Derivatives Flashcards
What does gamma (γ) represent in forward contract
Benefits
What does theta (θ) represent in forward contract
Costs
Formula for Forward contract
F0 = [S0 + Pv θ - Pv γ ] * (1+r)^t
Costs and benefits are discounted back to the present value
Forward Rate Agreement
Long
Floating Rate Receiver - Pays Fixed Rate
How does a forward contract look for a FRA 3 x 9 Contract
Forward Rate (3,6)
3 - Months from now
6 - Months duration
Forward Rate Agreement
Short
Fixed Rate Receiver - Pays Floating Rate
FRA Long Position Formula
Receives floating, pays fixed
NA( Floating - Fixed x (Days / 360) ) / (1+ Floating Rate x Days/360))
FRA short Position Formula
Short - Receive Fixed, Pay floating rate
[ Na x ( Fixed - Floating * Days /360] / (1+fixed * Days /360)
Formula for “Cost to purchase deliverable bond”
ST + AI
Bond present price + Accured Interest Interest
Formula for “Cost To Deliver”
CTD = ST - (Ft x CF)
Bond Present Value - (Forward Price x Conversion Factor)
Fixed Income Forward Price Formula
F0 = [(S0+AI)-I/(1+r)^t] x (1+r)^t - Accured Interest
Qouted Fixed Income Forward Fomula
QF0 = F0 /Conversion Factor
Formula For Currency Forward price
f/d
Ff/d = Sf/d x [(1+rf) ^t / (1+rd)^t]
Formula For Currency Forward price
d/f
Fd/f = Sd/f x [(1+rd) ^t / (1+rf)^t]
What will the Forward price be if
Rf = Rd
F0 = S0
What will the Forward price be if
Rf > Rd
Ff/d > Sf/d
Fd/f < Sd/F
What will the Forward price be if
Rf < Rd
Ff/d < Sf/d
Fd/f > Sd/f
What is the value of a forward and swap contract at time 0
Zero
No value
Receives fixed Rate, and pays floating is the same as
Long fixed bond and short floating bond
How to calculate PMT in Swap rate?
1 - Dfn / Sum of DF
Formula for Value of Interest Rate Swap
( R fixed 0 - R fixed 1) x Notional Amount x sum of DF
Who decideds which bond to deliver in a fixed income future contract
The seller after adjusting for conversion factor
Formula for Swap Value
(R0 - Rt+1) x Notional Amount x ∑DF
∑DF is based on the years remaning
What is the underlying in a interest rate swap
An interest rate
Formula for “Receive Equity” in equity swaps
(NA x P0 / Pt+1) - NA x (Rfix x ∑DF + DFn)
Company X is in the UK.
Company Y is in Japan.
They enter into a Fixed-for-Fixed currency Swap.
What kind of bond position is this similar to for both parties
Company X: Short a JPY bond and long GBP bond.
Company Y: Short GBP bond and Long JPY bond
Reason: They both have to make interest payment (short) in the counterparties currency, and receive (Long) interest payment of their domestic currency.
The value of a futuers contract is the difference between…
Future price at experation - Futurers price of the previous day
What does Δ represent in option
Delta: Change in the value of the option, for a change in underlying price
What is Δ hedging?
Taking an offsetting Δ postion so to be delta neutral
Δ = 0
Formula for Δ hedge
Δ Neutral = - Δ portfolio / Δ hedge
What is Γ in options
Γ: Gamma
Second derivative of Δ
The change in option Δ for a change in the underlying assets price
What does Γ measure
Measures the risk that remains once a portfolio is delta neutral
It can be managed to a specific level, but never eliminated
A portfolio that must be gamma neutral can become delta neutral by trading
The underlying securities.
What is θ in options
θ Theta
change in option value for the passage of time
estimates how much value slips away from an option with each passing day
Theta is the rate in which the time value decreases as time goes on
What will our θ be if we long options
Negative θ
Time is our enemy
What will our θ be if we short options
Positive θ
Option decay in value
What is ν in options
ν: vega
Change in option for change in volatility
How will our vega be if we long options?
Positive vega (Long volatility)
How will our vega be if we short options?
Negative Vega (Short volatility)
What is ρ in options
ρ: Rho
Change in option value for a change in the Risk Free Rate
What is Delta range for a call option at any moment in time
Non dividend: 0 to1
Dividend: 0 to e^(-δT)
What is the implied volatility in options based off of?
It is the volatility implied by the option prices observed in the market
What probability is N(d2) in the BSM?
probability the option expires in-the-money
With currency options, the volatility in the BSM model is the volatility of the log returns of…
The Spot exchange rates as expressed as Sd/f
What is the Stock component in the BSM
S x N(d1)
What is the Bond component in the BSM
e^(-r x T) X N(d2)
What is the underlying asset in a interest rate option?
Underlying = FRA = LIBOR
What position does a Long FRA have?
Borrower
What position does a Short FRA have?
Lender
Position of Long call in interest rate option
Call: Receive floating
Position of long put in interest rate option
Receive fixed rate
Position of Short put in interest rate option
Pay Fixed
Position of Short call in interest rate option
Pay floating
Payer Swaption
Pay fixed, Received floating
Receiver Swaption
Receiver Fixed
Pay floating
What is a Collar option strategy?
buying a downside put and selling an upside call to protect against large losses, but that also limits large upside gains.
Buy put, Sell call.
What is a straddle option strategy?
buying (or selling) both a call and a put with the same strike price and expiration on the same underlying asset.
Buy or sell put and call option witht he same stike and expiration
When does gamma at its highest value?
When the option is near, or at the money
What is the PV of expected option payoff at expiration in the BSM model?
- The PV is based on the Risk-free interest rate and not the investors required rate of return.
- The expected option payoff is based on the risk-neutral probabilities.
What kind of Greeks does a Long call have?
Long call
Delta: Positive
Gamma: Positive
Theta: Negative
Vega: Positive
What kind of Greeks does a Long puts have?
Long Puts
Delta: Negative
Gamma: Positive
Theta: Negative
Vega: Positive
Why is the hedge ratio for put options negative?
Option value is inversely proportional to the price of the underlying.
