Cristin Buescu

Counterparty Risk Pricing: Impact Of Closeout And First-To-Default Times

In the absence of a universally accepted procedure for the credit valuation adjustment (CVA) calculation, we compare a number of different bilateral counterparty valuation adjustment (BVA) formulas. First we investigate the impact of the choice of the closeout convention used in the formulas. Important consequences on default contagion manifest themselves in a rather different way depending on which closeout formulation is used (risk-free or replacement), and on default dependence between the two entities in the deal. Second we compare the full bilateral formula with an approximation that is based on subtracting two unilateral credit valuation adjustment (UCVA) formulas. Although the latter might be attractive for its instantaneous implementation once one has a unilateral CVA system, it ignores the impact of the first-to-default time, when closeout procedures are ignited. We illustrate in a number of realistic cases both the contagion effect due to the closeout convention, and the CVA pricing error due to ignoring the first-to-default time.

A Note on the Effects of Taxes on Optimal Investment

We integrate two approaches to portfolio management problems: that of Morton and Pliska (1995) for a portfolio with risky and riskless assets under transaction costs, and that of Cadenillas and Pliska (1999) for a portfolio with a risky asset under taxes and transaction costs. In particular, we show that the two surprising results of the latter paper, results shown for a taxable market consisting of only a single security, extend to a financial market with one risky asset and one bond: it can be optimal to realize not only losses but also gains, and sometimes the investor prefers a positive tax rate.

Funding, repo and credit inclusive valuation as modified option pricing

We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear mathematical problem features semilinear PDEs and FBSDEs. We show that for the benchmark vulnerable claim there is an analytical solution, and we express it in terms of the Black-Scholes formula with dividends. This allows for a detailed valuation analysis, stress testing and risk analysis via sensitivities.

A Note On The Self-Financing Condition For Funding, Collateral And Discounting

We present the derivation of the self-financing condition used in a derivative pricing framework with funding, collateral and discounting. This is done in a way that clarifies the structure of the relevant funding accounts. This clarification is achieved by properly distinguishing between price processes, dividend processes and gains processes. Without this explicit distinction, the resulting self-financing condition can be erroneous, as we illustrate in the case of two papers: Piterbarg (2010) and Burgard & Kjaer (2011a). In these papers, the self-financing condition is equivalent to assuming that a subportfolio is self-financing on its own and without including the cash position. We show that the final result in Piterbarg (2010) is correct, even if the related self-financing condition is not. In the process, we raise a further question on the supplementary source of randomness in the funding rate dynamics that has no hedging counterpart in the replicating portfolio.

An application of the method of moments to range-based volatility estimation using daily high, low, opening, and closing (HLOC) prices

We use the expectation of the range of an arithmetic Brownian motion and the method of moments on the daily high, low, opening, and closing prices to estimate the volatility of the stock price. This novel theoretical approach results in an estimator that is genuinely range-based on daily opening, high, low and closing data, unlike current estimators in the literature. The daily price jump at the opening is considered to be the result of the unobserved evolution of an after-hours virtual trading day. In comparison to an existing drift-independent estimator, we find that our estimator is actually more efficient when using a smaller number of data points, while for a larger number of points the efficiency of our estimator stays above 99% of the existing one. A toy example that uses this method to take advantage of mispricing opportunities in the options market illustrates potential applications of this method to algorithmic trading.