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We introduce an innovative theoretical framework for the valuation and replication of derivative transactions between defaultable entities based on the principle of arbitrage freedom. Our framework extends the traditional formulations based on credit and debit valuation adjustments (CVA and DVA). Depending on how the default contingency is accounted for, we list a total of ten different structuring styles. These include bi-partite structures between a bank and a counterparty, tri-partite structures with one margin lender in addition, quadripartite structures with two margin lenders and, most importantly, configurations where all derivative transactions are cleared through a central counterparty (CCP). We compare the various structuring styles under a number of criteria including consistency from an accounting standpoint, counterparty risk hedgeability, numerical complexity, transaction portability upon default, induced behaviour and macro-economic impact of the implied wealth allocation. -- Counterparty credit risk ; CVA ; DVA ; margin lending ; securitisation ; Basel III ; CCP ; clearing ; collateral ; OTC

In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced,
as one of the listed products, options on its implied volatility index (VIX).
This created the challenge of developing a pricing framework that can simultaneously handle European options, forward-starts, options on the realized variance and options on the VIX. In this paper we propose a new approach to this problem using spectral methods. We use a regime switching model with jumps and local volatility defined in [1] and calibrate it to the European options on the S&P 500 for a broad range of strikes and maturities. The main idea of this paper is to "lift" (i.e. extend) the generator of the underlying process to keep track of the relevant path information, namely the realized variance. The lifted generator is too large a matrix to be diagonalized numerically. We overcome this difficulty by applying a new semi-analytic algorithm for block-diagonalization. This method enables us to
evaluate numerically the joint distribution between the underlying stock price and the realized variance, which in turn gives us a way of pricing consistently European options, general accrued variance payoffs and forward-starting and VIX options.