The short answer: yes, this is partially the reason.
Options trading is making a bet that a stock will go up or down. To accomplish this, you buy the rights to sell/buy stock at a given stock price (we call this a strike price). You do not OWN the stock, you borrow it, with the guarantee you can exercise your right to the buy/sell the stock once it hits the strike price.
When you trade options, you typically don't buy the right to buy/sell individual stocks, you buy the right to sell 100 at a time. This means if Softbank buys 4bil in options in companies, they now have the risk/reward of 400bil in the market. In order to give Softbank the rights to the stock if they were to exercise their options, banks must back those options with shares. You may see where this is going. By making 4bil in options orders, Softbank has caused banks to be forced to buy 400bil in stocks, pumping the price.
TLDR; Softbank forced banks to buy 400bil in stocks, effectively pumping the market
This isn't correct. Option prices are quoted as the price for one share, but you have to pay 100x.
The leverage you get from options is the difference between the price of the option and the price of the stock. The total value of the stocks you have the right to buy or sell is called the notational value.
Your multiply by a 100 thing isn't at all how this works.
Options trading is making a bet that a stock will go up or down. To accomplish this, you buy the rights to sell/buy stock at a given stock price (we call this a strike price). You do not OWN the stock, you borrow it, with the guarantee you can exercise your right to the buy/sell the stock once it hits the strike price.
When you trade options, you typically don't buy the right to buy/sell individual stocks, you buy the right to sell 100 at a time. This means if Softbank buys 4bil in options in companies, they now have the risk/reward of 400bil in the market. In order to give Softbank the rights to the stock if they were to exercise their options, banks must back those options with shares. You may see where this is going. By making 4bil in options orders, Softbank has caused banks to be forced to buy 400bil in stocks, pumping the price.
TLDR; Softbank forced banks to buy 400bil in stocks, effectively pumping the market