Convex bounds on multiplicative processes, with applications to pricing in incomplete markets |
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Authors: | Cindy Courtois |
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Institution: | a Institut des Sciences Actuarielles, Université catholique de Louvain, Belgium b Institut de Statistique, Université catholique de Louvain, Belgium |
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Abstract: | Extremal distributions have been extensively used in the actuarial literature in order to derive bounds on functionals of the underlying risks, such as stop-loss premiums or ruin probabilities, for instance. In this paper, the idea is extended to a dynamic setting. Specifically, convex bounds on multiplicative processes are derived. Despite their relative simplicity, the extremal processes are shown to produce reasonably accurate bounds on option prices in the classical trinomial model for incomplete markets. |
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Keywords: | Convex order Extremal distributions Incomplete market Risk-neutral martingales Option pricing Trinomial model |
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