Self-funding Instalment Warrants

Jeff Dewynne and Nadima El-Hassan ()
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Jeff Dewynne: Mathematical Institute, University of Oxford

No 339, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: We present two simple models for the fair value of a self-funding instalment warrant. In the first model, we assume that the underlying share pays a continuous dividend yield and in the second we assume that it pays a series of discrete dividend yields. We show that both models admit similarity reductions and use these to obtain straightforward numerical solutions with both Monte Carlo and finite-difference methods. We use the method of multiple scales to connect these two models and establish the first-order correction term to be applied to the first model in order to obtain the second, thereby establishing that the former model is justified when many dividends are paid during the life of the warrant. Further, we show that the functional form of this correction may be expressed in terms of the hedging parameters for the first model and is, in fact, independent of the particular payoff in the first model. We also obtain approximate solutions for the first model which are valid in the small volatility limit by using singular perturbation techniques.

Keywords: Mathematical Modelling; Mathematical Finance; Asymptotic methods; Asian Options; Black-Scholes Partial Differential Equation (search for similar items in EconPapers)
Pages: 59 pages
Date: 2013-12-01
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Published as: Dewynne, J. and El-Hassan, N., 2017, "The Valuation of Self-funding Instalment Warrants", International Journal of Theoretical and Applied Finance, 20(4), 1-48.

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