Local Volatility Calibration Using An Adjoint Proxy
We document the calibration of the local volatility in a framework similar to Coleman, Li and Verma. The quality of a surface is assessed through a functional to be optimized; the specificity of the approach is to separate the optimization (performed with any suitable optimization algorithm) from the computation of the functional where we use an adjoint (as in L. Jiang et. al.) to obtain an approximation; moreover our main calibration variable is the implied volatility (the procedure can also accommodate the Greeks). The procedure performs well on benchmarks from the literature and on FOREX data.
Volume (Year): (2008)
Issue (Month): 2 (November)
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- Lishang Jiang & Qihong Chen & Lijun Wang & Jin Zhang, 2003. "A new well-posed algorithm to recover implied local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 451-457.
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- Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
- H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 61-69.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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