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17 Cards in this Set

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  • Back
General Concepts:
Fwd Price
Price of underlying that allows no arbitrage, so they're valued at zero. This is a No Arbitrage Price
Formula for FP
FP = So x (1 x Rf)^T

FP: Forward Price
So: Spot Price

Compound the Spot at the risk free rate
Day count on zero coupon bonds
6m forward on zero-coupon bond, Currently selling for $600 (1000 face), rf =3%, what's the future price?
600 x (1.03) ^ 6/12

Vt (value of long position during the life of a contract)
Vt = St - (FP / (1 +Rf)^ T-t
Value of Long position at maturity
St - FP

Value of underlying - Forward Price
Formula (another method)
You receive St
You pay FP

Value t: PV(St) - PV(FP)

"spot price - PV of the forward price"
Pricing Equity Forward Contracts (divs complicating feature)

(So - PVdivs) x (1+Rf)^t


So x (1=Rf)^T -FVD
Pricing equity fwd example:

90d equity fwd
Stock @ 60
Div at day 60: 2.00
FP: (So - PVdivs) x 1+Rf^t

PVdivs: 2.00 / (1+.03)^60/365

FP: (60-1.9903) x 1.03^90/365

Net investment's Future Value

58.43 is the zero arb fwd price
Value an Equity Forward Contract after initation
Vt (long)

(St - PVdivs) - (FP / (1+Rf)^T-t)

remember... discount FP by the days LEFT to expiry
Pricing Equity Index Forward Contracts
Think continuous dividend, just an offset to the cost of carry

FP: So x e^(Rfc -Rfdiv yldc) x T

5% annual compounded rate


Continuously compounded: 4.879%
Valuing Index Forward Contracts
Vt (long) =

(St / e^ dvld(cont) x (T-t)


(FP / e^Rfc x (T-t)

So / e^div yld x time left

- FP / re^skfr(cont) x time left

1x3 FRA

30d rate 2.4%
90d rate 3.0%
---------- -1 x 360/60

Longer rate: .03 x 90/360
Shorter rate: .024 x 30/360

----------- -1, then annualize

Fwd rate: 3.293%
Valuing a FRA, concepts
Long FRA is bullish on rates
Short FRA is bearing on rates

FRA is you're Fixed Rate Payer rate, Pay Fixed, Received Floating

Paid in arrears
Carrying forward 1x3 FRA, we priced it at 3.3%, notional 1m

10 days in

20d libor: 2.5% (de-ann!) d.00139
80d libor: 3.3% (de-ann!) s.00733
Price a new FRA
80d/20d -1 x 60/360

1.00733 / 1.00139 -1: d.00593
ann (60): 3.56

New Rate - Locked in Rate
(3.56 - 3.3) x 60/360 x 1m:

Value at end of b&l period
433.33/ 80d 1.00733 =

Valuing Currency Forwards:
1+RNum^ x/365
So x ______________
1+RDen^ x/365
Valuing a Currency Forward Contract:
___________ - ________
(1+Rdem)^T-t (1+Rnum)^T-t