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  • 1
    Electronic Resource
    Electronic Resource
    A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We present here the quantization method which is well-adapted for the pricing and hedging of American options on a basket of assets. Its purpose is to compute a large number of conditional expectations by projection of the diffusion on optimal grids designed to minimize the (square mean) projection error (Graf and Luschgy 2000). An algorithm to compute such grids is described. We provide results concerning the orders of the approximation with respect to the regularity of the payoff function and the global size of the grids. Numerical tests are performed in dimensions 2, 4, 5, 6, 10 with American style exchange options. They show that theoretical orders are probably pessimistic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2005.00213.x
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    DERIVATIVE ASSET PRICING WITH TRANSACTION COSTS (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 2 (1992), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In the modern theory of finance, the valuation of derivative assets is commonly based on a replication argument. When there are transaction costs, this argument is no longer valid. In this paper, we try to address the general problem of finding the optimal portfolio among those which dominate a given derivative asset at maturity. We derive an interval for its price. the upper bound is the minimum amount one has to invest initially in order to obtain proceeds at least as valuable as the derivative asset. the lower bound is the maximum amount one can borrow initially against the proceeds of the derivative asset. We show that, in some instances, this interval may be strictly bounded above by the price of the replicating strategy. Prima facie, the cost of a dominating strategy should appear to be higher than that of the replicating one. But because trading is costly, it may pay to weigh the benefits of replication against those of potential savings on transaction costs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1992.tb00039.x
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  • 3
    Electronic Resource
    Electronic Resource
    First-Order Schemes in the Numerical Quantization Method (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The numerical quantization method is a grid method that relies on the approximation of the solution to a nonlinear problem by piecewise constant functions. Its purpose is to compute a large number of conditional expectations along the path of the associated diffusion process. We give here an improvement of this method by describing a first-order scheme based on piecewise linear approximations. Main ingredients are correction terms in the transition probability weights. We emphasize the fact that in the case of optimal quantization, many of these correcting terms vanish. We think that this is a strong argument to use it. The problem of pricing and hedging American options is investigated and a priori estimates of the errors are proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.t01-1-00002
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    Paper (German National Licenses)
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