Arbitrage-Free Pricing Before and Beyond Probabilities

Arbitrage-Free Credit Pricing Using Default Probabilities and Risk Sensitivities

The relation between physical probabilities (rating) and risk-neutral probabilities (pricing) is derived in a large market with a quasi-factor structure. Factor sensitivities and default probabilities can be estimated for all kinds of credits on historical rating data. Since factor prices are obtainable from market data, the model allows the pricing of non-marketable credits and structured prod...

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

Pricing by hedging and no-arbitrage beyond semimartingales

We show that pricing a big class of relevant options by hedging and noarbitrage can be extended beyond semimartingale models. To this end we construct a subclass of self-financing portfolios that contains hedges for these options, but does not contain arbitrage opportunities, even if the stock price process is a nonsemimartingale of some special type. Moreover, we show that the option prices de...

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...