Fast Quantization of Stochastic Volatility Models

28 Pages Posted: 22 Apr 2017

See all articles by Ralph Rudd

Ralph Rudd

The African Institute of Financial Markets and Risk Management

Thomas McWalter

University of Cape Town (UCT); University of Johannesburg

Joerg Kienitz

University of Wuppertal - Applied Mathematics; University of Cape Town (UCT); Quaternion Risk Management

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group; University of Technology Sydney, School of Mathematical and Physical Sciences; Financial Research Network (FIRN)

Date Written: April 20, 2017

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.

Keywords: quantization, option pricing, stochastic volatility

Suggested Citation

Rudd, Ralph and McWalter, Thomas and Kienitz, Joerg and Platen, Eckhard, Fast Quantization of Stochastic Volatility Models (April 20, 2017). Available at SSRN: https://ssrn.com/abstract=2956168 or http://dx.doi.org/10.2139/ssrn.2956168

Ralph Rudd (Contact Author)

The African Institute of Financial Markets and Risk Management ( email )

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Cape Town, Western Cape 7700
South Africa
+27 21 650 2474 (Phone)

Thomas McWalter

University of Cape Town (UCT) ( email )

Private Bag X3
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South Africa

University of Johannesburg ( email )

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Joerg Kienitz

University of Wuppertal - Applied Mathematics ( email )

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42097 Wuppertal
Germany

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

Quaternion Risk Management ( email )

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Ireland

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group ( email )

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Sydney, NSW 2007, 2007
Australia
+61 2 9514 7759 (Phone)

HOME PAGE: http://datasearch.uts.edu.au/business/finance/staff/StaffDetails.cfm?UnitStaffId=90

University of Technology Sydney, School of Mathematical and Physical Sciences ( email )

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Australia
+61 (02) 9514 2271 (Phone)

Financial Research Network (FIRN)

C/- University of Queensland Business School
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Queensland
Australia

HOME PAGE: http://www.firn.org.au

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