We examine the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel markets. We propose that the market is incomplete and postulate the existence of an intrinsic risk in every contingent claim as a basis for understanding the phenomena. In a continuous time framework, we bring together the notion of intrinsic risk and the martingale theory to derive a martingale measure, namely risk-subjective measure, for pricing and hedging financial derivatives. The risk-subjective measure provides an internal consistency in pricing and hedging contingent claims and  explains the phenomena.
We examine the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel markets. We propose that the market is incomplete and postulate the existence of an intrinsic risk in every contingent claim as a basis for understanding the phenomena. In a continuous time framework, we bring together the notion of intrinsic risk and the martingale theory to derive a probability measure, namely risk-subjective measure, for pricing and hedging financial derivatives. The risk-subjective measure provides an internal consistency in pricing and hedging contingent claims and importantly explains the phenomena.
R
martingale
probability
A
importantly