# Financial Math FM/Derivatives

## Derivative

A derivative is a contract whose payoff depends on the behavior of some benchmark, which is known as the underlying asset. The underlying is typically a tradable asset, for example, a stock or commodity, but can be a non-tradable such as the weather (in the case of weather derivatives). Derivatives can be used to manage financial risk.

Derivatives are used as a means of hedging. Derivatives are used to reduce the likelihood of bankruptcy. Derivatives are used to reduce transaction costs. Derivatives are used as a form of insurance.

### Over-the-counter market

Over-the-counter (OTC) derivatives are contracts that are traded (and privately negotiated) directly between two parties, without going through an exchange or other intermediary. Products such as swaps, forward rate agreements, and exotic options are almost always traded in this way.

The bid-ask spread (also known as bid/offer or buy/sell spread) for securities is the difference between the prices quoted for an immediate sale (ask) and an immediate purchase (bid). The size of the bid-offer spread in a security is one measure of the liquidity of the market and of the size of the transaction cost.

## Short selling

Short selling (also known as shorting or going short) is the practice of borrowing an asset and selling it immediately with the intention of buying identical assets back at a later date to return to the lender.

### Example

Shares in XYZ currently trade at \$10 per share.

1. Sarah the short seller borrows 10 shares of XYZ at a 5% annual interest rate.
2. Sarah immediately sells the shares for \$100.
3. After one year the stock price drops to \$9 per share.
4. Sarah buys 10 shares of XYZ for \$90 and returns them to the lender along with the \$5 of interest.
5. Sarah sees a net profit of \$5.

### Short position

Represents either a right or an obligation to sell an underlying asset. Examples of short positions: Short Forward, Written Call, Purchased Put

### Long position

Represents either a right or an obligation to buy an underlying asset. Examples of short positions: Long Forward, Purchased Call, Written Put

## Stock index

Measure of the aggregate performance of predetermined group of stocks.

## Spot price

The price paid for the immediate delivery of an asset

## Credit risk

Credit risk: the risk that money owing will not be paid by an obligor. Since credit risk is the natural business of banks, but an unwanted risk for commercial traders, an early market developed between banks and traders that involved selling obligations at a discounted rate.