APPROXIMATION METHODS FOR INHOMOGENEOUS GEOMETRIC BROWNIAN MOTION

LUCA CAPRIOTTI; YUPENG JIANG; GAUKHAR SHAIMERDENOVA

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APPROXIMATION METHODS FOR INHOMOGENEOUS GEOMETRIC BROWNIAN MOTION

机译：非均匀几何布朗运动的近似方法

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We present an accurate and easy-to-compute approximation of the transition probabilities and the associated Arrow-Debreu (AD) prices for the inhomogeneous geometric Brownian motion (IGBM) model for interest rates, default intensities or volatilities. Through this procedure, dubbed exponent expansion, transition probabilities and AD prices are obtained as a power series in time to maturity. This provides remarkably accurate results?— for time horizons up to several years?— even when truncated after the first few terms. For farther time horizons, the exponent expansion can be combined with a fast numerical convolution to obtain high-precision results.

机译：我们介绍了过渡概率的准确且易于计算的近似值，以及用于利率的非均值几何褐色运动（IGBM）模型，默认强度或波动性的相关箭头-Debreu（AD）价格。通过此过程，将被称为扩展，过渡概率和广告价格及时获得功率系列。这提供了非常准确的结果？ - 对于长达几年的时间范围？ - 即使在前几个条款后截断。对于更远的时间视野，指数扩展可以与快速数值卷积相结合以获得高精度的结果。

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来源
《International journal of theoretical and applied finance》 |2019年第2期|共16页
作者
LUCA CAPRIOTTI; YUPENG JIANG; GAUKHAR SHAIMERDENOVA;
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作者单位

1Department of Mathematics University College London Gower Street London WC1E 6BT UK;

1Department of Mathematics University College London Gower Street London WC1E 6BT UK;

2Department of Computer Electrical and Mathematical Sciences and Engineering King Abdullah University of Science and Technology Al-Khawarizmi Thuwal 23955-6900 Kingdom of Saudi Arabia;

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原文格式 PDF
正文语种 eng
中图分类财政、金融;
关键词
Inhomogeneous geometric Brownian motion; constant elasticity of variance; Arrow-Debreu security; derivative pricing; power series expansions;

机译：不均匀的几何布朗运动;恒定弹性方差;箭头 - 德布鲁安全;衍生定价;电力系列扩展;

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专利

1. APPROXIMATION METHODS FOR INHOMOGENEOUS GEOMETRIC BROWNIAN MOTION [J] . LUCA CAPRIOTTI, YUPENG JIANG, GAUKHAR SHAIMERDENOVA International journal of theoretical and applied finance . 2019,第2期

机译：非均匀几何布朗运动的近似方法
2. Methods for Evaluating Density Functions of Exponential Functionals Represented as Integrals of Geometric Brownian Motion [J] . Kazuyuki Ishiyama Methodology and computing in applied probability . 2005,第3期

机译：几何布朗运动积分表示的指数函数密度函数的评估方法
3. A simulation-based product diffusion forecasting method using geometric Brownian motion and spline interpolation [J] . Najmeh Madadi, Azanizawati Ma’aram, Kuan Yew Wong Cogent Business & Management . 2017,第1期

机译：基于几何布朗运动和样条插值的基于仿真的产品扩散预测方法
4. Discrete Approximations to Solution Flows of Tanaka's SDE Related to Walsh Brownian Motion [C] . Hatem Hajri Seminaire de probabilites . 2012

机译：与沃尔什布朗运动有关的坦卡卡SDE的解决方案流动的离散近似值
5. A non-geometric Brownian motion model estimated by Markov chain approximation. [D] . Chang, Hung Yu. 2011

机译：通过马尔可夫链近似估计的非几何布朗运动模型。
6. Visual information and expert’s idea in Hurst index estimation of the fractional Brownian motion using a diffusion type approximation [O] . Ali R. Taheriyoun, Meisam Moghimbeygi -1

机译：视觉信息和专家的想法使用扩散类型近似来估计分数布朗运动的赫斯特指数
7. On the approximation of geometric fractional Brownian motion [O] . Espoo A, Esko Valkeila, Ab Teknillinen Korkeakoulu, 2007

机译：关于几何分数布朗运动的近似

APPROXIMATION METHODS FOR INHOMOGENEOUS GEOMETRIC BROWNIAN MOTION

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