Derivatives Models on Models

13

Space-time Finance the Relativity Theory's Implications for Mathematical Finance^*

Little or nothing is written about the relativity theory in relation to mathematical finance. I will here explore the relativity theory's implications for mathematical finance. One of the main results of my reflections on this topic is that the volatility σ is different for every observer. However, what we will call volatility-time σ√T is invariant, that is the same for any observer. Further, we will see how the relativity theory will lead possibly to fat tailed distributions and stochastic volatility. Parts of the chapter are admittedly speculative, but not even mathematical finance can escape the fundamental laws of physics.

1 Introduction

The wind was blowing through my hair, I was pushing my Harley to the limit. At 120 miles per hour the 50 mile trip felt like nothing, I slowed down and stopped in front of my girlfriend. She had been waiting on the side walk with a clock that we had synchronized with my wristwatch just before the ride. She gave me her clock. I compared it with my wristwatch. Huh, they showed exactly the same time, not even one hundredth of a second in difference, where was the time dilation? Well, this was some years ago, before I understood that my bike actually hardly moved and that my wristwatch was not accurate enough to measure the slight time dilation that should have been there as predicted by the special theory of relativity.

Einstein's special and general relativity ...