Dissertation: A new mathematical model for option pricing captures tail behavior

Financial markets throughout the modern world trade in derivative products such as options and futures. Options are financial instruments based on the underlying securities such as stocks. They give you a right to buy or sell a specified number of stocks or other securities at a predetermined price within a set time period.

Option pricing is an active area in financial industry. The value of an option is usually obtained by means of a mathematical option pricing model. Since, fractional Brownian motion and mixed fractional Brownian motion processes have some important features in order to get typical tail behavior from financial markets, such as self-similarity and long-range dependence. Then, they can play a significant role in option pricing models. In this thesis, the author introduces different extensions of the fractional models and applies them to value Asian, European and currency options.

One model used in this thesis is based on the stock price follows a time changed mixed fractional model. In this model, the subdiffusive mechanism of trapping events is applied in order to describe properly financial data exhibiting periods of constant value. For this object, the author replaced physical time with inverse alpha subordinator process to get subdiffusive characteristics from Asian and Asian power options.

The discrete time hedging in fractional Black-Scholes models is considered where the asset price follows a long-range dependent fractional Brownian motion. For a convex or concave European vanilla option, Shokrollahi constructs the conditional-mean hedge. This means that at each trading time the value of the conditional mean of the discrete hedging strategy coincides with the frictionless price. Frictionless means the continuous trading strategy price without transaction costs.

Further information

Foad Shokrollahi, tel +358 468856808, email: foad.shokrollahi@uwasa.fi

Shokrollahi, Foad (2019). Option pricing in fractional models. Acta Wasaensia 425. Doctoral Dissertation. University of Vaasa. Vaasan yliopisto.

Publication pdf:

http://urn.fi/URN:ISBN:978-952-476-870-2

Public defence

The public examination of Dr. Foad Shokrollahi´s doctoral dissertation in the field of mathematics ”Option pricing in fractional models” will be held on Friday, 28 July 2019  at 12 o’clock in Auditorium Nissi (K218) University of Vaasa.

Dr Lauri Viitasaari (University of Helsinki) will act as an opponent and professor Tommi Sottinen (University of Vaasa) as a custos. The examination will be held in English.