قيمت‌گذاري اختيارمعاملات اروپايي در شرايط عدم‌قطعيت براي قيمت بازار ريسك تلاطم

A proper understan‎ding of volatility behavior in financial markets plays a key role in option pricing. Owing to its assumption of constant volatility, the Black-Scholes model is limited in its ability to describe the actual behavior of market volatility. To overcome this limitation, the Heston model, by incorporating stochastic volatility, provides a more realistic framework for option pricing. Nevertheless, one of the major challenges in applying the Heston model is the uncertainty associated with the estimation of the market price of volatility risk. The main objective of this thesis is to investigate the impact of uncertainty in the market price of volatility risk on option pricing an‎d the option Delta. To this end, the Heston model with uncertainty in the market price of volatility risk is introduced. The pricing problem is then formulated as a stochastic optimal control problem, an‎d the corresponding partial differential equation is derived. This equation enables the computation of the upper an‎d lower pricing bounds under the extreme scenarios corresponding to the uncertainty interval of the market price of volatility risk. Next, an appropriate transformation is applied to the Heston equation, yielding a transformed formulation that provides a more suitable framework for numerical solution. A study of a butterfly option shows that uncertainty in the market price of volatility risk can lead to a significant difference between the upper an‎d lower pricing bounds. Furthermore, it has a considerable effect on the option Delta, particularly in the vicinity of the strike prices.

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