Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimizing the entropy of the price measure from the economic measure, subject to mark-to-market...

Option pricing is the most elemental challenge of mathematical finance. Knowledge of the prices of options at every strike is equivalent to knowing the entire pricing distribution for a security, as derivatives contingent on the security can be replicated using options. The available data may be...

Mathematical finance explores the consistency relationships between the prices of securities imposed by elementary economic principles. Commonplace among these are replicability and the absence of arbitrage, both essentially algebraic constraints on the valuation map from a security to its...

Mathematical finance explores the consistency relationships between the prices of securities imposed by elementary economic principles. Commonplace among these are replicability and the absence of arbitrage, both essentially algebraic constraints on the valuation map from a security to its...

This article describes the expectation and measure groups of the quadratic Gaussian algebra, and consider their application in the pricing of interest rate and cross asset derivatives. The discussion is motivated by the desire to construct consistent, arbitrage-free, term structure pricing...

For much of 2009 there was a static arbitrage in Euro CMS spread options, a consequence of the dislocation between the markets for options on CMS rates and CMS spreads. High volatility of volatility in the vanilla rates market pushed up the prices of long-dated CMS rate options, as these options...

For much of 2009 there was a static arbitrage in Euro CMS spread options, a consequence of the dislocation between the markets for options on CMS rates and CMS spreads. High volatility of volatility in the vanilla rates market pushed up the prices of long-dated CMS rate options, as these options...

Classical measure underpins the foundations of financial derivative pricing, as the classical expectation satisfies the essential principles of replicability (linearity) and no-arbitrage (positivity) required by any reasonable pricing model. Quantum measure extends this by allowing payoffs to be...

Collateral discounting recognises the value of funding for derivatives, which has gained prominence in recent years as basis spreads have widened in response to the financial crises. This article considers the impact of collateral volatility on discount factors and Libor and FX forwards, and...

Classical measure underpins the foundations of financial derivative pricing, as the classical expectation satisfies the essential principles of replicability (linearity) and no-arbitrage (positivity) required by any reasonable pricing model. Quantum measure extends this by allowing payoffs to be...