European Options in BS Markets

Norbert Hilber, Oleg Reichmann, Christoph Schwab and Christoph Winter
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Norbert Hilber: Zurich University of Applied Sciences
Oleg Reichmann: Swiss Federal Institute of Technology (ETH)
Christoph Schwab: Swiss Federal Institute of Technology (ETH)
Christoph Winter: Allianz Deutschland AG

Chapter Chapter 4 in Computational Methods for Quantitative Finance, 2013, pp 47-64 from Springer

Abstract: Abstract In the last chapters, we explained various methods to solve partial differential equations. These methods are now applied to obtain the price of a European option. We assume that the stock price follows a geometric Brownian motion and show that the option price satisfies a parabolic PDE. The unbounded log-price domain is localized to a bounded domain and the error incurred by the truncation is estimated. It is shown that the variational formulation has a unique solution and the discretization schemes for finite element and finite differences are derived. Furthermore, we describe extensions of the Black–Scholes model, like the constant elasticity of variance (CEV) and the local volatility model.

Keywords: Bilinear Form; Infinitesimal Generator; Geometric Brownian Motion; European Option; Barrier Option (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-642-35401-4_4

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DOI: 10.1007/978-3-642-35401-4_4

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