Derivatives
1 Derivatives
A financial asset is a tradable resource that has value and can be bought, sold, or exchanged.
A financial derivative is a financial instrument whose value is derived from some underlying asset, index, or rate.
Think of a derivative as a contract between two parties that specifies the terms notinf a financial transation based on the performance of the underlying asset.
Below we define some common types of financial derivatives:
Forwards: A forward contract is a customized agreement between two parties to buy or sell an asset at a specified price on a future date. Forwards are traded over-the-counter (OTC) and are not standardized.
Futures: A futures contract is a standardized agreement to buy or sell an asset at a predetermined price on a specified future date. Futures are traded on organized exchanges and are subject to daily settlement.
Options: An option is a contract that gives the holder the right, but not the obligation, to buy (call option) or sell (put option) an asset at a specified price (strike price) on or before a specified date (expiration date).
Swaps: A swap is a derivative contract in which two parties agree to exchange cash flows or other financial instruments over a specified period. Common types of swaps include interest rate swaps and currency swaps.
2 Payoff Functions
We can represent the value of an underlying asset over time using Stochastic Process. For example, let \(S_t\) denote the price of one share of Company XYZ stock at time \(t\).