Analytical Finance: Volume I by Jan R. M. Röman

Author:Jan R. M. Röman
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

When you cannot hedge. Examples: jump models; default models; transaction costs.

When you model stochastically a quantity that is not traded then the equation governing the pricing of derivatives is usually of diffusion form, with the market price of risk appearing in the “drift” term with respect to the non-traded quantity. To make this clear, here is a general example.

Suppose that the price of an option depends on the value of a quantity of a substance called sepofan. Sepofan is not traded but either the option’s payoff depends on the value of sepofan, or the value of sepofan plays a role in the dynamics of the underlying asset. We model the value of sepofan as

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