The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing
Oscillations in option price convergence have long been a problematic aspect of tree methods, inhibiting the use of repeated Richardson extrapolation that could otherwise greatly accelerate convergence, a feature integral to some of the most efficient modern methods. These oscillations are typically...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/7/964 |
| _version_ | 1797212311343071232 |
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| author | Guillaume Leduc |
| author_facet | Guillaume Leduc |
| author_sort | Guillaume Leduc |
| collection | DOAJ |
| description | Oscillations in option price convergence have long been a problematic aspect of tree methods, inhibiting the use of repeated Richardson extrapolation that could otherwise greatly accelerate convergence, a feature integral to some of the most efficient modern methods. These oscillations are typically caused by the fluctuating positions of nodes around the discontinuities in the payoff function or its derivatives. Our paper addresses this crucial gap that typically prohibits the use of lattice methods when high efficiency is needed. Focusing on double barrier options, we develop a trinomial tree in which the positions of the nodes are precisely adjusted to align with these discontinuities throughout the option’s lifespan and across various time steps. This alignment enables the use of repeated extrapolation to achieve high order convergence, including near barriers, a well-known challenge in many tree methods. Maintaining the inherent simplicity and adaptability of tree methods, our approach is easily applicable to other models and option types. |
| first_indexed | 2024-04-24T10:40:22Z |
| format | Article |
| id | doaj.art-a0448cdd6a2e4b3ca5eefea994a2a1a1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T10:40:22Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a0448cdd6a2e4b3ca5eefea994a2a1a12024-04-12T13:22:30ZengMDPI AGMathematics2227-73902024-03-0112796410.3390/math12070964The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option PricingGuillaume Leduc0Department of Mathematics and Statistics, American University of Sharjah, Sharjah P.O. Box 26666, United Arab EmiratesOscillations in option price convergence have long been a problematic aspect of tree methods, inhibiting the use of repeated Richardson extrapolation that could otherwise greatly accelerate convergence, a feature integral to some of the most efficient modern methods. These oscillations are typically caused by the fluctuating positions of nodes around the discontinuities in the payoff function or its derivatives. Our paper addresses this crucial gap that typically prohibits the use of lattice methods when high efficiency is needed. Focusing on double barrier options, we develop a trinomial tree in which the positions of the nodes are precisely adjusted to align with these discontinuities throughout the option’s lifespan and across various time steps. This alignment enables the use of repeated extrapolation to achieve high order convergence, including near barriers, a well-known challenge in many tree methods. Maintaining the inherent simplicity and adaptability of tree methods, our approach is easily applicable to other models and option types.https://www.mdpi.com/2227-7390/12/7/964double barrier optionstree methodrepeated Richardson extrapolation |
| spellingShingle | Guillaume Leduc The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing Mathematics double barrier options tree method repeated Richardson extrapolation |
| title | The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing |
| title_full | The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing |
| title_fullStr | The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing |
| title_full_unstemmed | The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing |
| title_short | The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing |
| title_sort | boyle romberg trinomial tree a highly efficient method for double barrier option pricing |
| topic | double barrier options tree method repeated Richardson extrapolation |
| url | https://www.mdpi.com/2227-7390/12/7/964 |
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