برآورد ارزش در معرض خطر شرطی با استفاده از فرایند‌های لوی تلاطم تصادفی در بورس اوراق بهادار تهران

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، گروه ریاضی مالی، دانشگاه علامه طباطبائی، تهران،‌ایران.

2 استادیار، گروه مالی و بانکداری، دانشگاه علامه طباطبائی، تهران، ‌ایران.

3 کارشناسی ارشد مهندسی مالی و مدیریت ریسک، دانشگاه علامه طباطبائی، تهران،‌ ایران.

چکیده

 پژوهش‌های نشان داده است که تلاطم تصادفی و پرش‌ها در روند بازار قیمت سهام نقش مهمی را‌ایفا می‌کنند و در نظر گرفتن‌این دو عامل تاثیر بسزایی در  توصیف بهتر دارایی‌ها دارد.  فرایندهای پرش نامتناهی لوی ویژگی‌های چولگی و دم سنگینی بازده دارایی را پوشش ‌می‌دهند اما بیانگر تلاطم خوشه‌ای نمی‌باشند. با زمان متغیر کردن‌این فرایند‌ها توسط انتگرال فرایند کاکس ـ‌اینگرسول ـ راس، مدل فرایندهای لوی تلاطم تصادفی بدست می‌آید که در‌این مقاله در تعیین ارزش در معرض خطر شرطی به‌کار گرفته شده است. با کمک روش تبدیل فوریه سریع فرم بسته‌ای از تابع چگالی احتمال را به دست آورده شده است. همچنین با استفاده از الگوریتم ‌بهینه‌سازی ترکیبی ازدحام ذرات پارامترهای مدل برآورد شده است. ارزش در معرض خطر شاخص کل بورس اوراق بهادار تهران را در بازه زمانی ۱۳۸۸ تا ۱۳۹۸ بر مبنای مدل معرفی شده، برآورد کرده و با رویکردهای شبیه‌ساز تاریخی و واریانس ـ کوواریانس مقایسه شد. نتایج تکنیک‌های پس آزمون در مورد محاسبه ارزش در معرض خطر، حاکی از برتری مدل‌های لوی تلاطم تصادفی در مقایسه با رویکردهای شبیه‌ساز تاریخی و واریانس ـ کوواریانس است.

کلیدواژه‌ها

عنوان مقاله [English]

Estimation of Conditional Value at Risk under Stochastic Volatility Levy Processes for Tehran Stock Market

نویسندگان [English]

  • Navideh Modarresi 1
  • Moslem Peymani 2
  • Moshtagh Darvishi 3
1 *Assistant Prof, Department of Financial Mathematics, Allameh Tabataba'i University, Tehran, Iran .
2 Assistant Prof, Department of Finance and Banking, Allameh Tabataba'i University, Tehran, Iran.
3 M.Sc. in Financial Engineering and Risk Management, Allameh Tabataba'i University, Tehran, Iran.
چکیده [English]

Research has shown that stochastic volatility and jumps play an important role in stock price trends market, and considering these two factors has a significant impact on a better description of assets. Infinite jump Levy processes cover skewness and heavy-tailedness properties but can not present volatility clustering. By time chainging these processes by integrating the Cox-Ingersoll-Ross, it is abtained a stochastic volatility Levy processes model that are applied to determine the conditional value at risk (VaR) in this paper. Applying the fast Fourier transform, a closed form formula of probability density function is derived. Moreover, by applying Hybrid Particle Swarm Optimization algorithm, Grid search method and univariate method algorithm, the parameters are estimated. Based on the introduced model, we estimate the VaR of along total Index of Tehran Stock Exchange in 1388 to 1398 and compare it by historical simulation and Variance-Covariance approaches. The results of Back-test techniques in computing the VaR indicate that the stochastic volatility Levy processes with infinite jumps have better performance than the Variance-Covariance methods.

کلیدواژه‌ها [English]

  • Stochastic Volatility
  • Infinte Activity Levy Processes
  • Hybrid Particle Swarm Optimization Algorithm
  • Fast Fourier Transform

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چشم انداز مدیریت مالی
دوره 11، شماره 34
شهریور 1400
صفحه 69-94

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