An improved framework for approximating option prices with application to option portfolio hedging |
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| Institution: | 1. Department of Mathematics, University of Dhaka, Bangladesh;2. School of Economics, Finance and Marketing, RMIT University, Melbourne, Australia;3. School of Economics and Finance, Massey University, Palmerston North, New Zealand;4. School of Business, University of Southampton, UK;1. THEMA, Université de Cergy-Pontoise and CREST, France;2. European Central Bank, Germany;3. Banque de France, International Macroeconomics Division, France;1. Université Côte d''Azur, SKEMA, France;2. Université Côte d''Azur, CNRS, GREDEG, France;3. Université Côte d''Azur, CNRS, GREDEG, SKEMA, OFCE-DRIC, France |
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| Abstract: | As the price of the underlying asset changes over time, delta of the option changes and a gamma hedge is required along with delta hedge to reduce risk. This paper develops an improved framework to compute delta and gamma values with the average of a range of underlying prices rather than at the conventional fixed ‘one point’. We find that models with time-varying volatility price options satisfactorily, and perform remarkably well in combination with the delta and delta-gamma approximations. Significant improvements are achieved for the GARCH model followed by stochastic volatility models. The new approach can ensure significant improvement in modelling option prices leading to better risk-management decision-making. |
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