0 Rho ```

Question 28

Deep ITM puts have a delta of

Answer 28

-1

Question 29

Deep OTM calls have a delta of

Answer 29

0

Question 30

Call option delta is between 0 and 1 if...

Answer 30

Assuming the So doesn't change 1) call option is OTM, the call delta moves closer to 0 as time passes 2) ITM the delta moves closer to 1 as time passes

Question 31

Gamma

Answer 31

Measures rate of chg in delta as the So chgs | graph: upside down v ATM and close to expiration options: higher gammas ITM/OTM: small gammas

Question 32

TBill Futures

Answer 32

Eurodollar & Tbill futures settled in cash Discount factor: 1- (quote*(t/360)) Rf Yield = (Par - discount factor)/(discount factor) FP = So*[(1+rf)^t]

Question 33

TBond Futures

Answer 33

FP = (bond price*[(1+rf)^t]) - FVC)/Conversion factor

Question 34

Stock Futures

Answer 34

(So*[(1+rf)^t] - FV(Div)

Question 35

EQ Div Futures

Answer 35

So*e^[(rf(cc) - div yield(cc))*t]

Question 36

FX Futures

Answer 36

So*{ [(1+rd)^t]/[(1+rf)^t] }

Question 37

Put Call Parity

Answer 37

Co + X/[(1+rf)^t] = Po + So

Question 38

FX Swap Price

Answer 38

1 party receives, 1 party pays ``` stick to curncy in qs freq: pmts 1) calc PV(interest & principal) use rf(A/360) 2) convert a side using current spot rate 3) net out both parties to see who pays ```

Question 39

Swap Rate

Answer 39

1-(last discount factor)/ (sum of discount factors)

Question 40

Payer Swaption (Long vs Short)

Answer 40

Long Payer: when IR falls, swaption value decreases Short Payer: when IR falls, swaption value increases

Question 41

Receiver Swaption (Long vs Short)

Answer 41

Long Receiver: when IR falls, swaption value increases Short Receiver: when IR falls, swaption value decreases

Question 42

Payer vs Receiver Swaption

Answer 42

Payer swaption: right to enter swap to pay the fixed leg and receive the floating leg. Receiver swaption: right to enter swap to receive the fixed leg, and pay the floating leg.

Question 43

At initiation of IR Swap

Answer 43

both parties exposed to potential credit risk (low exposure)

Question 44

Credit Risk on Payer Swaption

Answer 44

Long position (fixed receiver) exposed to credit risk due to chance counterparty will default if swaption expires ITM Short position isn't exposed to credit risk b/c they'll not receive a pmt at maturity no matter if the swaption expires in or out of the money

Question 45

Eurdollar vs Tbill Futures

Answer 45

the Eurodollar contract is better at hedging LIBOR based investments b/c it's a LIBOR based contract T-bill contract is based on T-bill rates, not perfectly correlated to LIBOR

Question 46

Long Eurodollar Contract

Answer 46

If IR falls, yield on LIBOR investment will fall, but the decrease will be offset by gains on a long Eurodollar futures contract

Question 47

2 year floor

Answer 47

equal to 1 yr European put option plus value of a 2 yr put option (floorlet) A 1yr floorlet with an annual payoff is the same as a 1yr put option on annual LIBOR value of 2 yr put option is equal to value of 2 yr floor LESS value of 1 yr put option

Question 48

Call Option (European vs American)

Answer 48

Early exercise is not valuable for call options on NON-DIVIDEND PAYING stocks, so American call = European call