On the correlation of the supremum and the infimum and of maximum gain and maximum loss of Brownian motion with drift

Date

2013-08-15

Author

Vardar Acar, Ceren
Szekely, Gabor J.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

177
views

0
downloads

Investors are naturally interested in the supremum and the infimum of stock prices, also in the maximum gain and the maximum loss over a time period. To shed light on these relatively complicated aspects of sample paths, we consider Brownian motion with and without drift. We provide explicit calculations of the correlation between the supremum and the infimum of Brownian motion with drift. We establish a number of results concerning the distributions of maximum gain and maximum loss. We present simulation studies of maximum gain and of maximum loss of Brownian motion with a range of values for the drift. We conjecture that the correlation between maximum gain and maximum loss has a minimum value of -0.5 at drift 2.

Subject Keywords

Applied Mathematics, Computational Mathematics

URI

https://hdl.handle.net/11511/48664

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2013.01.010

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

Analysis of volatility feedback and leverage effects on the ISE30 index using high frequency data Inkaya, A.; Okur, Y. Yolcu (Elsevier BV, 2014-03-15) In this study, we employ the techniques of Malliavin calculus to analyze the volatility feedback and leverage effects for a better understanding of financial market dynamics. We estimate both effects for a general semimartingale model applying Fourier analysis developed in Malliavin and Mancino (2002) [10]. We further investigate their joint behaviour using 5 min data of the ISE30 index. On the basis of these estimations, we look for the evidence that volatility feedback effect rate can be employed in the s...
RMARS: Robustification of multivariate adaptive regression spline under polyhedral uncertainty Ozmen, Ayse; Weber, Gerhard Wilhelm (Elsevier BV, 2014-03-15) Since, with increased volatility and further uncertainties, financial crises translated a high "noise" within data from financial markets and economies into the related models, recent years' events in the financial world have led to radically untrustworthy representations of the future. Hence, robustification started to attract more attention in finance. The presence of noise and data uncertainty raises critical problems to be dealt with on the theoretical and computational side. For immunizing against para...
Stochastic processes adapted by neural networks with application to climate, energy, and finance Giebel, Stefan; Rainer, Martin (Elsevier BV, 2011-10-01) Local climate parameters may naturally effect the price of many commodities and their derivatives. Therefore we propose a joint framework for stochastic modeling of climate and commodity prices. In our setting, a stable Levy process is drift augmented to a generalized SDE. The related nonlinear function on the state space typically exhibits deterministic chaos. Additionally, a neural network adapts the parameters of the stable process such that the latter produces increasingly optimal differences between si...
Solving optimal investment problems with structured products under CVaR constraints Korn, Ralf; Zeytun, Serkan (Informa UK Limited, 2009-01-01) We consider a simple investment problem where besides stocks and bonds the investor can also include options (or structured products) into the investment portfolio. The aim of the investor is to maximize the expected return under a conditional value-at-risk (CVaR) constraint. Due to possible intermediate payments, we have to deal with a re-investment problem which turns the original one-period problem into a multi-period one. For solving this problem, an iterative scheme based on linear optimization is deve...
Calibration of stochastic models for interest rate derivatives Rainer, Martin (Informa UK Limited, 2009-01-01) For the pricing of interest rate derivatives various stochastic interest rate models are used. The shape of such a model can take very different forms, such as direct modelling of the probability distribution (e.g. a generalized beta function of second kind), a short-rate model (e.g. a Hull-White model) or a forward rate model (e.g. a LIBOR market model). This article describes the general structure of optimization in the context of interest rate derivatives. Optimization in finance finds its particular app...

Citation Formats

C. Vardar Acar and G. J. Szekely, “On the correlation of the supremum and the infimum and of maximum gain and maximum loss of Brownian motion with drift,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 61–75, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48664.