الگوریتمی مبتنی بر شبکه عصبی برای قیمت‌گذاری اختیارهای مانع اروپایی

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه مازندران، بابلسر، ایران

چکیده

در دهه‌های اخیر، محققان در رشته‌های مختلف تلاش‌های زیادی برای یافتن رویکردهایی مناسب جهت پیش‌بینی بازارهای مالی انجام داده‌اند. با توجه به اینکه پیش‌بینی کامل بازارهای مالی بسیار دشوار است، روش‌های یادگیری ماشین، می‌توانند به بهبود این پیش‌بینی‌ها کمک کنند. روش شبکه عصبی یکی از این روش‌های یادگیری ماشین است که در مدل‌سازی رفتارهای اقتصادی خوب عمل کرده است. در این مطالعه، از الگوریتم شبکه عصبی مبتنی بر روش ماشین ﯾﺎﺩﮔﯿﺮﯼ حداکثری بهبود یافته با پایه چندجمله‌ای لژاندر، برای تعیین قیمت ﺍﺧﺘﯿﺎﺭ ﻣﺎﻧﻊ ﺩﻭﮔﺎﻧﻪ استفاده شده است. حاصل‌ضرب کرونکر دو چندجمله‌ای لژاندر به‌عنوان توابع پایه شبکه‌های پنهان انتخاب می‌شود. مدلی که برای ارزش‌گذاری اختیار مانع دوگانه در نظر گرفته شده، تعمیم مدل کاکس است که نشان‌دهنده رابطه معکوس بین قیمت دارایی پایه و نوسانات آن است. در این مدل، پارامترهای مسأله به‌صورت توابع وابسته به زمان انتخاب می‌شوند. ابتدا روش شبکه عصبی را بر روی مدل پیشنهادی پیاده‌سازی و سپس با ارائه برخی نتایج عددی صحت روش مورد بررسی قرار می‌گیرد.

کلیدواژه‌ها

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