Tenor Specific Pricing

Abstract

Observing that pure discount curves are now based on a variety of tenors giving rise to tenor specific zero coupon bond prices, the question is raised on how to construct tenor specific prices for all financial contracts. Noting that in conic finance one has the law of two prices, bid and ask, that are nonlinear functions of the random variables being priced, we model dynamically consistent sequences of such prices using the theory of nonlinear expectations. The latter theory is closely connected to solutions of backward stochastic difference equations. The drivers for these stochastic difference equations are here constructed using concave distortions that implement risk charges for local tenor specific risks. It is then observed that tenor specific prices given by the midquotes of bid and ask converge to the risk neutral price as the tenor is decreased and liquidity increased when risk charges are scaled by the tenor. Square root tenor scaling can halt the convergence to risk neutral pricing, preserving bid ask spreads in the limit. The greater liquidity of lower tenors may lead to an increase or decrease in prices depending on whether the lower liquidity of a higher tenor has a mid quote above or below the risk neutral value. Generally for contracts with a large upside and a bounded downside the prices fall with liquidity while the opposite is the case for contracts subject to a large downside and a bounded upside.