Abstract
In this study, we first present a time-fractional L e ^ vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L e ^ vy-time fractional diffusion equation of European-style options. Further, we introduce a more general model based on the L e ^ vy-time fractional diffusion equation and review some recent findings associated with risk-neutral free European option pricing.
Highlights
One of the significant problems in finance is to derive value from financially traded assets that is known as the pricing of financial instruments, for example, stocks, and it is a very interesting problem
Merton (1990, [1]) was among the first researchers who gave the systematic solution for this problem, and proposed the Black-Scholes (BS) model where the model rests on the assumption that the natural logarithm of the stock price St defined as follows: d(ln St ) = (μ − σ2 )dt + σdBt where μ > 0 is the average compounded growth rate of the stock St, and dBt is the increment of Brownian motion which assumed to have the Normal or Gaussian distribution, and σ ≥ 0 represents the volatility of the returns from holding St
The distribution of Lêvy process is characterized by the Lêvy-Khintchine formula and it is considered as a modified model that characterize the Lêvy process in a very compact way
Summary
One of the significant problems in finance is to derive value from financially traded assets that is known as the pricing of financial instruments, for example, stocks, and it is a very interesting problem. An example of a Lêvy process that is well-known from, for instance, the Black–Scholes–Merton option pricing theory is the Brownian motion (or Wiener process), where the increments are normally distributed. That was the finite-difference method for option pricing, having jump-diffusion as well as exponential Lêvy process models, see Lewis [7]. We modify European-style options under a risk-neutral probability condition for the stock-price assets, followed by liquidity market in the financial literature. We consider to generate some partial integro-differential equation for possible application to less-studied issues such as barrier options for finite moment having log-stable (FMLS) processes in the future.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
