• The swap market developed in the late 1970s.
• Swap is an agreement between two parties
(called counter parties) to exchange payments
with each other.
• Four general classifications of swaps:
– Interest rates
• Since it is often difficult for individuals to
find parties who have need that can be
matched with their swaps, swap dealers
and brokers have emerged.
– Swap dealers: Take the other side of each
deal and earn a spread difference for their
– Brokers: Simply match up counter parties and
receive a fee for their efforts.
• The most popular interest rate swap is the fixed
– Where one counterparty exchanges (swaps) her
floating interest rate payment to another counterparty
for his fixed rate payment.
• Swaps are very flexible. They can be
constructed to match long-term needs over
several time periods, for various amounts and
can be tailor made to suit individual company
• If properly done, they can control interest rate
risks, currency risks and commodity price risks.
• A foreign exchange swap is a trade that
combines both a spot and a forward transactions
into one deal.
– Example: Suppose Citibank wants pounds now. It
could enter into a swap agreement with another bank.
Under the swap agreement, it will trade dollar to the
other bank and in return will receive pounds. After
the specified time period, the trade is reversed.
Citibank will pay out pounds to the other bank and
Futures vs Swaps
• Futures are much more standardized and
• However, futures are openly traded and
backed by clearing house at each
exchange. Default risk for futures is almost
nil. Not so with swaps. They are only as
good as the parties and dealers who
construct and trade them.
Option Hedging Considerations
• To properly hedge with options, a few
considerations need to be observed.
– The relationship between the change in the
price of the underlying futures and the option
premium will impact the effectiveness of the
– The relationship between the price of the
underlying futures and the cash price (i.e.,
basis) will affect certain hedge.
• The relationship between the change in the
option premium and the price of the underlying
futures is called delta (Δ).
• Delta=Change in the option premium/
Change in the price of the futures
• Delta normally ranges between zero and one.
– A delta of 0.9 means that when the underlying futures
price changes by $1.00, the option premium changes
by only $0.90.
– Deltas of 1 means perfect correlation between
changes of the futures price and the option premium
and deltas of 0 means that the option premium did not
change when the futures price changes.
• Delta (D) is the rate of change of the
option price with respect to the underlying
Slope = D
A Stock price
• As a general rule, delta value increases as
the option gets deeper in-the-money and
becomes the value of one.
• As the option goes deeper out of the
money the delta value becomes close to
• Delta takes on the values of zero or one as
the option approaches maturity when the
time value is eroded away and the
probability of a significant price moves is
• Delta can be calculated after the fact with
certainty, but they can serve as a guide for
future premium values, if only as an estimate.
• General rule of thumb:
– If the underlying futures price remains stable, deltas
will decrease in value for those premiums with time
value- the more time value in a premium, the more
the delta will decline.
– If the underlying futures price increases, put deltas
decrease and call deltas increase.
– If the underlying futures price decreases, put deltas
increase and call deltas decrease
• What do deltas mean for hedger: Delta
can serve as guides for what the hedger
can expect as price protection.
Effects of Delta on Hedging
• Nov. 1
Buys corn at $3/bu Buys one put option on
Dec. corn at strike
price of $3/bu and a
premium of $0.10/bu
Sells put at a premium
Sells corn at $2.90 of $0.15/bu
• A multiple is simply a term applied to an
options hedge that contains more than one
option contract. Multiples are used to
achieve dollar equivalency with an option
– M = number of option contracts necessary to
achieve dollar equivalency.
• If the delta is 0.5, then the number of
options contracts necessary to achieve
dollar equivalency is two.
• If the price starts to move, the value of
delta will change and thus the size of the
multiple will also change
Effects of Changing Delta on
• Nov. 1 • Delta=0.5
Buy corn at $3/bu Buy two put option on Dec. corn
at strike price of $3/bu and a
premium of $0.10/bu
Cash corn at $2.80
Sell one put option
Nov. 20 Delta=0.95
Cash corn at $2.75 Premium $0.2375
• For an option hedger the most important is
not knowing about delta for the options
premium (DeltaF) and the underlying
futures but a delta for the options premium
and the cash market (DeltaC) .
Hedging in Practice
• Traders usually ensure that their portfolios
are delta-neutral at least once a day
• Whenever the opportunity arises, they
improve gamma and vega
• As portfolio becomes larger hedging
becomes less expensive
• What does it mean to assert that the delta
of a call option is 0.7? How can a short
position in 1,000 call options be made
delta neutral when the delta of each option