The historical daily closing prices of an instrument can be found in the GET charts/v1/chart endpoint. Set the Horizon to 24 hours (1440 minutes) such that you get bars that covers 1 day each. For example create a request with UIC=21 (EURUSD) and AssetType=FxSpot:
GET chart/v1/charts/?AssetType=FxSpot&Horizon=1440&Uic=21
And you will get a response that looks like so:
{
  "Data": [
    ..,
    {
      "CloseAsk": 1.12199,
      "CloseBid": 1.12179,
      "HighAsk": 1.12966,
      "HighBid": 1.12946,
      "LowAsk": 1.11941,
      "LowBid": 1.11921,
      "OpenAsk": 1.12091,
      "OpenBid": 1.12071,
      "Time": "2017-06-14T00:00:00.000000Z"
    },
    ...
  ]
}
For Forex Instruments we provide both the bid and asks OHLC values. That's why there is both CloseAsk and a CloseBid. For charting these you can use the mid price defined as (CloseAsk+CloseBid)/2. Other instruments like shares only provides a closing price reflecting the last traded price of that day.
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