• Corpus ID: 237420894

On the dependence between a Wiener process and its running maxima and running minima processes

@inproceedings{Dkabrowski2021OnTD,
  title={On the dependence between a Wiener process and its running maxima and running minima processes},
  author={Karol Dkabrowski and Piotr Jaworski},
  year={2021}
}
We study a triple of stochastic processes: a Wiener process Wt, t ≥ 0, its running maxima process Mt = sup{Ws : s ∈ [0, t]} and its running minima process mt = inf{Ws : s ∈ [0, t]}. We derive the analytical formulas for the joint distribution function and the corresponding copula. As an application we draw out an analytical formula for pricing double barrier options. 

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References

SHOWING 1-10 OF 13 REFERENCES
An Introduction to Copulas
These notes provide an introduction to modeling with copulas. Copulas are the mechanism which allows us to isolate the dependency structure in a multivariate distribution. In particular, we can
Martingale Methods in Financial Modelling
Spot and Futures Markets.- An Introduction to Financial Derivatives.- Discrete-time Security Markets.- Benchmark Models in Continuous Time.- Foreign Market Derivatives.- American Options.- Exotic
Copula methods in finance
TLDR
The author examines the implications of Sklar's theorem in financial applications: toward a non-Black-Scholes world for derivatives pricing, Hedging and Risk Management and the application of VaR bounds to copulas.
Multivariate Models and Dependence Concepts
Introduction. Aspects of Interpretation. Technical Considerations. Statistical Analysis. Special Methods for Joint Responses. Some Examples. Strategical Aspects. More Specialized Topics. Appendices.
Theory and applications of stochastic processes
Dependence modeling with copulas
Mathematical Handbook for Scientists and Engineers
Copula Theory and Its Applications
TLDR
The most important properties of copulas, several families of copula that have appeared in the literature, and which have been applied in various fields, and several methods of constructing multivariate copulas are reviewed.
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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