Hedging and Regression
Hedging and Regression
Returns
The discrete return on a stock is the percentage change:
Si Si 1
Si 1 .
The index i can represent days, weeks, hours etc.
What happens if we compute returns at innitesimally short
intervals of time?
Si
Examples 7.2 and 7.3
Example 7.2:
Financial institution pays 6month Libor and receives 8% per
anuum with semiannual compounding on $100, 000, 000.
The swap has a remaining life of 1.25 years.
The Libor rates for 3month, 9month and 15month are 10%,
10.5% a
Convenience Yield
Convenience Yield
Convenience Yield
Two dierent structures: Contango and Backwardation.
Gold Contango
Crude Backwardation (many times in recent history)
Heating Oil Mixture
We know that F (0, T ) = S0 e (r q)T where q is the dividend yie
Another look at swaps: Commodity Swaps
Another look at swaps: Commodity Swaps
Swaps
Very similar to forwards.
Deals with a stream of risks (rather than a single one).
They are traded OTC.
Example:
We will need to buy 1 bbl of crude oil on 10/1/08 and anot
Valuation of bonds paying oating coupons
Valuation of bonds paying oating coupons
Floating coupon paying bonds
How much would you pay for a bond expiring in three months and
paying 100 plus a coupon equal to todays three-month rate?
B=
100 + c 100
(1 + r
Example 4.4
Example 4.4: The following table contains LIBOR rates and the
corresponding forwards (all continuously compounded). Consider
an FRA where we will receive a rate of %6 measured with annual
compounding, on a principal of $1, 000, 000 between the
Tailing the Hedge
Tailing the Hedge
Tailing the Hedge
As we know Futures are exchange traded and marked to market
whereas Forwards are OTC and settle at the end.
Tailing the Hedge
Tailing the Hedge
As we know Futures are exchange traded and marked to mark
Forward Rates
Forward Rates
Forward Rates
Zero-coupon bonds and zero-coupon rates
If P (0, T1 ) is the price of a zero-coupon bond maturing at time T1
then the corresponding zero-coupon rate is dened by
P (0, T1 ) = e R (0,T1 )T1
Writing a zero rate as a
Duration
Duration
Duration
It is a measure to compare bonds (among other things).
It provides an estimate of the volatility or the sensitivity of the
market value of a bond to changes in interest rates.
There are two very closely related measures: Macaula
Hedging and Regression
Hedging and Regression
Returns
The discrete return on a stock is the percentage change:
Si Si 1
Si 1 .
The index i can represent days, weeks, hours etc.
What happens if we compute returns at innitesimally short
intervals of time?
Si
Valuation of bonds paying oating coupons
Valuation of bonds paying oating coupons
Floating coupon paying bonds
How much would you pay for a bond expiring in three months and
paying 100 plus a coupon equal to todays three-month rate?
B=
100 + c 100
(1 + r