According to Quran:
الَّذِينَ يَأْكُلُونَ الرِّبَا لَا يَقُومُونَ إِلَّا كَمَا يَقُومُ
الَّذِي يَتَخَبَّطُهُ الشَّيْطَانُ مِنَ الْمَسِّ ذَٰلِكَ بِأَنَّهُمْ
قَالُوا إِنَّمَا الْبَيْعُ مِثْلُ الرِّبَا وَ*أَحَلَّ اللَّهُ
الْبَيْعَ وَحَرَّمَ الرِّبَا* فَمَن جَاءَهُ مَوْعِظَةٌ مِّن رَّبِّهِ
فَانتَهَىٰ فَلَهُ مَا سَلَفَ وَأَمْرُهُ إِلَى اللَّهِ وَمَنْ عَادَ
فَأُولَٰئِكَ أَصْحَابُ النَّارِ هُمْ فِيهَا خَالِدُونَ
Those who devour usury will not stand except as stand one whom the
Evil one by his touch Hath driven to madness. That is because they
say: "Trade is like usury," but Allah hath permitted trade and
forbidden usury. Those who after receiving direction from their
Lord, desist, shall be pardoned for the past; their case is for Allah
(to judge); but those who repeat (The offence) are companions of the
Fire: They will abide therein (for ever). [2:275]
Thus, any trade that is reasonably correct (like any new trade based on financial theories) is allowed as long as it is not or does not include Ribaa (interest). The Islamically allowed set of trades contains Islamic Banking (although there exists some debates on the details), stock and insurance. However, if the question is about the details (e.g. for the rules of banking, stock and insurance in your region) then you may better ask a Fatwa from the scholar that you follow. See e.g. here, here and here.
PS. Only as a hint let me add that at the present era for trades we commonly use money or things like that (artificially or realistically) backed by gold, instead of gold and silver themselves. So for example we have the issue of economical inflation and there is a debate how interest and inflation should be dealt with in a new society. For example you borrow some money this year and aim to pay back the other year, but then we have the economical inflation, so that if you pay back the exact same money the other year the person who has lent you the money would have less "functional" money in hand. So that maybe increasing the money that you should pay back being larger in amount can be accounted as not an interest. However, the exact value of inflation during the period that the money is borrowed is not known before the lend-borrow deal, but only statistically estimated based on experiments. This is one issue regarding new trade methods, however, there are a number of similar issues to discuss about and these overall have resulted in the rules for Islamic Banking and etc. So I recommend you ask this from the scholar that you follow, or study such rules by yourself (you can start here).