Risk Latte - BJN Approach to Option Pricing

BJN Approach to Option Pricing

Rahul Bhattacharya
Aug 5, 2006

In 1996 Britten-Jones and Neuberger (BJN) introduced a novel way of looking at the problem of option pricing. Their approach highlighted the special role that quadratic variation plays in option pricing.

In BJN approach - numerically implemented through a BJN tree - the upper and the lower rational bounds for the price of an option, or any other contingent claim, is established under various scenarios where obtaining a unique price of the option via risk neutral replication in not possible. BJN option prices have very tight upper and lower bounds and the width of the bounds have a continuous dependence on a certain parameter in the model. As this parameter becomes small, the width of the bounds shrinks as well and finally at zero value the Black-Scholes value is recovered. One novelty of the approach is that the BJN model does not require a priori knowledge of whether the process is diffusion, jump-diffusion or a pure jump process; and the model also does not require that the volatility be deterministic. All the model stipulates is that the quadratic variation of the process over a finite time interval should be exactly known. Actually, this assumption is both the attraction and the limitation of the model.

We found the approach quite interesting and novel, especially the concept of mapping the "residual volatility" (as defined in the model) while building a BJN tree. It should however, be noted, that the practical application of this approach for option pricing is limited.

Reference : We would like to refer the reader to an excellent book by Riccardo Rebonato ("Volatility and Correlation, 2 nd Edition, John Wiley & Sons) which deals with this subject in great detail

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