Chapter 28
The No-Arbitrage Condition in Financial Engineering: Its Use and Misuse
INTRODUCTION
Valuation techniques used in financial engineering typically incorporate two fundamental assumptions regarding investor behavior. The first is that investors prefer more wealth to less, and will take actions to maximize future wealth. The second is that investors have an aversion to risk, which leads them to make trade-offs between expected future wealth and uncertainty (or risk) concerning future wealth.
The “preference of more to less” assumption is analytically quite tractable. Intuitively, it seems reasonable as a broad generalization, and the notion of wealth maximization can be well defined quantitatively. In contrast, the risk aversion assumption is much less tractable. It is somewhat less appealing as a broad generalization, but, more significantly, the notion of risk aversion can neither be defined unambiguously nor measured in a straightforward manner. As a consequence, valuation techniques that are able to rely solely on the first assumption have proven to be much more effective in practice than techniques that must also rely on the second assumption.
However, as powerful as these valuation approaches have proven to be in practice, there are certain limitations to their effectiveness that tend to magnify in times of market dislocation. In addition to the investor behavior assumption, these approaches also require a range of other conditions ...
