Dupire’s formulas in the Piterbarg option pricing model

Black, 1973, The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637, 10.1086/260062 Brigo, 2002, Lognormal-mixture dynamics and calibration to market volatility smiles, International Journal of Theoretical and Applied Finance, 5, 427, 10.1142/S0219024902001511 Derman, 1996, The local volatility surface: Unlocking the information in index option prices, Financial Analysts Journal, 52, 25, 10.2469/faj.v52.n4.2008 Del Moral, 2004 Dupire, B. (1994). Pricing with a smile. RISK. Gatheral, 2006 Harrison, 2006, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and their Applications, 11, 215, 10.1016/0304-4149(81)90026-0 Isaacson, 2012 Johannesburg Stock Exchange. Website: https://www.jse.co.za/downloadable-files?RequestNode=/Safex, as on 31 May 2014. Johannesburg Stock Exchange. Website: https://www.jse.co.za/downloadable-files?RequestNode=/Safex/mtmdata/Vol%20Skew%20Indices, as on 31 May 2014. Kotze, A., Joseph, A. (2009). Constructing a South African index volatility surface from exchange traded data. JSE. Piterbarg, 2010, Funding beyond discounting: Collateral agreements and derivatives pricing, Risk Magazine, 23, 97 Risken, 1984 Ross, 1996, Vol. 2 Rouah, F. (1998). Derivation of local volatility. van der Kamp, R. (2009). Local volatility modelling. Masters dissertation. University of Twente, Netherlands.