Fast Quantization of Stochastic Volatility Models

Ralph Rudd, Thomas McWalter, Jorg Kienitz and Eckhard Platen ()
Additional contact information
Ralph Rudd: University of Cape Town
Jorg Kienitz: Bergische Universit¨at Wuppertal

No 382, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is usually performed using stochastic methods, e.g., Lloyd’s algorithm or Competitive Learning Vector Quantization. In this paper, a new algorithm is proposed that allows RMQ to be applied to two-factor stochastic volatility models, which retains the efficiency of gradient-descent techniques. By margining over potential realizations of the volatility process, a significant decrease in computational effort is achieved when compared to current quantization methods. Additionally, techniques for modelling the correct zero-boundary behaviour are used to allow the new algorithm to be applied to cases where the previous methods would fail. The proposed technique is illustrated for European options on the Heston and Stein-Stein models, while a more thorough application is considered in the case of the popular SABR model, where various exotic options are also priced.

Pages: 29 pages
Date: 2017-05-01
New Economics Papers: this item is included in nep-dcm and nep-ets
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Citations: View citations in EconPapers (6)

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https://www.uts.edu.au/sites/default/files/QFR-rp382.pdf (application/pdf)

Related works:
Working Paper: Fast Quantization of Stochastic Volatility Models (2017)
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