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Equity options in Lévy models: pricing, sensitivity analysis, and existence proofs
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When
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2.00pm on Friday 23rd November
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Where
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B617, Leverhulme Library, Columbia House
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Presentations
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Speaker
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Adrian Gfeller
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From
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London School of Economics & Political Science
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Abstract
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Option prices in the Black Scholes model can often be expressed as solutions to partial differential equations (PDE). In general exponential Lévy models an additional integral term has to be added and the prices and greeks can be expressed as solutions of partial integro-differential equations (PIDE). The sensitivity of a price function to changes in its arguments is given by its derivatives, in finance known as greeks. The PDE or PIDE for the greeks are obtained by differentiating the equation and side conditions of the price function. We derive systems of equations both for vanilla and for exotic options in a financial market where the underlying stock prices are driven by an exponential Lévy processes. In exponential Lévy models we are not guaranteed that the price function is smooth enough to ensure that the PIDE has a classical solution. We investigate the smoothness of the price function and give conditions that guarantee the existence of the derivatives.
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For further information
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Thomas Hewlett (Postgraduate Administrator) Ext. 6879
Department of Statistics, Columbia House
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