• Corpus ID: 59937451

An extremal fractional Gaussian with a possible application to option-pricing with skew and smile

@article{Jurisch2018AnEF,
  title={An extremal fractional Gaussian with a possible application to option-pricing with skew and smile},
  author={Alexander Jurisch},
  journal={arXiv: Pricing of Securities},
  year={2018}
}
  • A. Jurisch
  • Published 8 April 2018
  • Mathematics
  • arXiv: Pricing of Securities
We derive an extremal fractional Gaussian by employing the L\'evy-Khintchine theorem and L\'evian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and exponentially convergent option-pricing formula for fractional markets. We also carry out an analysis of the structure of the implied volatility in this system. 

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References

SHOWING 1-10 OF 24 REFERENCES
A non-Gaussian option pricing model with skew
Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative
Non-Gaussian Analytic Option Pricing: A Closed Formula for the Lévy-Stable Model
We establish an explicit pricing formula for the class of L\'evy-stable models with maximal negative asymmetry (Log-L\'evy model with finite moments and stability parameter $1
Option pricing formulas based on a non-Gaussian stock price model.
TLDR
A generalized form of the Black-Scholes (BS) partial differential equation and some closed-form solutions are obtained and a good description of option prices using a single volatility is obtained.
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and
Theory of Rational Option Pricing
The long history of the theory of option pricing began in 1900 when the French mathematician Louis Bachelier deduced an option pricing formula based on the assumption that stock prices follow a
A Theory for the Term Structure of Interest Rates
TLDR
The discretised theoretical distributions matching the empirical data from the Federal Reserve System are deduced from aDiscretised seed which enjoys remarkable scaling laws and may be used to develop new methods for the computation of the value-at-risk and fixed-income derivative pricing.
Stock index futures markets: stochastic volatility models and smiles
This study examined whether the inclusion of an appropriate stochastic volatility that captures key distributional and volatility facets of stock index futures is sufficient to explain implied
The Pricing of Options and Corporate Liabilities
If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this
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