## Archive for August, 2010

August 29, 2010

Interesting topic : analyitical derivation market deadlock scenarios. Current regulatory logic revolves around idea of optimal capital requrements and periodical system stress-testing. A question is – can we come up with a analytical model of total set of all possible positions, under set of constraints, such as total liquidity available, maximum risk tollerance, etc. For example, model could be represented as “cross-position matrix” to which we could apply analytical tools such as independence-analysis, eigenvector partitioning, etc.

Another idea : weighted-graph-representation of pre-clearing positions between financial intermediaries, graph partitioning, spectral clustering, complexity, etc. Financial system micro-modelling using CS artillery.

### The CAP Theorem :: presentation

August 28, 2010

Here are the slides of presentation I recently gave on CAP Theorem and corresponding proof by Nancy Lynch and Seth Gilbert:

August 25, 2010

August 14, 2010

### P !=(?) NP week

August 11, 2010

P != NP “proof” buzz week in links:

August 7, 2010

August 6, 2010

### 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
*/


### daily snapshot | 04 august 2010

August 4, 2010
• Pricing / validating prices of new options using regression analysis ? Black-Scholes pricing essentially represents non-linear relationship between option price and price determinants (time to maturity, spot price, strike price, risk free rate, volatility + quantiles of normal distribution)
• The question is using option market trade data to create nonlinear model of this dependency – predict future prices using regression , calculate BS prices and compare values with actual traded prices.
• Computational Complexity and Information Asymmetry in Financial Products
• Thirty Books Everyone Should Read Before They’re Thirty – interesting selection
• Use and abuse of dummy variable regression – differences between regression trees and single regression with dummies ? The danger of perfect collinearity with large number of boolean dummy variables.