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The martingale assumption is used to derive the conditional distribution of the underlying state of the stock, where … stock returns, and is not directly observable. The martingale characterization of returns reflects the 'rational expectation …
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Consider a semimartingale of the form Y_{t}=Y_0+\int _0^{t}a_{s}ds+\int _0^{t}_{s-} dW_{s}, where a is a locally bounded predictable process and (the volatility) is an adapted right - continuous process with left limits and W is a Brownian motion. We define the realised bipower variation process...
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the particular way that the variance is changing over time. The martingale hypothesis is tested with daily and weekly … daily data from 1981 to 1985. This rejection of the martingale hypothesis may be attributed to trading day effects in … foreign currency prices and the resulting day-of-the-week patterns in futures prices. When the martingale hypothesis is tested …
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