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How much is the gap?—Efficient jump risk-adjusted valuation of leveraged certificates

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  • Ally Quan Zhang
  • Matthias Thul

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 spatial and time grid than finite-difference methods. We confirm its robustness and accuracy through Monte Carlo simulations.

Suggested Citation

  • Ally Quan Zhang & Matthias Thul, 2017. "How much is the gap?—Efficient jump risk-adjusted valuation of leveraged certificates," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1387-1401, September.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:9:p:1387-1401
    DOI: 10.1080/14697688.2016.1276299
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