Risk 2002 Europe: Derman highlights new behavioural finance direction

Traditional Black-Scholes theory uses the idea of constructing a replicating portfolio of securities with known prices to value a risky asset. But most risky assets cannot be replicated, even in theory, Derman told delegates at Risk 2002 Europe.

As an alternative to replication, Derman presented a different kind of model that uses the concept of intrinsic time – a dimensionless timescale that counts the number of trading opportunities that occur, rather than the calendar time that passes between them. “I hope this model will have some relevance to the behaviour of investors expecting inordinate returns in highly speculative markets,” he said.

The model’s construction is inspired by thermodynamics: Derman wanted to show how macroscopic results about financial risk can be obtained from a few basic principles, similar to the way in which large-scale properties such as an object’s temperature arise from simple interactions between atoms.

During periods of speculation, market participants such as day traders instinctively focus on the flow of trading opportunities - suggesting that intrinsic time is a more appropriate timescale on which to formulate models.

This rationale naturally leads to the concept of the temperature of a stock – a function of both standard volatility and trading frequency. The ‘hotter’ a stock is, the higher its expected returns. The theory of intrinsic time can also be extended to include options valuation and perhaps even account for part of the volatility skew, Derman claimed.