How Much Is the Gap? Efficient Jump Risk-Adjusted Valuation of Leveraged Certificates

Quantitative Finance, Vol. 17, No. 9

49 Pages Posted: 2 Feb 2014 Last revised: 4 Jan 2018

See all articles by Ally Zhang

Ally Zhang

Department of Finance, Lancaster University Management School; Swiss Finance Institute

Matthias Thul

IMC Financial Markets

Date Written: February 26, 2017

Abstract

This paper develops a novel and highly efficient numerical algorithm for the gap risk-adjusted valuation of leveraged certificates. The existing literature relies on Monte Carlo simulations, which are not fast enough to be used in a market making environment. This is because issuers need to compute thousands of price updates per second. By valuing leveraged certificates as multi-window barrier options, we explicitly model random jumps that occur at known times, such as between the exchange closing and re-opening. Our algorithm combines the one-day transition probability with Simpson's numerical integration rule. This yields a backward induction scheme which requires a significantly coarser spacial and time grid than finite difference methods. We confirm its robustness and accuracy through Monte Carlo simulations.

Keywords: leveraged certificates, barrier options, overnight gap, risk management

JEL Classification: G13, C63

Suggested Citation

Zhang, Quan and Thul, Matthias, How Much Is the Gap? Efficient Jump Risk-Adjusted Valuation of Leveraged Certificates (February 26, 2017). Quantitative Finance, Vol. 17, No. 9. Available at SSRN: https://ssrn.com/abstract=2388734 or http://dx.doi.org/10.2139/ssrn.2388734

Quan Zhang (Contact Author)

Department of Finance, Lancaster University Management School ( email )

Economics Department,
LUMS,
Bailrigg Lancaster, LA1 4YX
United Kingdom
+441524592776 (Phone)

HOME PAGE: http://www.allyquanzhang.com/wordpress/

Swiss Finance Institute ( email )

Plattenstrasse 32
Zurich, ZH 8032
Switzerland

Matthias Thul

IMC Financial Markets ( email )

Strawinskylaan 377, WTC D-tower
Amsterdam, 1077 XX
Netherlands

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