THE PURPOSE OF THIS CHAPTER

This is not going to be a chapter that will set pulses racing, but it is a useful one. In it we define the financial quantities that we are going to use in the book, we fix our vector notation and we try to clarify possible sources of notational confusion.

We also present (in the appendices at the end of the chapter) some elementary mathematical results that we shall use throughout the book.

THE BUILDING BLOCKS

Arbitrage

For the purposes of this book, an arbitrage is a strategy that is too good to be true – and, therefore, one that in an efficient market does not exist.

A bit more precisely, one says that a strategy is an arbitrage if it costs nothing to set up, if it never produces a negative payoff, and if in at least one possible state of the world it produces a strictly positive payoff.

It pays to look at the definition carefully. First we require that the strategy should cost nothing to set up. Very often, when we buy an asset and sell another to crystallize the value of an arbitrage strategy, the resulting portfolio will not be self-financing – which means that the proceeds from the sale of the asset we are shorting will not exactly match the cost of the asset we want to buy. This means that we must either borrow or lend some money. Since the interest on the borrowing or lending up to the end of the investment horizon of the strategy must be locked in for the strategy to be an arbitrage (why?), this means that we must buy or sell a discount bond. The price of this discount bond is the ‘balancing item’ that makes the initial set-up cost of the portfolio equal to zero.