2. Mechanics of Financial Instruments#
2.1. Introduction#
As discussed in the previous chapter, a financial instrument is a exchangeable contract that specifies the conditions for the transfer of funds between two parties, namely amounts exchanged, times, clauses and rights, among others. Given the multiple objectives of the parties both issuing and acquiring them, it is not surprising that a lot of innovation has been done around financial instruments.
Classical financial instruments like stocks and bonds articulate the concept of funding corporations and governments (not stocks), the former in exchange of ownership and a share of profits (reinvested or in form of dividends), the latter purely in terms of a fixed periodic income and the promise of returning the funds in a specified time.
Derivatives markets take innovation a step further, providing a lot of customization to accommodate specific needs of market participants in terms of speculation or risk management.
2.2. Stocks#
2.3. Bonds#
2.4. Derivatives#
Derivatives are financial instruments whose value depends on the price of an underlying instrument, hence the name “derivative”.
2.4.1. Linear derivatives: Forwards, Futures and ETFs#
2.4.2. Options#
Options are derivatives contracts that grant the holder the the option (hence the name) to buy or sell (depending on the option) a given financial instrument (the underlying) at a price at time contingent to the clauses of the contract. The most simple option, the European option, pre-specifies a given time \(T\), the expire, and price \(K\), to exercise this option. But there are many other variations in the market. An option to buy a financial instrument is referred as a call option, and an option to sell is a put option.
Let us consider european options of stocks. If the market price of the stock at the expiry is \(S_T\), a call option will be exercised by a rational investor only if the price is higher than the strike \(K\), making a profit of \(S_T-K\), which in some cases is directly paid in cash, in others the actual stock is received, but of course it could be directly sold in the market at a favorable price. Therefore, the payoff of a call option can be written as:
where \((.)^+\) denotes the positive part of the argument. On the contrary, a put option will only be exercised if the market price is below the strike, hence the payoff is:
Options can be traded in regulated markets or be quoted by bank dealers. Since the investor that holds the option cannot lose money from it, such option does not come for free, and the question is how much is worth such option, which is called the premium of the option. At expiry, the price is naturally the payoff function. What at at time \(t < T\) there is still uncertainty about the price \(S_T\) which will determine the final profit (if any), so the premium will be different. But how much? That is the subject of the theory of option pricing.