How much is the gap?—Efficient jump risk-adjusted valuation of leveraged certificates |
| |
Authors: | Ally Quan Zhang Matthias Thul |
| |
Institution: | 1. Swiss Finance Institute, Zürich, Switzerland.;2. Institut für Banking &3. Finance, Universit?t Zürich, Plattenstr. 32, 8032Zürich, Switzerland.quan.zhang@bf.uzh.ch;5. Commerzbank AG, Equity Derivatives Flow Trading, Equity Markets and Commodities, Mainzer Landstr. 153, 60327Frankfurt am Main, Germany. |
| |
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 |
|
|