Black-Scholes Valuations

Basic types of derivatives

Although the variations of derivatives are almost endless, there are two building blocks upon which they are built:

  • forwards
  • AND
  • options

Forwards. A forward contract is the simplest form of derivative.

Party A is obliged to buy and Party B to sell a specified quantity of something on a specified date. The something must have a market (for example: commodities, currencies, stocks, etc.). There are markets for a wide variety of somethings.

Variations to forward contracts are swaps and futures contracts.

Options. An option gives a party the right (but not the obligation) to buy or sell the underlying something for a set price on a set date.

Here’s an example…

Benjamin is leasing a home for one year. At the end of that year, his contract specifies that he can purchase the home for a set price. Benjamin has an option. He doesn’t have to purchase the home at that time for that price, but he can. If the market has gone up during that year and he likes the house, Benjamin might just exercise his option.

However, if the price of homes falls, he might decide to allow the option to lapse and either continue to rent or move.

There are two main types of options:

  • Calls: The purchaser has the right to buy something at a set price.
  • Puts: The purchaser has the right to sell something at a set price.

The something is called the underlying asset. It’s the price movement in this underlying asset that makes the option worth something or nothing.

Here’s an example…

In 30 days, Sarah has a call option on a stock at $75. (The $75 is called the strike price.)

After 30 days…

Stock selling for $85 Stock selling for less than $75
It’s worth exercising the option since Sarah is purchasing it at $75 and could turn around and sell it for $85. That’s a $10 profit. Sarah wouldn’t exercise the option in this case. Her loss would be limited to the price she paid for the call option.

Q: What happens to the seller of the call option in the event that the stock is selling for less than $75?

A: The call seller is obligated to come up with the stock regardless of the stock price after 30 days. So, the seller’s gain is limited to the price Sarah paid for the option, but the risk is the seller may get stuck with stock nobody wants to buy.

Memory Jogger

A stock option creates an obligation on the part of:

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