Peter Laurence's publications in Mathematical Finance


  • Books

    Quantitative Modeling of Derivative Securities : From theory to Practice,'' by Marco Avellaneda and Peter Laurence CRC Press- Chapman Hall, 1999.

    Articles

         P. Laurence, E. W. Stredulinsky, A comparison principle for an American option on several assets: Index and spread options Electronic Journal of Differential Equations, 2003

    • The method of symmetrization to obtain a reduced problem for the valuation of american options on multiple assets.


  • P. Laurence, TH Wang, What's a basket worth? Risk Magazine, February 2004

    • Optimal upper and lower bounds and hedging ratios in closed form when hedging with calls on single name options and cash


  • P.M. Laurence and TH Wang, Sharp Upper and Lower Bounds for Basket Options Paper

    • Enlarged version of Risk paper, including optimal discrete solutions in the two asset case.
    Appeared in Applied Mathematical Finance.


  • D. Hobson, P. Laurence, TH Wang, Static arbitrage upper bounds for the prices of basket options Paper

    • Optimal model independent upper bounds and hedging strategies when hedging with all available options on each component and cash.
    Appeared in Quantitative Finance 2005.


  • D. Hobson, P. Laurence, TH Wang, Static arbitrage optimal sub-replicating strategies for basket options Paper

    • Optimal lower bounds for basket options assuming a continuum of strikes. A striking class of alternating long and short positions in suitably chosen strikes. Appeared in Insurance Mathematics and Economics 2005.


  • P. Carr and P. Laurence, Multi-asset local stochastic variance

    • Featuring an extension of Breeden and Litzenberger to basket options and the exploration of multi-asset local variance contracts and the PDE's to describe them. To appear in Mathematical Finance.
  • A non technical, unpublished discussion of the method in [HLW1] super-replicating strategies for basket options here.


  • P. Laurence, TH. Wang, Closed form solutions for quadratic and inverse quadratic term structure models.

    • Featuring the use of Lie Groups to construct solutions in closed form for models of the term structure. Available here . Appeared in 2005 in International Journal of Theoretical and Applied Finance 2005.

  • P. Carr, P. Laurence, TH. Wang, Generating Integrable one dimensional Diffusions.

    Available here . Featuring a necessary and sufficient criterion on a time and state dependent volatility coefficient to generate a diffusion with a 4 dimensional symmetry group and a procedure for determining broad families of new diffusions of this sort. A shorter version has appeared in Comptes Rendus de l'Academie des Sciences.

  • Peter Laurence and Tai-Ho Wang, Distribution free bounds for spread options and market implied antinomonotonicity gap,

    • (first version Nov. 2006) published online in European Journal of Finance, download here. This paper extends earlier results to the so-called generalized spread options and introduces a new measure of dependence of assets in a basket, the co and antimonotonicity gaps.

  • Peter Laurence and Tai-Ho Wang, Distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios,

    • publsihed online in: Insurance Mathematics and Economics. This paper extends earlier results in both the discrete and in the continuous case to spread options. In addition it explores the application of the co and anti-monotonicity gap introduced in an earlier paper to real data on the Nymex crack spread option.

  • Peter Laurence and Sandro Salsa, Regularity of the free boundary of an american option on several assets, accepted for publication in Communications on Pure and Applied Mathematics, June 2008.

    • This paper establishes for the first time the C-infinity regularity of the free boundary for an american option on n-assets, in the multivariate Black-Scholes setting, for a broad class of payoffs arising in mathematical finance, such a call or put on an index. It thus settles a long standing open problem in this field, at least in the Black-Scholes setting.

  • Tai-Ho Wang, Peter Laurence and Shen-Li Wang, Generalized SABR MODELS with a high degree of symmetry

    , submitted to Quantitative Finance, July 2007. This paper provides a complete classification of the symmetry group for a broad class of generalized SABR models, in the uncorrelated case.

  • Peter Laurence, Tai-Ho Wang and Luca Barone. "Geometric Properties of Multivariate correlation in De Finetti's approach to insurance theory".

    This publication is in two parts: a translation by Luca Barone and mine of a lost paper by de Finetti, that was never translated into English, until now and contains several interesting ideas. The second part is a commentary by the three of us on de Finetti's paper, in which we put the results into a modern context and supply some missing proofs. To appear in Journal Electronique de l'histoire de la Probabilite et de la Statistique".

  • Gerard Ben Arous, Peter Laurence, Tai-Ho Wang, `` Can you hear the curvature of the market''

    In preparation.