Sunday, December 19, 2010

Merton's Jump Diffusion Model: market completeness etc.

Recall:
Existence of martingale measure <=> no-arbitrage
Uniqueness of martingale measure <=> market completeness

When there are jumps, the market is no longer complete because the jump process 'creates' many more states so that the number of asset becomes too few. Hence we are left with the unknown "market price of jump risk". Merton proposes that this price of risk should be zero because the jump in a stock is non-systematic, i.e. diversifiable.

Note that empirical study suggests that Merton's assumption is quite wrong.

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