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Highs and lows: Some properties of the extremes of a diffusion and applications in finance
Author(s) -
Mcleish Donald L.
Publication year - 2002
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315950
Subject(s) - volatility (finance) , geometric brownian motion , economics , econometrics , currency , brownian motion , financial economics , diffusion , stochastic volatility , implied volatility , diffusion process , monetary economics , mathematics , statistics , economy , physics , thermodynamics , service (business)
Observations on security prices, currency exchange rates, interest rates, and other financial time series usually include not only an open and close, but also a high and low price for the period. For Brown‐ian motion and certain diffusion processes, the information on high and low prices is of considerable value, particularly for estimating volatility, correlations between processes, and in the pricing of look‐back and barrier options. For pricing more general derivatives, this information is useful to the extent that change in volatility is an important ingredient in the price. The author gives a simple geometric device for generating the extremes of Brownian motion, and geometric Brownian motion; he then uses these extremes in the estimation of the volatility of the processes and to study survivorship bias.