Lie Algebraic Approach for Pricing Moving Barrier Options with Time-Dependent Parameters

Journal of Mathematical Analysis and Applications, Vol. 323, No. 2, pp. 1455-1464, 2006

10 Pages Posted: 27 Jul 2007

See all articles by Chi-Fai Lo

Chi-Fai Lo

The Chinese University of Hong Kong

Cho-Hoi Hui

Hong Kong Monetary Authority - Research Department

Abstract

In this paper we apply the Lie-algebraic technique for the valuation of moving barrier options with time-dependent parameters. The value of the underlying asset is assumed to follow the constant elasticity of variance (CEV) process. By exploiting the dynamical symmetry of the pricing partial differential equations, the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly, and thus provides an efficient way for computing the prices of the moving barrier options. The method is also able to provide tight upper and lower bounds for the exact prices of CEV barrier options with fixed barriers.

In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.

Keywords: Options, Constant elasticity of variance, Partial differential equation, Lie algebra

JEL Classification: G13

Suggested Citation

Lo, Chi-Fai and Hui, Cho-Hoi, Lie Algebraic Approach for Pricing Moving Barrier Options with Time-Dependent Parameters. Available at SSRN: https://ssrn.com/abstract=1003354

Chi-Fai Lo (Contact Author)

The Chinese University of Hong Kong ( email )

Department of Physics
Shatin, N.T., Hong Kong
China

Cho-Hoi Hui

Hong Kong Monetary Authority - Research Department ( email )

Hong Kong
China

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