morning snapshot | 05 august 2010

August 5, 2010
  • Measuring and marking counterparty risk (Eduardo Canabarro, Darrell Duffie, 2003)  – addressing counterparty default risk in OTC contracts. Periodically exchanging collateral in the mark-to-market sense reduces this risk, but unlike futures contracts there are no daily-settlements. OTC-traded Credit Default Swaps on subprime mortgages are a classical example of real-world counterparty defaults. Collateral agreements are essential in reducing risks – but they affect liquidity. Dealers use various systems for tracking and estimating PFE (potential future exposure). What are the right tools for modelling PFE for each OTC contract ?
  • Option Pricing and the Dirichlet problem (Mark Joshi) – classical “finding function that satisfies boundary conditions of given PDE” on Laplace equation. Introducing potential financial interpretations.
  • Kakutani’s fixed point theorem – sufficient conditions for a set-valued function defined on convex, compact subset of Eucledian space to have a fixed point.
  • quantlib : stochastic processes | geometric Brownian motion:
    dS(t, S)= \mu S dt + \sigma S dW_t.
  • quantlib : stochastic processes | Bates process:
        //! Square-root stochastic-volatility Bates process
        /*! This class describes the square root stochastic volatility
            process incl jumps governed by
            \f[
            \begin{array}{rcl}
            dS(t, S)  &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\
            dv(t, S)  &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\
            dW_1 dW_2 &=& \rho dt \\
            \omega(J) &=& \frac{1}{\sqrt{2\pi \delta^2}}
                          \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right]
            \end{array}
            \f]
            \ingroup processes
        */
    
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