### Derivatives Contracts

As defined by International Swaps and Derivatives Association (ISDA):

"A derivative is a risk-shifting agreement, the value of which is derived from the value of an underlying asset. The underlying asset could be a physical commodity, an interest rate, a company’s stock, a stock index, a currency, or virtually any other tradable instrument upon which two parties can agree."

A derivative is a contract between two parties. In the contract, the counterparties agree terms of a transaction which refer to another security (the underlying or 'reference' asset.)

For example, they may be agreeing the terms of a trade in the underlying asset to take place at an actual or possible future time. Historically, the earliest derivatives contracts were 'futures'. That is, traders agree to exchange an amount of the reference asset at a future date, but at a price set now. Next came 'options' - contracts setting the terms of a future trade which will only be carried out if the option buyer chooses to 'exercise' the contract.

In many derivatives contracts, though, the underlying asset will never actually change hands. The counterparties may just be agreeing to make some exchange of cash or other securities, but with amounts determined by what happens to the value of the reference asset.

### risk trading and gambling

As the ISDA definition shows, derivative contracts are seen essentially as means of trading risk. Of course all trading in securities can be seen in this light - allocating investment capital so as to maximise expected returns on a portfolio, in part through spreading risk. But derivatives are particularly viewed in these terms. Other securities and their structures tend to involve other immediate motivations (eg. funding corporate expansion through raising debt or selling equity.) Derivatives are often created specifically by agents looking for ways to buy or sell exposures to particular risks.

Derivative contracts are often most easily described as bets, gambles on the performance of the reference asset.

More specifically, many derivative contracts can be interpreted as 'contracts for differences'.

### contracts for differences

The 'spot price' is the actual price of the reference asset (or often a reference 'index' of assets) at a given time. The 'strike' is a given price level of the reference asset specified in the contract. The contract specifies payments between the counterparties based on the difference between spot price and strike at a given date in the future, or on a number of occasions over a given period.

For example, a 'forward contract' is more technical term for the basic type of 'future'. Counterparties agree to exchange an amount of the asset at a set price (effectively the 'strike') at a given future date. Here one party is gambling that the difference between the actual future price (spot price) and the strike will be positive, the other that it will be negative. (Technically, a trade where actual assets are handed over is not a 'contract for differences'. But in essence the calculation is the same - it is the difference that counts.)

For example, a very common derivative trade is an 'interest rate swap'. Eg., a corporate borrows some money at a given interest rate. But the corporate doesn't want to carry the risk of the interest rate going up. It uses a swap to sell this interest rate risk to eg. a bank which is happy to gamble on interest rates for the right odds. The contract is: over a given period (eg. three years) bank B pays corporate C (a given 'nominal amount', eg. £10 million) x (a given interest rate, eg 3-month LIBOR.) Over the same period B pays A a fixed amount of (the nominal amount £10 million) x (a fixed rate eg. 3%).

In fact there is no need to hand large sums back and forth each time. Counterparties exchange just the net difference between the reference 'spot price' (libor interest rate) and the strike (the fixed rate of 3%). If libor > 3% then the bank pays the corporate; if libor < 3% then the corporate pays up. So: the bank is betting that libor > 3%, the corporate is betting the other way.

### why markets like derivatives

Financial agents are very keen on contracts of this type. They have a number of advantages over investing directly in underlying securities. In the example, the corporate is effectively buying exposure to the interest rate (to counteract the interest rate risk on its original loan) - but without actually having to buy £10 million worth of interest bearing bonds. Investors do not need to tie up the same amounts of cash (or regulatory / economic capital) in the investment. Simple 'gambles' are easy to arrange, and there are generally much lower transaction costs than transferring equivalent amounts of 'real' assets. Derivatives create greater opportunities for investors who want to go 'short' on an asset, bet on their underperformace - eg. the bank betting on interest rates falling - whereas 'standard' securities are bets on things going up.

