Delta by yurtgc548


• 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
  –   Currencies
  –   Commodities
  –   Equity
• 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
  for floating
  – 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
    receive dollars.
          Futures vs Swaps
• Futures are much more standardized and
  less flexible.
• 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
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
  effectively zero.
• 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
Cash                   Futures

• 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=1/delta
  – 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
Cash                  Futures

• 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
                     Delta=0.95, premium
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
  is 0.7?

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