Bankers and advisers say the pace of issuance has been swift as inflation fears and the potential for rising interest rates have come to the front of many investors’ minds.

The terms have been so good for companies selling convertible debt that 28 of them are paying no interest on the bonds, the highest number since 2001. The average interest coupon on convertible debt in 2021 is 1.41%, the lowest on record. On average, this year’s crop of issuers will only need to convert bonds into stock if their share price rises 39% typically within a five-year period, the highest so-called conversion premium since 2003, according to Dealogic.

“These are the best terms in the history of the market,” said Vijay Culas, the founder and chief executive officer of Matthews South, which advises issuers on convertible-debt offerings. “We’ve never seen anything like this.”

The pace of issuance also shows just how optimistic many companies are about their business prospects and the future of the stock market. A rising market and strong business performance would help the companies’ stocks hit the conversion target, wiping out the debt and exchanging it for stock while investors largely remain happy—despite some dilution—because their shares have risen so much.

Even with such a low cost of capital, companies often enter into derivatives contracts where they are willing to pay $10 million or more to protect against dilution if their shares move above the conversion price.

The backdrop has been relatively ideal for many issuers, as investors have been eager to find any way they can into fast-growing technology companies, which constitute a large portion of the firms that issue this debt. The terms for tech companies have been even better, as they have paid 0.31% on average in interest rates and have had conversion premiums of 44%. Many companies that issue convertible debt are also ones that have recently gone public, largely through traditional initial public offerings.

Issuing convertible debt is viewed as preferable to selling stock because with a convertible issuance, companies would only issue stock later if its shares rise, and much of that dilution could be hedged through those contracts.

Serkan Savasoglu, a managing director and head of global equity solutions at

Morgan Stanley,

said many issuers this year have sold convertible bonds to raise money because they see opportunities for acquisitions, business investments or stock buybacks. “This year is more positive and bullish and confidence driven,” he said.

That is in contrast to last year, where particularly in the first half as the coronavirus pandemic raged, many issuers were raising capital defensively. 2020 was a record year for convertible-bond issuance, with 186 companies issuing $111.2 billion of them. If 2021 stays on pace, it would easily eclipse last year.

Some of the best terms ever came in February and March before interest rates started to tick higher. In February,

Expedia Group Inc.

issued $1 billion in convertible debt with no coupon and with a so-called conversion premium of 72.5%, meaning that investors would only get shares if Expedia’s stock jumped that much. Expedia’s stock is up nearly 20% since then.

Airbnb Inc.

issued $2 billion in convertible bonds in February with a zero coupon and a 60% conversion premium. That was done partially to refinance high-interest debt Airbnb took on last year to weather the pandemic.

Still, even as interest rates have ticked up, activity remains robust. Over the past week, four companies, including

Coinbase Global Inc.,

have raised more than $2 billion in convertible debt. Coinbase went public in April through a direct listing and didn’t raise any new capital in the process. The company raised $1.25 billion in convertible bonds last week.

“Convertible debt was the most natural instrument because of the low dilution and the speed to market,” Coinbase Chief Financial Officer

Alesia Haas

said in an interview.

Of the still small number of companies that have pursued direct listings in lieu of traditional IPOs, several have opted to raise capital through convertible-debt offerings, including

Spotify Technology SA

and

Slack Technologies Inc.

Even with rates on the rise, industry observers predict that companies, including those pursuing direct listings, will continue to see the convertible-bond market as a compelling alternative for investors who want another way into hot companies.

“There’s a broad buyer base that will keep things busy and a more diversified universe of issuer clients,” said Morgan Stanley’s Mr. Savasoglu.

Write to Maureen Farrell at maureen.farrell@wsj.com