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Bernoulli speculator and trading strategy risk

✍ Scribed by Abraham Lioui; Professor Patrice Poncet


Book ID
101322833
Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
115 KB
Volume
20
Category
Article
ISSN
0270-7314

No coin nor oath required. For personal study only.

✦ Synopsis


In a continuous-time model of a complete information economy, we examine the case of a "pure" speculator who chooses to trade only on forward or futures contracts written on interest-rate-sensitive instruments. Assuming logarithmic utility, we assess whether his strategy exhibits the same structure as when he uses primitive assets only. It turns out that when interest rates follow stochastic processes, as in the model of Heath, Jarrow, and Morton (1992), where the instantaneous forward rate is driven by an arbitrary number of factors, the speculative trading strategy involving forwards exhibits an extra term vis-a-vis the one using futures or primitive assets. This extra term, different from a Merton-Breeden dynamic hedge, is novel and can be interpreted as a hedge against an "endogenous risk," namely the interest-rate risk brought about by the optimal trading strategy itself. Thus, only the strategy using futures (or the cash assets themselves) involves a single speculative term, even for the Bernoulli speculator. This result illustrates another major aspect of the marking to market feature that differentiates futures and forwards, and thus has some bearing on the issue of the optimal design of financial contracts. Real financial markets being, in fact, incomplete, the additional "endoge-We are grateful to an anonymous referee and to the Editor for their comments and suggestions. The usual caveat of course applies.


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