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Derivative Pricing by Using Stochastic Volatility Model

Jahangiri, Eshagh | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51726 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Zohuri Zangeneh, Bijan; Zamani, Shiva
  7. Abstract:
  8. Option Pricing is one of the most challenging topics in the world of Finance. There are a lot of option pricing models such as Black-Scholes model, Binomial Trees model, Monte Carlo method and Stochastic Volatility model. The last one is the most famous among all of them. The profound financial crisis generated by the collapse of Lehman Brothers and the European sovereign debt crisis in 2011 have caused negative values of government bond yields both in the USA and in the EURO area. Therefore, Option Pricing Models should consider this fact. The stochastic volatility model of Oosterlee et al, notice a dynamic for interest rate and heeds interest rate as a stochastic factor. However, it does not cover the negative interest rate. Thus, the proposed model in this thesis is the generalized version of this model and considers Vasicek model for interest rate dynamic to tackle this problem and prices options with more accuracy than previous models. Specifically, the dynamics of the options underlying asset is described by two factors: a stochastic variance and a stochastic interest rate. The volatility is not allowed to be negative, but the interest rate is. The proposed model is examined by use of US S&P 500 index and options on it
  9. Keywords:
  10. Negative Interest Rate ; Stochastic Volatility Model ; Volatility ; Implied Volatility ; Option Pricing ; Heston Model ; Multifactor Pricing Model ; Derivative Pricing

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  • مقدمه
    • مروری بر ادبیات موضوع
    • نرخ بهره‌ی منفی
      • تعریف
      • تاریخچه
    • ساختار پایان نامه
  • تعاریف و مقدمات
    • آنالیز تصادفی
    • مالی
    • روش سریع‌ترین کاهش
  • مدل هستون
    • مدل تلاطم تصادفی هستون
    • جواب فرم بسته مدل هستون
  • مدل هستون-هال-وایت ترکیبی تعمیم یافته
    • سیستم معادلات دیفرانسیل تصادفی مدل HHW
    • تابع چگالی احتمال گذر مدل HHW
    • گشتاور متغیر قیمت
  • فرمول‌های قیمت‌گذاری اختیار اروپایی در مدل HHW
  • تحلیل و نتایج مدل HHW
  • نتیجه‌گیری
    • افق‌های پیش رو
  • چکیده انگلیسی
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