Browsing by Subject "Incomplete markets"

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    Measures of model uncertainty and calibrated option bounds
    (Taylor & Francis, 2009) Pınar, M. Ç.
    Recently, Cont introduced a quantitative framework for measuring model uncertainty in the context of derivative pricing [Model uncertainty and its impact on the pricing of derivative instruments, Math. Finance, 16(3) (2006), pp. 519-547]. Two measures of model uncertainty were proposed: one measure based on a coherent risk measure compatible with market prices of derivatives and another measure based on convex risk measures. We show in a discrete time, finite state probability setting, that the two measures introduced by Cont are closely related to calibrated option bounds studied recently by King et al. [Calibrated option bounds, Inf. J. Ther. Appl. Financ., 8(2) (2005), pp. 141-159]. The precise relationship is established through convex programming duality. As a result, the model uncertainty measures can be computed efficiently by solving convex programming or linear programming problems after a suitable discretization. Numerical results using S&P 500 options are given.
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    Mixed-integer second-order cone programming for lower hedging of American contingent claims in incomplete markets
    (2013) Pınar, M. Ç.
    We describe a challenging class of large mixed-integer second-order cone programming models which arise in computing the maximum price that a buyer is willing to disburse to acquire an American contingent claim in an incomplete financial market with no arbitrage opportunity. Taking the viewpoint of an investor who is willing to allow a controlled amount of risk by replacing the classical no-arbitrage assumption with a "no good-deal assumption" defined using an arbitrage-adjusted Sharpe ratio criterion we formulate the problem of computing the pricing and hedging of an American option in a financial market described by a multi-period, discrete-time, finite-state scenario tree as a large-scale mixed-integer conic optimization problem. We report computational results with off-the-shelf mixed-integer conic optimization software.