2.3 Derivatives
7
volatility of the market and guarantees a known, albeit potentially lower, price. This
makes the producer’s planning safer. And the purchaser of the forward contract has
the chance to make a profit in case the market swings upwards and the later marketor spot-price is higher. The agreed-upon price of the forward contract remains fixed
for the duration of the contract.
A relative to the forward contract is a future contract, which also stipulates a trade
at a later time, but the trading is done at an exchange, such as the CME, rather than
in a two-party contract. Whereas the price of a forward contract is fixed, the value of
a future contract varies with time and approaches the spot price as the delivery time
approaches.
Arguably the most prominent tools of financial engineering are options, which
are contracts that give the owner of the option the right to sell or to buy an asset
at a later time for a fixed, agree-upon price. The owner has the choice to exercise
the option, but can forfeit as well. There are many types of options, where the two
simplest ones are: call options, which give the owner the right to buy an asset at time
T at price K . The second is a put option, which gives the owner the right to sell at
time T at price K . At this point in time the option reaches maturity and K is called
the strike price of the option.
Options come in two main flavors; European options have a fixed expiration
date and American options have flexible expiration dates. The names European and
American have nothing to do with geographic prevalence, they are just used as labels,
so European means fixed and American means flexible expiration date.
Let us consider an example: I sell a European call option for a price c that will
permit the purchaser of the option at to buy some asset at the strike price K from me
at maturity T . The purchaser of the option therefore limits the maximum price he
will later have to pay for the asset to K . At time T the price of the asset S T may be
below the agreed strike price K . Then it is more advantageous for the purchaser to
directly buy at the market price S T and forfeit the call option. In that case I, the seller,
have made a profit c. If the market price S T is above K , the purchaser will exercise
the option and I, the seller have to provide the asset at price K and might incur a loss,
unless I already own a share. Note that the seller of the call option receives some
money up front, the purchasing price c of the option, and hopes that the market price
drops so he can keep the money. If, on the other hand, the market price increases,
the seller has to invest c, and potentially a lot more in order to satisfy the option,
when the purchaser exercises it at maturity. Note that at maturity the value of the call
option is zero, if the price of the asset is below the strike price K and it is S–K if the
price of the asset is above the strike price.
So, why do I want to issue an option? One reason is to hedge the acquisition of the
underlying asset, say some share. Assume that I buy a share and, at the same time,
sell a call option. If the share price increases, but stays below the strike price K , I
make a profit by keeping the money I received for the call option. If the share price
increases above the strike price K , I have to give the share I own to the purchaser
of the option. I will make a loss, but a least not more than what I own anyway—the
share. Balancing the number of options with the acquired asset is part of hedging and
7
volatility of the market and guarantees a known, albeit potentially lower, price. This
makes the producer’s planning safer. And the purchaser of the forward contract has
the chance to make a profit in case the market swings upwards and the later marketor spot-price is higher. The agreed-upon price of the forward contract remains fixed
for the duration of the contract.
A relative to the forward contract is a future contract, which also stipulates a trade
at a later time, but the trading is done at an exchange, such as the CME, rather than
in a two-party contract. Whereas the price of a forward contract is fixed, the value of
a future contract varies with time and approaches the spot price as the delivery time
approaches.
Arguably the most prominent tools of financial engineering are options, which
are contracts that give the owner of the option the right to sell or to buy an asset
at a later time for a fixed, agree-upon price. The owner has the choice to exercise
the option, but can forfeit as well. There are many types of options, where the two
simplest ones are: call options, which give the owner the right to buy an asset at time
T at price K . The second is a put option, which gives the owner the right to sell at
time T at price K . At this point in time the option reaches maturity and K is called
the strike price of the option.
Options come in two main flavors; European options have a fixed expiration
date and American options have flexible expiration dates. The names European and
American have nothing to do with geographic prevalence, they are just used as labels,
so European means fixed and American means flexible expiration date.
Let us consider an example: I sell a European call option for a price c that will
permit the purchaser of the option at to buy some asset at the strike price K from me
at maturity T . The purchaser of the option therefore limits the maximum price he
will later have to pay for the asset to K . At time T the price of the asset S T may be
below the agreed strike price K . Then it is more advantageous for the purchaser to
directly buy at the market price S T and forfeit the call option. In that case I, the seller,
have made a profit c. If the market price S T is above K , the purchaser will exercise
the option and I, the seller have to provide the asset at price K and might incur a loss,
unless I already own a share. Note that the seller of the call option receives some
money up front, the purchasing price c of the option, and hopes that the market price
drops so he can keep the money. If, on the other hand, the market price increases,
the seller has to invest c, and potentially a lot more in order to satisfy the option,
when the purchaser exercises it at maturity. Note that at maturity the value of the call
option is zero, if the price of the asset is below the strike price K and it is S–K if the
price of the asset is above the strike price.
So, why do I want to issue an option? One reason is to hedge the acquisition of the
underlying asset, say some share. Assume that I buy a share and, at the same time,
sell a call option. If the share price increases, but stays below the strike price K , I
make a profit by keeping the money I received for the call option. If the share price
increases above the strike price K , I have to give the share I own to the purchaser
of the option. I will make a loss, but a least not more than what I own anyway—the
share. Balancing the number of options with the acquired asset is part of hedging and