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

Vardar-Acar C., Zirbel C. L., Szekely G. J.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.248, ss.61-75, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 248
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.cam.2013.01.010
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.61-75
  • Anahtar Kelimeler: Brownian motion with drift, Scaling property, Uniform continuity, Markov property, Correlation coefficient
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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. (C) 2013 Elsevier B.V. All rights reserved.