What are financial derivatives?

Derivatives are a particularly diverse set of contracts that derive their value from other assets called underlying. Primitive forms of derivatives have been in use for centuries.

They are mainly used for hedging and risk management, arbitrage and speculation purposes.

Some of the most common underlyings are the price of a stock or the value of an index, an interest rate level, or a currency exchange level. However, the underlying could literally be anything, even the price of a slice of pizza at a future date.

Contract types

• Forward contracts: standardized contracts traded on an organized exchange. Buyers and sellers agree to trade the underlying on a set date at a predetermined price.

• Future contracts: similar to forward contracts, but futures are not standardized.

• Options: they give the buyer the right (but not the obligation) to buy (call options) or sell (put options) the underlying at a set price at a future date.

• Swaps: the parties agree to exchange cashflows based on different financial instruments

Moreover, these basic contracts can be embedded within traditional assets such as bonds (thus making structured notes) or be combined to make more complex derivatives such as swaptions.

Underlying-based distinction

Depending on the kind of underlying, derivatives can broadly be cathegorized as:

• Equity derivatives

• Interest rate derivatives

• Credit derivatives

• Commodity derivatives

• Basket derivatives

Since the value of derivative securities is dependent on the future value of the underlying, in order to price them we need to define a model for the price evolution of the underlying. The easiest way to do so is by defining a diffusive model with constant parameters, just like the Black-Scholes-Merton model.