Approximation of prices for average-type options via bounds

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The problem of pricing multi-dimensional arithmetic average-type options is a complex problem both analytically and numerically, analytically because the distribution of the average on which the payoff function depends is unknown in closed-form and numerically because of the high dimensionality of the problem. In this thesis we develop methods that avoid these issues by providing price approximations in the form of lower and upper bounds. We do so by approximating the event that the option finishes in-the-money with a closely related proxy and use an optimisation procedure to tighten up the bounds. The result is a pricing tool that provides accurate approximations without suffering from the exponential curse of dimensionality associated with other techniques. The method is developed for underlying assets modelled as exponential Lévy processes and numerical examples are provided under a variety of these models.
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