Rights statement: This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 7/3/2017, available online: https://www.tandfonline.com/doi/full/10.1080/14697688.2016.1276299
Accepted author manuscript, 404 KB, PDF document
Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - How Much is the Gap?
T2 - Efficient Overnight Jump Risk-Adjusted Valuation of Leveraged Certificates
AU - Zhang, Quan
AU - Thul, Matthias
N1 - This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 7/3/2017, available online: https://www.tandfonline.com/doi/full/10.1080/14697688.2016.1276299
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
U2 - 10.1080/14697688.2016.1276299
DO - 10.1080/14697688.2016.1276299
M3 - Journal article
VL - 17
SP - 1387
EP - 1401
JO - Quantitative Finance
JF - Quantitative Finance
SN - 1469-7688
IS - 9
ER -