“How Much is the Gap? Efficient Overnight Jump Risk-Adjusted Valuation of Leveraged Certificates” (2016), Quantitative Finance (forthcoming), joint with Ally Quan Zhang
This paper develops a novel and highly efficient numerical algorithm for the gap risk-adjusted valuation of leveraged certificates. The existing literature relies exclusively on Monte Carlo simulations for this purpose. These are not sufficiently fast to be used in a market making environment where issuers need to compute thousands of price updates per second. By valuing leveraged certificates as multi-window barrier options, we explicitly model jumps that occur at deterministically 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 that requires a significantly coarser spacial and time grid than finite difference methods. We demonstrate its robustness and accuracy through Monte Carlo simulations.
Published version: http://www.tandfonline.com/doi/full/10.1080/14697688.2016.1276299
Preprint available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2388734
Presented or Accepted for Presentation at:
- 9th World Congress of the Bachelier Finance Society, July 2016, New York