I am recently studying mathematical finance, and I am not really familiar with how the financial system works. This might be a naive question: when reading some books on mathematical finance, "hedging" acts as a core concept. I understand that in some cases hedging does make sense, e.g., a farmer who wants to sell his wheat a few months later might prefer to short a forward to hedge against the risk. However, there are some cases that I really don't understand.
For example, "delta-hedging" seems to be a very important strategy. I can understand it mathematically, but I don't know why in practice people needs to implement delta hedging, because by the arbitrage free condition, a perfect delta-neutral hedging (rebalance the portfolio continuously to make it delta-neutral) is no more than making it a risk-free asset. Then why don't we directly buy a risk free asset? What's more, in practice perfect delta-hedging is impossible, then to hedge the portfolio, we have to finance more money...
It looks to me unreasonable that an investor bother to long/short some derivative and then hedge against the position, so I would like to know about some circumstances in the real world that we really need to hedge against the derivatives. Could you explain to me some reasons? Thanks in advance!
long/short some derivative and then hedge against the positionAre you sure this is the case, as it seems to go totally against the whole idea of derivatives ? Which book and which relevant part mentions this ?