# one-step-ahead Stochastic Volatility for 5-minute VWAP prices

I'm trying to run an SV model against prices of Euro/USD. For those not familiar with SV, its a volatility model in which each point gets its own volatility parameter $h_t$ with 3 main parameters that are derived using a monte carlo simulation (MCMC),

• $\mu$ = average of the volatility across the entire sample set
• $\phi$ = the weighting that the volatility of the last point has on thenext (predicted) volatility
• $h_t$ = the most recent - {time interval}'s volatility.
• $\sigma$ = volatility of the volatility

Once we have $\mu$, $\phi$, and $h_t$ we can predict $h_{t+1}$, that is, the predicted volatility of the next point, by $h_{t+1} \sim \text{Normal}(\mu+\phi(h_t-\mu), \sigma)$.

I'm wondering if I'm doing the next part correctly:

To put this into practice, we run a MCMC every 5 minutes, gathering those variables and predicting $h_{t+1}$. This results in a graph like this, for CME futures contract 6EU4 (September euro) with 5-period BBands also displayed. Ignore the shapes that appear on the graph. It feels inaccurate, so I'm not sure if I'm doing something wrong. Did I understand the process correctly? phi is around .55 for the first half of the day, then jumps to .95 and stays there, which seems wrong, but I guess it isn't too surprising given the data...

R's package stochvol is taking care of the parameter estimation, so assume that the numbers themselves are accurate.

Should I paste the 5-minute Volume Weighted Average Prices here? its a pretty long data set. I'll edit it to do that if so.

## migrated from stats.stackexchange.comAug 19 '14 at 16:29

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• You might want to migrate this question over to the Quantitative Finance forum, and get more/better responses there. If you feel your data/code are too long to post here, just link to it instead from pastebin, Google docs, etc. – rocinante Aug 18 '14 at 23:36
• Ok, thanks. Is there a way to just switch it over or do I have to repost? And thanks to Patrick Coulombe for adding LaTeX. I looked around to try to do that and couldn't figure it out, now that I can see the side-by-side markdown in edits it helps. – hedgedandlevered Aug 19 '14 at 12:35
• Why Volume Weighted average price? Why not EMa or WMA? You wrote good description for stochastic volatility – John Apr 16 '15 at 10:08