随机波动率模型的算子分裂格式模拟
Simulation of stochastic volatility models via operator splitting schemes
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中文总结 AI 辅助
本文提出基于Strang算子分裂的通用模拟框架，用于随机波动率模型，避免条件积分方差评估，兼具精度、效率与可靠性，并证明二阶收敛。
中文摘要 AI 辅助
已知在随机波动率模型下，用于数值期权定价的标准Euler离散化格式存在高偏差和潜在不可靠性。另一种选择是使用精确（无偏）模拟方法，但该方法不可避免地涉及在给定终端方差（或波动率）值的条件下，对积分方差（和/或波动率）进行数值评估。为解决这一技术难题，大多数模拟方案要么采用条件特征函数的繁琐Fourier反演，要么采用矩匹配分布的数值近似。我们提出了一个通用框架，通过Strang算子分裂近似，为随机波动率模型构建高效且可靠的模拟方案。该模拟过程完全规避了评估条件积分方差（和/或波动率）的必要性。我们的模拟方案在精度、效率、可靠性和实现简便性方面，与大多数现有的精确模拟方案和有偏的Euler方案相比，具有显著优势。我们进行了广泛的数值测试，以展示我们的算子分裂方法在大多数常见随机波动率模型（如Heston型模型、lifted Heston模型、Hull-White模型以及Barndorff-Nielsen和Shephard模型）中的通用性和成功性。我们还建立了算子分裂格式二阶收敛性的证明。
英文摘要
The standard Euler discretization schemes for numerical option pricing under stochastic volatility models are known to exhibit high biases and potential unreliability. The alternative use of the exact (unbiased) simulation approach invariably involves numerical evaluation of integrated variance (and / or volatility) conditional on terminal variance (volatility) value. To resolve the technical challenge, most simulation schemes either employ the tedious Fourier inversion of conditional characteristic function or numerical approximation by moment matched distribution. We propose a general framework of constructing efficient and reliable simulation schemes for stochastic volatility models via the Strang operator splitting approximation. The simulation procedure completely circumvents the necessity of evaluation of conditional integrated variance (and / or) volatility. Our simulation schemes compete favorably well with most existing exact simulation schemes and the biased Euler schemes in terms of accuracy, efficiency, reliability and ease of implementation. Extensive numerical tests were conducted to illustrate the versatility and success of our operator splitting approach for most common stochastic volatility models, such as the Heston-type models, lifted Heston model, Hull-White model, and Barndorff-Nielsen and Shephard model. We also establish the proof of second-order convergence of the operator splitting schemes.
发表机构
- University of Waterloo（滑铁卢大学）
- Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
- Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
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