Let (P_{t}) be the observed market price of an asset, which is related to the fundamental value

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Let \(P_{t}\) be the observed market price of an asset, which is related to the fundamental value of the asset \(P_{t}^{*}\) via Equation (6.9). Assume that \(\Delta P_{t}^{*}=P_{t}^{*}-P_{t-1}^{*}\) forms a Gaussian white noise series with mean 0 and variance 1.0. Suppose that the bid-ask spread is 2 cents. What is the lag-1 autocorrelation of the price change series \(\Delta P_{t}=P_{t}-P_{t-1}\) when the tick size is 1 cent.

\(P_t=P_t^*+I_t \frac{S}{2}, \tag{6.9}\)

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