Derv Flashcards
3 types of CDS
- Single name CDS: reference obligation is FI
- Index CDS
- Tranche CDS
CDS pays when:
When the reference entity(issuer) defaults in ANY other issue ranked park passu or higher
CDS payoff
Based on MV of cheapest to deliver bond with same seniority as reference obligation
CTD: Debt purchased at lowest cost but same seniority
CDS:
Protection buyer/seller
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
Hazard Rate
Probability that an event will occur given that it hasn’t already occurred
Credit curve
Credit spread for a range of maturities of company’s debt make up its credit curve
IR Cap
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
IR Floor
Agreement which one party agrees to pay when benchmark IR
For a call option on a FI:
When IR rises, price falls, call option value decreases
When IR falls, price rises, call option value rises
For a put option on FI:
When IR rises, price falls, put option value rises
When IR falls, price rises, put option value falls
Interest rate collar
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.
2 types of collars
- Buy cap, sell floor
Investor has LIBOR liability, borrowing cost will stay within collar (floor-cap) - Buy floor, sell cap
Investor has LIBOR asset, return will stay within collar (floor-cap)
Fiduciary Call
(Call option on stock) + (zero coupon rf bond)
Protective Put
(Put option on stock) + (share of stock)
Pay prem for limited downside
Unlimited upside
Hedging (Covered Call)
Receive call premium
No upside potential
Delta Hedging
Hedge needs to be continually rebalanced even if stock price doesn’t chg, b/c delta chgs as time passes and option approaches maturity
1-period binomial model
U: size of up move
D: 1 - U
prob(u): prob of up move
prob(d): 1 - prob(u)
Risk Neutral Probability
prob(u) = (1+ rf - D)/(U-D) prob(d) = 1 - prob(u)
Lower/Upper Bounds
call option
Lower: Max(0, So- (X/(1+rf)^t))
Lower/Upper Bounds
put option
Lower:
European Put: Max(0, (X/(1+r)^t) - So)
American Put: Max(0,X-So)
Price options on bonds
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
BSM assumptions
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
BSM inputs
1) Stock price
2) Exercise price
3) Stock volatility
4) Time to expiration
5) rf rate
Vega
measures sensitivity of option price to chgs in volatility of So
Rho
option price doesnt chg much with chgs in rf rate
Theta
Time
Delta
Vega
Rho
Theta
Calls: Delta > 0 Vega > 0 Rho > 0 Value approaches $0 as option approaches maturity (Theta 0 Rho
Deep ITM puts have a delta of
-1
Deep OTM calls have a delta of
0
Call option delta is between 0 and 1 if…
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
Gamma
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
TBill Futures
Eurodollar & Tbill futures settled in cash
Discount factor: 1- (quote*(t/360))
Rf Yield = (Par - discount factor)/(discount factor)
FP = So*[(1+rf)^t]
TBond Futures
FP = (bond price*[(1+rf)^t]) - FVC)/Conversion factor
Stock Futures
(So*[(1+rf)^t] - FV(Div)
EQ Div Futures
Soe^[(rf(cc) - div yield(cc))t]
FX Futures
So*{ [(1+rd)^t]/[(1+rf)^t] }
Put Call Parity
Co + X/[(1+rf)^t] = Po + So
FX Swap Price
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
Swap Rate
1-(last discount factor)/ (sum of discount factors)
Payer Swaption (Long vs Short)
Long Payer:
when IR falls, swaption value decreases
Short Payer:
when IR falls, swaption value increases
Receiver Swaption (Long vs Short)
Long Receiver:
when IR falls, swaption value increases
Short Receiver:
when IR falls, swaption value decreases
Payer vs Receiver Swaption
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.
At initiation of IR Swap
both parties exposed to potential credit risk (low exposure)
Credit Risk on Payer Swaption
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
Eurdollar vs Tbill Futures
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
Long Eurodollar Contract
If IR falls, yield on LIBOR investment will fall, but the decrease will be offset by gains on a long Eurodollar futures contract
2 year floor
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
Call Option (European vs American)
Early exercise is not valuable for call options on NON-DIVIDEND PAYING stocks, so American call = European call
