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


Zhang, Quan; Thul, Matthias (2017). How Much Is the Gap? Efficient Jump Risk-Adjusted Valuation of Leveraged Certificates. Quantitative Finance, 17(9):1387-1401.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:2017
Deposited On:22 Nov 2017 14:29
Last Modified:19 Feb 2018 09:22
Publisher:Taylor & Francis
ISSN:1469-7688
OA Status:Closed
Publisher DOI:https://doi.org/10.1080/14697688.2016.1276299
Related URLs:http://www.tandfonline.com/doi/full/10.1080/14697688.2016.1276299 (Publisher)
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2388734 (Organisation)
Other Identification Number:merlin-id:14643

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