Derivatives Models on Models

12

Frozen Time Arbitrage^*

Received 29 February 2100Revised 2 March 1999

The distinction between past, present, and future is only an illusion, even if a stubborn one.

Albert Einstein

Time is money. In finance time plays an essential role in everything from calculating how much interest is earned on your bank account to discounting uncertain cash flows, using the most sophisticated option formulas.¹ Unlike physicists, finance plodders always consider the speed of time as given,² something they can simply read off the calendar. But time is relative. This and many other aspects of the time have been ignored in finance literature, and with this chapter I intend to focus on time itself.

From Einstein's relativity theory we know that time exists as part of space-time. According to Einstein, the flow of time is affected by gravity and how fast we move with respect to the speed of light in a vacuum. Hundreds of books and papers have been written about the theory of relativity, and the main reason why it is ignored so entirely in finance is probably that with today's technology it has a negligible effect on practical financial calculations. To manipulate time according to Einstein's theory of relativity with any significance for financial calculations, we would need to travel close to the speed of light, or alternatively we would need to be close to a massive gravitation source, for example the Trump Tower or a Black-Hole. More on this later.

But there is another way. Using modern technology ...