Monte Carlo Methods in Financial Engineering
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摘要
本报告系统介绍了蒙特卡洛方法在金融工程中估值衍生品的理论基础及应用，涵盖随机数生成、样本路径构造、方差缩减、拟蒙特卡洛方法、时间离散误差矫正、敏感性估计、美国期权定价及风险管理。重点阐述了基于风险中性定价的估值原理，结合路径依赖特征，深入解析了各类模型的模拟方法及其有效性验证，并针对复杂多维情形，提出了包括布朗桥及主成分分析等降维策略，以及基于回归和随机网格的数值算法，辅以丰富的算法实现与实验结果，特别指出了量化因子构建与改进蒙特卡洛模拟效率的关键技术[page::5][page::6][page::8][page::9][page::10][page::11][page::13][page::14][page::15][page::16][page::22][page::25][page::26][page::28][page::29][page::31][page::41][page::44][page::51][page::53][page::56][page::59][page::60][page::62][page::63][page::75][page::76][page::85][page::92][page::93][page::95][page::99][page::102][page::104][page::107][page::111][page::114][page::115][page::116][page::117][page::119][page::120][page::122][page::126][page::132][page::134][page::136][page::137][page::138][page::139][page::143][page::144][page::145][page::147][page::149][page::153][page::156][page::157][page::159][page::165][page::176][page::177][page::179][page::181][page::182][page::183][page::185][page::196][page::197][page::201][page::204][page::210][page::216][page::220][page::223][page::236][page::244][page::247][page::249][page::252][page::254][page::266][page::270][page::273][page::279][page::282][page::287][page::291][page::293][page::297][page::303][page::306][page::309][page::313][page::317][page::320][page::324][page::326][page::328][page::331][page::333][page::336][page::337][page::338][page::339][page::340][page::343][page::344][page::346][page::347][page::350][page::353][page::355][page::356][page::359][page::360][page::362][page::364][page::366][page::368][page::371][page::373][page::375][page::386][page::388][page::389][page::395][page::396][page::399][page::400][page::406][page::414][page::415][page::417][page::418][page::419][page::421][page::427][page::431][page::432][page::434][page::435][page::437][page::440][page::441][page::444][page::446][page::448][page::449][page::450][page::452][page::453][page::455][page::457][page::459][page::460][page::462][page::464][page::466][page::467][page::469][page::470][page::472][page::474][page::475][page::476][page::478][page::479][page::480][page::483][page::485][page::489][page::490][page::491][page::492][page::493][page::495][page::497][page::499][page::501][page::503][page::504][page::505][page::507][page::508][page::509][page::510][page::511][page::513][page::517][page::520][page::521][page::523][page::525][page::527][page::528][page::530][page::531][page::532][page::533][page::534][page::535][page::536][page::537][page::538][page::539][page::540][page::541][page::542][page::544][page::545][page::546][page::547][page::548][page::551][page::552][page::553][page::555][page::556][page::557][page::558][page::559][page::563][page::564][page::565][page::566][page::567][page::568][page::569][page::572][page::573][page::574][page::577][page::578][page::579][page::580][page::581][page::582][page::583][page::584][page::585][page::586][page::587][page::590][page::592][page::594][page::595][page::597][page::598][page::599][page::600][page::601]
