Quantization Under the Real-world Measure: Fast and Accurate Valuation of Long-dated Contracts

23 Pages Posted: 1 Feb 2018

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: January 24, 2018

Abstract

This paper provides a methodology for fast and accurate pricing of the long-dated contracts that arise as the building blocks of insurance and pension fund agreements. It applies the recursive marginal quantization (RMQ) and joint recursive marginal quantization (JRMQ) algorithms outside the framework of traditional risk-neutral methods by pricing options under the real-world probability measure, using the benchmark approach. The benchmark approach is reviewed, and the real-world pricing theorem is presented and applied to various long-dated claims to obtain less expensive prices than suggested by traditional risk-neutral valuation. The growth-optimal portfolio (GOP), the central object of the benchmark approach, is modelled using the time-dependent constant elasticity of variance model (TCEV). Analytic European option prices are derived and the RMQ algorithm is used to efficiently and accurately price Bermudan options on the GOP. The TCEV model is then combined with a $3/2$ stochastic short-rate model and RMQ is used to price zero-coupon bonds and zero-coupon bond options, highlighting the departure from risk-neutral pricing.

Keywords: quantization, option pricing, benchmark approach, real-world measure

Suggested Citation

Rudd, Ralph and McWalter, Thomas and Kienitz, Joerg and Platen, Eckhard, Quantization Under the Real-world Measure: Fast and Accurate Valuation of Long-dated Contracts (January 24, 2018). Available at SSRN: https://ssrn.com/abstract=3106631 or http://dx.doi.org/10.2139/ssrn.3106631

Ralph Rudd (Contact Author)

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

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Thomas McWalter

University of Cape Town (UCT) ( email )

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University of Johannesburg ( email )

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Joerg Kienitz

University of Wuppertal - Applied Mathematics ( email )

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University of Cape Town (UCT) ( email )

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Quaternion Risk Management ( email )

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Eckhard Platen

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

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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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Financial Research Network (FIRN)

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Australia

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