Giovanni Ceccarelli at the University of Parma is the modern economic historian who happens to have looked most extensively at the workings of late medieval insurance, and I’ll be picking from his various writings for this answer. Ceccarelli's findings won't link up perfectly with your time period or your broader question though: insurance as we would understand it only emerged about two centuries after the period you mention (in the fourteenth century - and Ceccarelli certainly didn't come up with that assessment; Florence Edler de Roover pointed out as much in Early Examples of Marine Insurance way back in 1945) and generally focused on elaborate but subjective probabilistic models mostly focused on long-distance sea travel. Insurance is fundamentally a medium to reduce risk, and for a long time the only people really dealing in risk reduction experiments were merchants (whose risk-reward tradeoff was generally highest in the medieval economy). Before the emergence of insurance contracts, reducing risk was generally achieved via dividing the investment up amidst many partners (and the names and shapes of these partnerships could vary enormously from place to place) or via more expensive “Sea Loans” shifting the risk from the merchant to a lender. Sea Loans are actually similar to modern Trade Finance loans in that the merchant finances a trip with the expectation that it will be repaid once the goods arrive to the destination, with the significant difference that Sea Loans needed only be repaid if the ship actually arrived in the destination harbor. These contracts were risky for the lender though, and they were understandably expensive for the borrower. How expensive was “expensive?” Venetian or Genoese bankers (in other words, bankers with the most liquid financial networks whose rates should be lowest) regularly charged interest of 40% or 50% as a matter of course — an oft-cited example which has been well-documented is a Venetian merchant in Constantinople who in 1167 borrowed 88 Perpers (a Byzantine coin common in the eastern Mediterranean) and promised to repay 129 Perpers upon the safe return of his ship from its voyage. That’s an interest rate of around 45%.

So the first answer to your question is that “insurance” in the period you mention would probably take the form of a “Sea Loan” to be repaid upon safe return from the venture with an interest payment between 40% and 50%: more towards 40% for a solid ship and experienced captain and crew on a safe voyage, and more towards 50% if the ship was in poor condition, the captain and crew unproven, and if the voyage was known to be longer or riskier. More commonly though, risk reduction would be achieved by involving multiple partners such that in the instance of a failed venture, the loss would split up among multiple investors.

But what about actual insurance? Well, the reason it didn’t really exist before the 14th century is that in order to calculate an insurance premium a rudimentary knowledge of probability is required (a study which in Western and Southern Europe emerged precisely in the fourteenth century, although it wouldn’t be truly formalized until at least the 17th) as well as requiting an understanding of accounting such that probabilities can be assigned a monetary value (accounting has a longer history than probability theory, but generally this sort of assessment required the more detailed systems which were emerging in the late middle ages, even though the discipline wouldn’t be truly formalized until the late 15th century — meaning that overall, “winging it” was a big component of the first few centuries of insurance premium calculation, with all the inconsistencies and gaps in logic which we would expect an emergent and as yet unformalized process to have).

Can we look at the empirical evidence to give us an idea of what an emergent insurer need to know in order to judge the value of a premium? We can try; one of Ceccarelli’s favorite sources is the library of the Datini Foundation, which contains a large number of 14th century insurance contracts that we can examine to see what went into calculating an insurance premium:

• The kind of ship and its construction would be the first thing to consider, in that insurers were very meticulous in assessing the condition and construction of sailing ship. An ordinary merchant vessel might add 3% or 4% to the premium, but a ship armed in the venetian arsenal would only add a mere 1.5%. Any well-armed ship could see its insurance rate cut in half compared to its unarmed peers.

• The crew would also be an important item to consider for the insurer. This was not limited to the captain’s track record and reputation (which could improve an insurance appraisal, but doesn’t actually seem to have been cited as a factor harming an appraisal): a merchant leading an expedition who had a history of being unreliable could see see up to 8% added to the premium for their expeditions (with some particularly unreliable merchants charged even more!) while a more standard reputation would set the added premium at around 5%;

• The route of the journey. Insurers were actually surprisingly disinterested in the actual distance an expedition was expected to travel. Rather, beyond the risks tied to war and piracy, ports-of-call were seen as the most important factor in determining risk. This means that short voyages to a harbor considered “risky” could be more expensive to insure than a long voyage destined for safer harbors (by margins of up to 4% to 5%!). Insurance contracts could even specify that cargo lost in particularly risky harbors could disqualify merchants from collecting the insurance due altogether, as could cargo lost in known war zones. Further, scheduling calls in certain harbors might also trigger increases in premiums depending on the season (this was generally the case if the winter was known to cause particularly averse conditions, although it only seems to have affected certain harbors and insurers were generally surprisingly indifferent to weather and seasons);

• Lastly, the nature of the expedition and goods being transported. Naturally, more delicate goods which risked breaking or being damaged over the journey were more expensive to insure than hardier goods (although while insurers were very detailed in their appraisals of cargo, there appears to be little consistency as to how these appraisals ultimately influenced premiums; it would seem that this was the most subjective metric of all).

So in all, summing the individual factors insurance premiums generally hovered between 6% to 8% at the low end (a well-armed venetian vessel carrying hardy goods to a safe harbor, guided by a seasoned captain with trustworthy merchants organizing the expedition) and up to 15% or even 20% at the higher end (a vessel in poorer shape carrying fragile goods, contracted by an untrustworthy merchant traveling to a risky harbor, or through a war zone). Where was the average? Probably around 10%, with various positive and negative factors influencing the ultimate number in their own way.

What does this mean for your question? I’m afraid I wasn’t very helpful. Late medieval insurance was mostly focused on mercantile expeditions with clear objectives which were could be assessed and cited in insurance contracts. The goal was to reduce risk for the merchants organizing the expedition. In order to accurately appraise the risk involved and the premium to charge, insurers meticulously documented the variety of factors involved, meaning that the insurance premium would be dependent on those factors.