Pricing and Valuation of Forward Commitments Flashcards
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 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
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
