Excerpts from Demystifying Modern Convertible Notes (April 2024) (pdf):

To determine the magnitude of the short position, the investor uses a convertible note valuation model to generate an estimated fair value for the convertible note using the most currently available values for the model’s inputs. The investor then varies the common stock price input to the model while keeping all other inputs constant and observes how the estimated fair value of the convertible note changes. By doing so, the investor can estimate the sensitivity of the trading price of the notes to the trading price of the common stock. This sensitivity is called “delta.”
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For various reasons, short sales of the underlying stock are currently the most common means of implementing a delta-neutral convertible note hedging strategy.
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If the stock price tends to oscillate, which may be expected of highly volatile stocks, then these dynamic adjustments can themselves drive profits, since they will consist of short sales at relatively high prices and the closing of short sales by buying shares at relatively low prices.