The counter to this is that, to have liquidity in a derivatives market, you need to have a sufficient number of people looking to gamble both ways.

### Symmetry, asymmetry

In both Futures and Swaps, there is an essential symmetry with one counterparty betting that spot will go up relative to strike, and the other betting against. (Note there can also be swaps with one moving reference asset swapped against another - eg. an interest rate against an equity index. But the structure is essentially the same.)

An Option introduces asymmetry. Again, we can think of the trade in terms of a difference between a spot price (actual future price of reference asset) and a strike (pre-set price in contract). The option buyer buys the right to buy (call option) or sell (put option) the asset at strike at a given date or within a given period. If the difference is in the option buyer's favour, it will exercise the option. If the difference favours the option seller, it will not be exercised.

Obviously the option buyer is at an advantage here, and this advantage has to be paid for. The option buyer pays a fee to the seller at the outset.

### pricing

For symmetrical derivatives, the contract can (in theory) be set so that the expected present values of the contract to the two counterparties are equal.

For example, in a forward contract, the buyer of the forward pays up front a price equal to the expected discounted present value of the underlying asset on maturity (the agreed future date).

For example, swaps generally involve no (up-front) fee. Suppose, eg., I 'buy' exposure to interest rates (Libor) in a swap. That is, I am receiving libor and paying a fixed rate (or, rather, I am receiving the difference between libor and the fixed rate.) Then you can say that (from my point of view) the fixed rate in the swap is the 'price' I pay for the swap. In an efficient market, this price should be set such that the present value of fixed rate payments over the lifetime of the swap equals the expected present value of the libor-rate payments over that same period.

In a slightly more involved swap, I might be buying exposure to eg. an equity index (equity swap) in return for exposure to interest rates. It is unlikely that the expected present value of the index-based payments will not equal the epv of the interest rate. I will thus pay a premium (or discount) to equalise the two sides: eg. I pay libor + x%.

Because of the asymmetry, options pricing is a bit more complex ...

### market structures

Derivatives exchanges are public markets for trading more standardised futures and options. These are highly liquid markets - sometimes more so than the underlying assets themselves.

'Over the counter' derivatives are tailored contracts between two counterparties, generally set up by an arranging *InvestmentBank*. Less standard futures and options, and all swaps, are traded OTC.

The ISDA (International Swaps and Derivatives Association) approves model contract structures for OTC derivatives.

As above, derivatives contracts are set up initially to (in theory) equalise the value of both sides of the contract. These calculations incorporate expectations hed at the time the contract is arranged about future price movements. Over time these expectations may change. So if a *SecondaryMarket* exists, the contract can be traded on for a premium/discount.

### agents

Like any securities, derivatives are part of the choice set of investors looking to maximise risk-adjusted returns on their portfolios. Investors who would anyway be looking to invest in particualr underlying assets might prefer to use derivatives to get exposure to the same assets - eg. if derivatives have less transaction costs, the derivative market is more liquid. But some special types of derivative counterparties are often identified.

'Hedgers' are agents using derivatives to reduce or balance their exposure to particular risks. For example, the corporate who has to pay back a loan at a given interest rate, but is worried about rate rises, can pass on interest rate risk through a swap. Effectively it is now paying the loan at a fixed rate.

'Speculators', in contrast, are investors using derivatives just to make money in their own right, not because of any risk management concerns. In some contexts, hedgers are praised - they are using derivatives for legitimate reasons; whilst speculators are chastised. Commentators fear that naughty speculators (eg. Nick Leeson) exploit the fiendish complexity of derivatives to hide their crimes or losses. Or they might get hooked on risk, threatening to gamble the whole financial system into crisis. Contrarily, amongst derivatives market players there is often a recognition that speculators play a vital role boosting liquidity in the markets. In particular, you need agents willing to take both sides of a derivatives contract, without more 'speculative' investors hedgers might not find anybody to buy their risk.

DariusSokolov

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