How much is the gap?—Efficient jump risk-adjusted valuation of leveraged certificates
提出一种高效数值算法，用于杠杆凭证的缺口风险调整估值，结合一日转移概率和辛普森积分法，比蒙特卡洛模拟快得多，适合做市商环境。
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.