Neural Networks for Contingent Claim Pricing via the Galerkin Method
We use Neural Networks as a Semi-NonParametric technique to approximate, by means of the Galerkin method, contingent claim prices defined by a no-arbitrage Partial Differential Equation. The Neural Networks’ weights are determined as to satisfy the no-arbitrage Partial Differential Equation. A general solution procedure is developed for European Contingent Claims. The main feature of the Neural Network is that its weights are time varying, they change as the time to expiration of the claim changes. The method has been evaluated for option pricing in the standard Black and Scholes framework.
KeywordsAsset Price Galerkin Method Option Price Trial Function Implied Volatility
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- Duffle, D., 1992, Dynamic Asset Pricing Theory, Princeton: Princeton University Press.Google Scholar
- Dupire, B., 1993, ‘Pricing and hedging with smiles’, in Proceedings of the AFFI Conference, La-Baule.Google Scholar
- Grenander, U. (1981), Abstract Inference, New York: WileyGoogle Scholar
- Kantorovich, L.V. and V.I. Krilov, 1958, Approximate Methods of Higher Analysis, New York: Noordhoff, Gröningen and Interscience.Google Scholar
- Meade, A. and A. Fernandez, 1994b, ‘Solution of nonlinear ordinary differential equations by feedforward neural networks’, Mathematical and Computer Modelling, to appear.Google Scholar
- Mikhlin, S.G., 1971, The Numerical Performance of Variational Methods, Wolters-Noordhoff.Google Scholar
- Panton, R.Z. and H.B. Sallee, 1975, Computers and Fluids, Vol. 3, pp. 257–269, New York: Springer-Verlag.Google Scholar
- Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, 1992, Numerical Recipies in C, Cambridge: Cambridge University Press.Google Scholar
- Rumelhart, D.E., G.E. Hintos, R.J. Williams, 1986, ‘Learning internal representation by error propagation’, in Parallel Distributed Processing: Exploration in the Microstructure of Cognition. Vol. 1: Foundations, D. Rumelhart and J. McClelland (Eds), Cambridge, MA: MIT Press.Google Scholar