Title: Arbitrage-Free Derivatives Pricing in Nonlinear Markets

Speaker: Prof. Marek Rutkowski,Professor of Financial Mathematics, The University of Sydney, Australia

Time: 14:30, November 3, 2016

Location: Room B1238, ZhiXin Building, Central Campus

Abstract: We study arbitrage-free pricing of financial derivatives in the presence of funding costs,the counterparty credit risk and market frictions affecting the trading mechanism, such as collateralization and capital requirements. We extend in several respects the nonlinear pricing approach developed in El Karoui and Quenez (1997) and El Karoui et al. (1997). The issues of the existence of arbitrage opportunities for the hedger and for the trading desk in a nonlinear trading framework are examined. We introduce the concept of no-arbitrage with respect to the null contract and a stronger notion of no-arbitrage for the trading desk. We then proceed to the issue of unilateral fair valuation of a given contract by the hedger endowed with an initial capital. A link between the concept of no-arbitrage for the trading desk and the financial viability of prices computed by the hedger is examined. Next, we introduce and analyze the concept of a regular market model, which extends the concept of a non-linear pricing system in El Karoui and Quenez (1997). The goal is to identify a class of models, which are arbitrage-free for the hedger and, in addition, have the desirable property that for contracts that can be replicated, the replication cost is also the fair price for the hedger. Finally, we discuss the BSDE approach to the valuation and hedging of contracts in a model with differential funding rates, the counterparty risk and trading adjustments and illustrate this approach using also results from Dumitrescu et al. (2015).