2. College of Economic and
Management Sciences
Department of Finance, Risk Management
& Banking
By CF Erasmus,
adapted from Chance (2003), Botha (2010) & Marozva (2012)
4. Definition
A forward contract is an
agreement between two parties in
which one party, the buyer, agrees to
buy from the other party, the seller,
an underlying asset at a future date at
a price established today. The contract
is customised and each party is
subject to the possibility that the
other party will default.
6. Forwards Futures
Over the counter Futures exchange
Private Public
Customized Standardized
Default risk Default free
Not marked to market Marked to market
Held until expiration Offset possible
Not liquid Liquid
Unregulated Regulated
7. Differentiate between the positions held by the
long and short parties to a forward contract
LF LA
Long party SA Short party SF
• Party that agrees to buy the asset has a long forward
position
• Party that agrees to sell the asset has a short forward
position
8. Pricing and valuation of forward contracts
Are pricing and valuation not the same thing?
• The price is agreed on the initiation
date (Forward price or forward rate)
i.e. pricing means to determining the
forward price or forward rate.
• Valuation, however, means to
determine the amount of money that
one would need to pay or would
expect to receive to engage in the
transaction
9. Pricing and valuation of forward contracts cont…
F(0,T)- The forward contract price initiated at
time 0 and expiring at time T
Vo(0,T) – the value of a forward contract
initiated at time 0 and expiring at time T
Vt(0,T) – the value of a forward contract
at the point in time during the life of a
contract such as t
Today
(0)
Time
between
Today and
Expiration
(t)
Expiration
(T)
VT(0,T)- Value at expiration
10. F(0,T) =S0(1+r)^T
The transaction is risk-free and should
equivalent to investing S0 Rands in
risk free asset
Pricing and valuation of forward contracts cont…
Buy asset at
So
Sell forward
contract at
F(0,T)
Outlay: S0
Hold asset
and lose
interest on
out lay
Deliver
asset
Receive
F(0,T)
11. Vo(0,T) = S0 –F(0,T)/(1+r)^T
For forward contract Vo(0,T) should
be ZERO (0)
If Vo(0,T) ≠ 0 arbitrage would the
prevail
Pricing and valuation of forward contracts cont…
The forward price that eliminates arbitrage:
F(0,T) =S0(1+r)^T
12. By definition an asset’s
value is the present value
of future value thus,
Vt(0,T) = St –F(0,T)/(1+r)^(T-t)
Pricing and valuation of forward contracts cont…
(T-t) is the remaining time
to maturity
13. F(0,T) =(S0-PV(D,0,T))*(1+r)^T
When dividends are paid continuously
F(0,T) =So℮^(-∂c*t) . ℮^(rc*t)
To convert discrete risk-free interest(r)
to continuosly compounded
equivalent(rc):
rc = Ln(1+r)
Pricing and valuation of forward contracts cont…
PV (D,0,T) =∑(Di/(1+r)^(T-ti)
14. Pricing and valuation of forward contracts cont…
A portfolio manager expects to purchase a portfolio
of stocks in 60 days. In order to hedge against a
potential price increase over the next 60 days, she
decides to take a long position on a 60-day forward
contract on the S&P 500 stock index. The index is
currently at 1150. The continuously compounded
dividend yield is 1.85 percent. The discrete risk-free
rate is 4.35 percent.
Calculate the no-arbitrage forward price on this
contract, the value of the forward contract 28 days
into the contract (index value 1225), and the value
of the contract at expiration (index value 1235).
15. 0.0185 60 365 LN 1.0435 60 365
F 0,T 1,150e e $1,154.56
Decrease the spot index value by the
dividend yield and thereafter calculate the
future value (first convert the discrete rate
to a continuously compounded rate).
16. The value of a contract is the difference between the discounted
current spot price (at the dividend yield) and the discounted
forward price (at the converted risk-free rate) for the remaining
period.
0.0185 32 365 LN 1.0435 32 365
tV 0,T 1,225e 1,154.56e
1,223.00 1,150.26
$72.76
17. At expiration, the value is simply the
difference between the end-period spot
index and the forward contract price, as
calculated.
TV 0,T 1,235 1,154.56 $80.44
18. Identify the characteristics of
forward rate agreements
• Forward contract to borrow/lend money at a
certain rate at some future date
Long position
Borrows money (pays interest)
Benefit when forward rate < market rate
Short position
– Lends money (receives interest)
– Benefit when forward rate > market rate
Fixed-Income and interest rate forward
contracts
19. Calculate and interpret the payment at
expiration of a FRA and identify each of
the component terms
20. • ESKOM P/L is expecting to receive a cash inflow of
R20, 000,000.00 in 90 days. Short term interest
rates are expected to fall during the next 90 days. In
order to hedge against this risk, the company decides
to use an FRA that expires in 90 days and is based
on 90day LIBOR. The FRA is quoted at 6%. At
expiration LIBOR is 5%. Indicate whether the
company should take a long or short position to
hedge interest rate risk. Using the appropriate
terminology, identify the type of FRA used here.
Calculate the gain or loss to ESKOM P/L as a
consequence of entering the FRA.
