An Axiomatic Framework for No-Arbitrage Relationships in Financial Derivatives Markets ∗

No-arbitrage relationships are statements about prices of financial derivative contracts that follow purely from the assumption that no market participant can make a risk-free profit. They are a fundamental tool of modern finance and basis to all modern market models. The ever-growing complexity of financial derivatives impairs the effectiveness of conventional approaches based on expected payments for understanding these relationships. In this paper, we introduce the Logic Portfolio Theory (LPT), a new framework in typed first-order logic with higher-order functions that allows users to prove no-arbitrage relationships based on the syntactic structure of contracts. We first show that LPT is rich enough to replace informal or stochastic arguments by proving the well-known put-call parity and Merton’s theorem inside the theory. This also yields the most general versions of these no-arbitrage relationships to date. We second show that LPT is general enough to encompass both a simple stochastic model and a purely cash flow oriented model.