Question

Suppose that the daily volatilities of asset A and asset B, calculated at the close of trading yesterday, are $1.6 \%$ and $2.5 \%$, respectively. The prices of the assets at close of trading yesterday were $\$ 20$ and $\$ 40$ and the estimate of the coeflicient of correlation between the returns on the two assets was 0.25 . The parameter $\lambda$ used in the EWMA model is 0.95 . (a) Calculate the current estimate of the covariance between the assets. (b) On the assumption that the prices of the assets at close of trading today are $$\$ 20.5$$ and $$\$ 40.5$$, update the correlation estimate.

   Suppose that the daily volatilities of asset A and asset B, calculated at the close of trading yesterday, are $1.6 \%$ and $2.5 \%$, respectively. The prices of the assets at close of trading yesterday were $\$ 20$ and $\$ 40$ and the estimate of the coeflicient of correlation between the returns on the two assets was 0.25 . The parameter $\lambda$ used in the EWMA model is 0.95 .
(a) Calculate the current estimate of the covariance between the assets.
(b) On the assumption that the prices of the assets at close of trading today are $$\$ 20.5$$ and $$\$ 40.5$$, update the correlation estimate.

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 23, Problem 9

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Step 1

The formula for the EWMA covariance is: $$ Cov_t = \lambda \cdot Cov_{t-1} + (1-\lambda) \cdot (r_{A,t} - \bar{r}_A) \cdot (r_{B,t} - \bar{r}_B) $$ where $Cov_t$ is the current estimate of the covariance, $Cov_{t-1}$ is the previous estimate of the covariance, Show more…

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Suppose that the daily volatilities of asset A and asset B, calculated at the close of trading yesterday, are $1.6 \%$ and $2.5 \%$, respectively. The prices of the assets at close of trading yesterday were $\$ 20$ and $\$ 40$ and the estimate of the coeflicient of correlation between the returns on the two assets was 0.25 . The parameter $\lambda$ used in the EWMA model is 0.95 . (a) Calculate the current estimate of the covariance between the assets. (b) On the assumption that the prices of the assets at close of trading today are $$\$ 20.5$$ and $$\$ 40.5$$, update the correlation estimate.

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