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Is that what OTC purchases are?
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I believe OTC refers to trades that don't necessarily use an exchange and order book to find trading partners. So more like a trade between two traders directly (or more likely) via some broker.
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some examples:
Coinbase Custody + Coinbase OTCCoinbase Custody + Coinbase OTC
Coinbase Custody is now directly integrated with Coinbase’s OTC desk. Custody clients can leverage the OTC desk to price and confirm trades before moving funds. Additionally, we’ve honed this process to make it as simple and smooth as possible — our OTC and Custody client service teams work together to provide a single point of contact throughout the entire process. For clients initiating positions, the process is even simpler: they can buy OTC and settle assets directly into Custody.
https://www.coinbase.com/en-pt/blog/coinbase-custody-agency-otc-instant-liquidity-on-offline-funds
What is Binance OTC & Execution Services?What is Binance OTC & Execution Services?
Binance OTC & Execution Services is a premier one-stop solution for executing large or complex trades with precision, confidence, and discretion.
It provides seamless access to deep liquidity and advanced execution tools, including Request for Quote (RFQ), Indication of Interest (IOI), and algorithmic Direct Market Access (DMA), all supported by white-glove service when required.
https://www.binance.com/en/otc
Your strategic trading edge: Execute at the right moment with flexible settlement and premium service.
https://www.kraken.com/institutions/otc
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If Strategy buys from Coinbase and Coinbase is Strategy's custodian, then it doesn't even need to be paper bitcoin (which I take to mean bitcoin that is sold but which doesn't actually exist as a UTXO -- ie. rehypothication) -- it could just be Coinbase changing database numbers for its clients.