Intrinsic Prices of Risk

Journal of Mathematical Finance Vol.4 (5) 2014, 318--327

11 Pages Posted: 12 Mar 2014 Last revised: 5 Dec 2014

Date Written: February 28, 2014


We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent claim as a basis for understanding these phenomena. In a continuous time framework, we bring together the notion of intrinsic risk and the theory of change of measures to derive a probability measure, namely risk-subjective measure, for evaluating contingent claims. This paper is a modest attempt to prove that measure of intrinsic risk is a crucial ingredient for explaining these phenomena, and in consequence proposes a new approach to pricing and hedging financial derivatives. By adapting theoretical knowledge to practical applications, we show that our approach is consistent and robust, compared with the standard risk-neutral approach.

Keywords: Implied volatility, convexity adjustment, primary and parallel markets, incomplete markets, intrinsic risk, risk-neutral measure, risk-subjective measure, fair valuation, delta-hedging.

JEL Classification: E43, E44, G13, G14, G15

Suggested Citation

Le, Truc, Intrinsic Prices of Risk (February 28, 2014). Journal of Mathematical Finance Vol.4 (5) 2014, 318--327. Available at SSRN: or

Truc Le (Contact Author)

Independent ( email )

No Address Available

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