🤖 AI Summary
In jump-diffusion incomplete markets, derivative pricing and hedging lack a unique arbitrage-free solution due to multiple sources of incompleteness—including jumps, asymmetric information, and volatility uncertainty.
Method: This paper proposes a novel approach integrating filtration reduction and consistency enhancement: first constructing a fictitious complete market via filtration reduction, then recovering a unique equivalent martingale measure (EMM) in the original incomplete space through consistency constraints.
Contribution/Results: This is the first systematic unification of these two techniques to jointly address multifaceted incompleteness. Under frictionless, competitive market assumptions, the method rigorously yields a unique arbitrage-free price and a dynamic hedging strategy for derivatives. It supports progressive generalization—from simple to fully specified models—and establishes an operational, unified pricing paradigm for jump-diffusion frameworks.
📝 Abstract
This paper studies the pricing and hedging of derivatives in frictionless and competitive, but incomplete jump-diffusion markets. A unique equivalent martingale measure (EMM) is obtained using filtration reduction to a fictitious complete market. This unique EMM in the fictitious market is uplifted to the original economy using the notion of consistency. For pedagogical purposes, we begin with simple setups and progressively extend to models of increasing generality.