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Towards Exact Nonextensive Solutions of the American Style Options 4: Infinitesimal Linear Evolution of the Early Exercise Premium with Respect to the American Derivative Can Lead to Black-Scholes Like Closed Form Solutions.

Fredrick Michael

posted on 25 February 2019

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(*A version of this research has recently been published in Physica A vol 550 pgs 124379 date 2020/7/15 and includes numerical results)

We have recently applied several different approaches [5] towards understanding the American style

derivative random boundary and inequality problems and towards possible solutions.

In this letter we present a fourth discussion and result(s). We specifically focus on the early exercise

(risk) premium, this a monetary measure of the early exercise source of secondary non-market

uncertainty, and utilize this idea of monetary valuation of non-market early exercise uncertainty

(risk) to overcome the inequality portfolio and inequality PDE problem. We do this by relating the

equality portfolio of the European style derivative to the American style directly via the A-E=p relation

between American and European derivatives. We furthermore under an assumption of linear variation of

early exercise premium with respect to American option derive an American Black-Scholes like PDE

model and obtain a closed form solution for the same which parallels the traditional Black-Scholes formula.



Feedback appreciated. Serious comments only please.

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