THE 3/2 MODEL AS A STOCHASTIC VOLATILITY APPROXIMATION FOR A LARGE-BASKET PRICE-WEIGHTED INDEX

Ben Hambly () and Juozas Vaicenavicius ()
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Ben Hambly: Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
Juozas Vaicenavicius: Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 06, 1-25

Abstract: We derive large-basket approximations of a price-weighted index whose component prices follow a single sector jump-diffusion model. As the basket size approaches infinity, a suitable average converges to a Black–Scholes model driven by the common factor process. We extend this by considering the behavior of the residual idiosyncratic noise and show that a version of the 3/2 model emerges as a natural stochastic volatility model approximation. This provides a theoretical justification for its use as a model for jointly pricing index and volatility derivatives.

Keywords: Index models; stochastic volatility models; large portfolio limit; diffusion approximation; volatility derivatives (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0219024915500417

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