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Monte Carlo Pricing
  • Uncertain Volatility Model: A Monte-Carlo Approach The uncertain volatility model has long ago attracted the attention of practitioners as it provides worst-case pricing scenario for the sell-side. The valuation of a financial derivative based on this model requires solving a fully non-linear PDE. One can rely on finite difference schemes only when the number of variables (that is, underlyings and path-dependent variables) is small - in practice no more than three. In all other cases, numerical valuation seems out of reach. In this paper, we outline two accurate, easy-to-implement Monte-Carlo-like methods which hardly depend on dimensionality. The first method requires a parameterization of the optimal covariance matrix and consists in a series of backward low-dimensional optimizations. The second method relies heavily on a recently established connection between second-order backward stochastic differential equations and non-linear second-order parabolic PDEs. Both methods are illustrated by numerical experiments. , J.Guyon, P.H.Labord?re (2010)
  • Monte Carlo Pricing using Operator Methods and Measure Changes A large class of generic stochastic processes which are not necessarily analyti- cally solvable but are still numerically tractable can be described by giving transition probability kernels over a contiguous set of time intervals. From the numerical view- point, this procedure is highly effective on current microchip architectures as kernels can be conveniently evaluated using GPU co-processors and then used for scenario generation while storing them in CPU caches. This paper describes the pricing methodology and a mathematical framework for Finance based on direct kernel ma- nipulations, i.e. operator methods. We also discuss a number of techniques based on measure changes to accomplish tasks such as variance reduction and sensitivity calculations. Numerical experiments are included along with performance bench- marks. Source code is distributed separately online under GPL license in a library named OPLib. , C.Albanese, H.Li (2009)
  • Quantitative Finance Collector This document is an index with different piece of codes you can find on the web , (2009)
  • Efficient, Almost Exact Simulation of the Heston Stochastic Volatility Model , A.V.Haastrecht, A.Pelsser (2008)
  • Efficient Simulation of the Heston Stochastic Volatility Model , L.Andersen (2006)
  • Fast strong approximation Monte-Carlo schemes for stochastic volatility models , C.Kahl, P.Jaeckel (2006)
  • Monte-Carlo for the Newbies , S.Leger (2006)
  • Monte-Carlo Methods : Paris 7 , A.Millet (2005)
  • Monte-Carlo Methods: ENSAI , N.Baud (2004)
  • Exact Simulation of Stochastic Volatility and other Affine Jump Diffusion Processes , M.Broadie, O.Kaya (2004)
  • Honey, I Shrunk the Sample Covariance Matrix , O. Ledoit, M. Wolf (2003)
  • Adaptative Monte Carlo Method, A Variance Reduction Technique , B. Arouna (2003)
  • Derivative Pricing, Numerical Methods , K.R. Vetzal (2003)
  • Efficient Monte Carlo Methods for Value-at-Risk , P.Glasserman, P.Heidelberger, P.Shahabuddin (2000)
  • The law of the Euler scheme for stochastic differential equations: I. Convergence rate of the distribution function , V. Bally, D. Talay (1996)
  • The law of the Euler scheme for stochastic differential equations. II. Convergence rate of the density , V. Bally, D. Talay (1996)

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