Contact:Elizna Huysamen
- 021 808 3244
Location: Van der Sterr building, 2nd Floor, Room 2048
??In this talk we show how the Surface Stochastic Volatility Inspired (SSVI) parametric local volatility surface may be quantized. To provide context, we first describe what Vector Quantization (VQ) is, and why it useful as a method for pricing options and other financial contingent claims. We also provide a description of Recursive Marginal Quantization (RMQ), which is an algorithm that allows the quantization of general stochastic differential equations. The novel work of quantizing the SSVI surface is then presented. This is accomplished by applying the Breeden-Litzenberger equations in order to derive the various distribution related equations necessary for VQ. While this allows the derivation of the correct marginal distributions, approximation of conditional probabilities is accomplished using Ito-Taylor expansions of various accuracy. Techniques from Optimal Transport Theory are used to ensure consistency between the conditional and marginal probabilities computed. Finally, we produce numerical simulations to show the accuracy of the outcome and to efficiently price American options.?
