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I would like to examine the impact of the volatility on the transaction costs (Bid-ask spread). In my case I would like to examine this for power prices. However, I don't have access to actual order book data. My approach would be now to test this theoretically by simulating for different bid-ask spread percentages of the prices two series with predetermined volatility (by using an Ornstein-Uhlenbeck process) to then somehow quantify the impact on the volatility. My question is if this approach is somewhat valid or if there are other possibilities.

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    $\begingroup$ Why do you think it is the bid offer which is a determining factor of volatility? I would posit that the volatility (amongst other things) is a factor in the width of the bid/offer. $\endgroup$ – will Sep 7 '20 at 8:44
  • $\begingroup$ @will sorry I misphrased the question. I edited it now. The question is how much the volatility of the price series is contributing to the bid ask spread. $\endgroup$ – Question Anxiety Sep 7 '20 at 10:08
  • $\begingroup$ I think it really depends on what you plan on doing with it. Realistically, there are multiple factors of both the volatility and the bid/offer spread, some of them are the same, some are unrelated, and the vol will influence the bid/offer spread, and also in some scenarios the bid/offer will influence the vol. There will also be seasonal aspects on multiple time scales (i.e. morning bid/offer vs. afternoon vs. during the settlement window, as well as prices getting wider in the summer as trading volumes drop). You'll also have the underlying price playing a roll, as well as recent price mo... $\endgroup$ – will Sep 7 '20 at 11:28
  • $\begingroup$ ...ves. It is not a simple thing to model, and so depending on what you want to actualyl investigate, you should limit your similation to those aspects (and the factors which influence them strongly). Can you provide any more information on your use case? $\endgroup$ – will Sep 7 '20 at 11:29
  • $\begingroup$ Volatility and the bid-ask spread are different and identifying the different effects may be difficult. An O-U process is not exactly what you want; rather, you want something much more like a Roll model. $\endgroup$ – kurtosis Sep 7 '20 at 20:23
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If you want to model bid-ask spreads, I suggest you first read up on estimating bid-ask spreads. I have an overview here, but the gist of it is that the bid-ask spread affects estimates of the volatility. Microstructure models such as Kyle (1985) and Glosten and Milgrom (1985) show that the volatility affects the bid-ask spread. Note that none of these presumes an O-U model. Rather, the existence of a bid-ask spread induces a negative autocorrelation. You might want to consult Foucault, Pagano, and Röell's Market Liquidity for more information and background.

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  • $\begingroup$ my approach would be a monte-carlo simulation based way, where I would use the O-U model (it captures some of the features of power prices) to simulate price paths for different input parameters. Do you think that this might be a valid approach as well? $\endgroup$ – Question Anxiety Sep 8 '20 at 15:05
  • $\begingroup$ Ah, you did not mention you are modeling power prices. In that case, an O-U model might make sense for the base power prices but not the bid or ask. Also, the difficulty of storage for power makes an O-U have a slower and less forceful reversion than for, say, natgas. Just something to keep in mind. $\endgroup$ – kurtosis Sep 8 '20 at 18:19
  • $\begingroup$ So there is not a way to somehow simulate the bid-ask spread by some kind of SDE? The problem is I do not have access to order book data I only have the time series of hourly/daily etc. prices. Is there maybe a way to use that information included in there to do some kind of a simulation? $\endgroup$ – Question Anxiety Sep 9 '20 at 8:56
  • $\begingroup$ There are SDEs which can be built, but they are closer to the jump-diffusion type of evolution -- except the jumps immediately revert. If you follow the link and read the articles, you will probably find that the Roll (1984) model is a good place to start. That link also is probably more than you will find almost anywhere on estimating bid-ask spreads without quote or order book data -- though that's just my opinion as someone who has done research in that area. $\endgroup$ – kurtosis Sep 9 '20 at 13:29

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