Arbitrage Pricing and Equilibrium Pricing: Compatibility Conditions

Arbitrage and universal pricing

This paper considers two methods for pricing assets and examines the relations between them. The +rst method is based on the principle of no-arbitrage, which asserts that introduction of the new asset should not create an arbitrage in a market that was before arbitrage free. This condition is satis+ed by prices for the new asset between speci+c lower and upper limits, determined as the values o...

Virtual Arbitrage Pricing Theory

We generalize the Arbitrage Pricing Theory (APT) to include the contribution of virtual arbitrage opportunities. We model the arbitrage return by a stochastic process. The latter is incorporated in the APT framework to calculate the correction to the APT due to the virtual arbitrage opportunities. The resulting relations reduce to the APT for an infinitely fast market reaction or in the case wh...

Option Pricing, Arbitrage and Martingales

This paper provides a short introduction into the mathematical foundations of the theory of valuing derivative securities. We discuss the mathematical setting of option price theory and derive the relationship between no-arbitrage and mar-tingales. We provide examples how this theory can be applied to equity and foreign-exchange derivatives. We also explain how the theory can be applied to inte...

No-arbitrage pricing beyond semimartingales

We show how no-arbitrage pricing can be extended to some non-semimartingale models by restricting the class of admissible strategies. However, this restricted class is big enough to cover hedges for relevant options. Moreover, we show that the hedging prices depend essentially only on a path property of the stock price process, viz. on the quadratic variation. As a consequence, we can incorpora...

Arbitrage-free pricing of XVA