Pricing discretely-monitored double barrier options with small probabilities of execution
Abstract
In this paper, we propose a new stochastic simulation-based methodology for pricing discretely-monitored double barrier options and estimating the corresponding probabilities of execution. We develop our framework by employing a versatile tool for the estimation of rare event probabilities known as subset simulation algorithm. In this regard, considering plausible dynamics for the price evolution of the underlying asset, we are able to compare and demonstrate clearly that our treatment always outperforms the standard Monte Carlo approach and becomes substantially more efficient (measured in terms of the sample coefficient of variation) when the underlying asset has high volatility and the barriers are set close to the spot price of the underlying asset. In addition, we test and report that our approach performs better when it is compared to the multilevel Monte Carlo method for special cases of barrier options and underlying assets that make the pricing problem a rare event estimation. These theoretical findings are confirmed by numerous simulation results.
Additional Information
© 2020 Elsevier B.V. Received 26 September 2019, Revised 18 July 2020, Accepted 21 July 2020, Available online 26 July 2020. We are extremely grateful to the three anonymous reviewers and handling editor Emanuele Borgonovo who have afforded us considerable assistance in enhancing both the quality of the findings and the clarity of their presentation. The authors would like to thank Siu-Kui (Ivan) Au, James Beck, Damiano Brigo, Gianluca Fusai, Otto Konstadatos, Steven Kou, Ioannis Kyriakou, Zili Zhu, and the participants at the Global Finance 2018, Quantitative Methods in Finance 2018 and Quantitative Finance and Risk Analysis 2019 Conferences and seminars at Caltech, University of Liverpool, Monash University and Shanghai University for helpful comments. Any remaining errors are ours.Attached Files
Submitted - 1803.03364.pdf
Submitted - SSRN-id3132336.pdf
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Additional details
- Alternative title
- Efficient Pricing of Barrier Options on High Volatility Assets using Subset Simulation
- Eprint ID
- 104583
- Resolver ID
- CaltechAUTHORS:20200727-091611276
- Created
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2020-07-28Created from EPrint's datestamp field
- Updated
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2023-06-01Created from EPrint's last_modified field