Arbitrage Opportunities in Arbitrage-Free Models of Bond Pricing

Arbitrage-free pricing of XVA

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...

From arbitrage to arbitrage-free implied volatilities

We propose a method for determining an arbitrage-free density implied by the Hagan formula. (We use the wording “Hagan formula” as an abbreviation of the Hagan– Kumar–Leśniewski–Woodward model.) Our method is based on the stochastic collocation method. The principle is to determine a few collocation points on the implied survival distribution function and project them onto the polynomial of an ...

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...

Arbitrage and investment opportunities

We consider a model in which any investment opportunity is described in terms of cash flows. We don’t assume that there is a numéraire, enabling investors to transfer wealth through time; the time horizon is not supposed to be finite and the investment opportunities are not specifically related to the buying and selling of securities on a financial market. In this quite general framework, we sh...