Gaussian moving averages, semimartingales and option pricing
نویسندگان
چکیده
منابع مشابه
Gaussian Moving Averages and Semimartingales
In the present paper we study moving averages (also known as stochastic convolutions) driven by a Wiener process and with a deterministic kernel. Necessary and sufficient conditions on the kernel are provided for the moving average to be a semimartingale in its natural filtration. Our results are constructive meaning that they provide a simple method to obtain kernels for which the moving avera...
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A generalized option-pricing formula is found, based on a nonGaussian stock price model. The dynamics of the underlying stock are assumed to follow a stochastic process with anomalous nonlinear diffusion, phenomenologically modelled as a statistical feedback process within the framework of the generalized thermostatistics proposed by Tsallis. A generalized form of the Black-Scholes differential...
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We show how no-arbitrage pricing can be extended to some non-semimartingale models by restricting the class of admissible strategies. However, this restricted class is big enough to cover hedges for relevant options. Moreover, we show that the hedging prices depend essentially only on a path property of the stock price process, viz. on the quadratic variation. As a consequence, we can incorpora...
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More generally, weighted averages may also be used. Moving averages are also called running means or rolling averages. They are a special case of “filtering”, which is a general process that takes one time series and transforms it into another time series. The term “moving average” is used to describe this procedure because each average is computed by dropping the oldest observation and includi...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2004
ISSN: 0304-4149
DOI: 10.1016/j.spa.2003.08.002