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

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.

Keywords:

• Leveraged certificates
• Barrier options
• Overnight gap
• Risk management

JEL Classification:

• G13
• C63

Acknowledgements

We thank David Colwell, David Feldman, Felix Kübler, Detlef Mages, participants at the 9th World Congress of the Bachelier Finance Society as well as one anonymous reviewer for their helpful comments and suggestions. Ally Quan Zhang acknowledges financial support from the Swiss Finance Institute.

Notes

No potential conflict of interest was reported by the authors.

The opinions expressed in this article are solely those of the authors and do not reflect any views by Commerzbank AG.