Svetlana Boyarchenko, Sergei Levendorskii
arXiv 6 Dec 2023 · Finance — Computational · 2 citations (OpenAlex)
arXiv:2312.03915 · PDF · DOI · OpenAlex · Extracted main text
We analyze the qualitative differences between prices of double barrier no-touch options in the Heston model and pure jump KoBoL model calibrated to the same set of the empirical data, and discuss the potential for arbitrage opportunities if the correct model is a pure jump model. We explain and demonstrate with numerical examples that accurate and fast calculations of prices of double barrier options in jump models are extremely difficult using the numerical methods available in the literature. We develop a new efficient method (GWR-SINH method) based of the Gaver-Wynn-Rho acceleration applied to the Bromwich integral; the SINH-acceleration and simplified trapezoid rule are used to evaluate perpetual double barrier options for each value of the spectral parameter in GWR-algorithm. The program in Matlab running on a Mac with moderate characteristics achieves the precision of the order of E-5 and better in several several dozen of milliseconds; the precision E-07 is achievable in about 0.1 sec. We outline the extension of GWR-SINH method to regime-switching models and models with stochastic parameters and stochastic interest rates.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | S. Boyarchenko and S. Levendorskii (2022) Efficient evaluation of double barrier options and joint cpdf of a Lévy process and its two extrema | 1.000 | 21 | 5 | 100% |
| 2 | S. Levendorskii (2014) Method of paired contours and pricing barrier options and CDS of long maturities | 1.000 | 6 | 3 | 100% |
| 3 | S. Boyarchenko and S. Levendorskii (1950) Sinh-acceleration: Efficient evaluation of probability distributions, option pricing, and Monte-Carlo simulations | 1.000 | 5 | 5 | 100% |
| 4 | M. Boyarchenko, M. de Innocentis, and S. Levendorskii (2011) Prices of barrier and first-touch digital options in Lévy-driven models, near barrier | 0.928 | 5 | 3 | 80% |
| 5 | S. Boyarchenko and S. Levendorskii (1902) Static and semi-static hedging as contrarian or conformist bets | 0.928 | 4 | 4 | 100% |
| 6 | S. Boyarchenko and S. Levendorskii (2022) Efficient evaluation of expectations of functions of a Lévy process and its extremum | 0.928 | 4 | 4 | 100% |
| 7 | S. Boyarchenko and S. Levendorskii (2002) Non-Gaussian Merton-Black-Scholes Theory, volume 9 of Adv. Ser. Stat. Sci. Appl. Probab | 0.916 | 13 | 5 | 77% |
| 8 | M. Boyarchenko and S. Levendorskii (2012) Valuation of continuously monitored double barrier options and related securities | 0.909 | 12 | 6 | 75% |
| 9 | S. Boyarchenko and S. Levendorskii (2002) Barrier options and touch-and-out options under regular Lévy processes of exponential type | 0.874 | 6 | 3 | 67% |
| 10 | S. Boyarchenko and S. Levendorskii (2022) Lévy models amenable to efficient calculations | 0.874 | 6 | 2 | 100% |
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