I have read about futures and options ( from online resources ). I only have the basic understanding,not math heavy ( for eg. for Black Scholes I know only the intuitive idea from the khan academy video mentioned ). So I decided to go through J.C. Hull on derivates being a complete beginner, to get more better idea.
I currently completed going through the first 3 chapters ( majorily introduction and furures pricing). I thought I'll try to answer this stupid question of mine once I reach the chapter on Black Scholes in the book. But seems it will take time.
In european options we assume some distribution of stock returns. Using it we know the probablity $p$ such that $S_T$ the stock price at expiry will be greater than $X$ the strike price. We also get to know $E[S_T|S_T \gt X]$, the expectation given option ends in money. So we price our option at current time to be $p*(E[S_T|S_T \gt X] -X)*d$, where $d$ is discount factor ( discounting to present value).
Likewise why is a future not priced at $E[S_T]$ assuming log normal distribution of stock returns ( like we did for options ). The current future price $F_0 = E[S_T]$ seems fair to me from the persepectives of both seller and buyer.
- From buyer side if price is above $E[S_T]$ (ie. $F_0 \gt E[S_T]$), the buyer is getting kind of a bad deal, as the buyer at this point is agreeing to buy it at $F_0$ at a future time when he expects that at that time the stock price would be less than $F_0$.
- From seller side if $F_0 < E[S_T]$ , the seller is kind of under paid for his asset.
But J.C. Hull also proves that an arbitrage free pricing of a future ( of asset like wheat) would be $S_0 + C$ ( $S_0$ is spot price, and $C$ is cost of carry ). Which also seems correct to me.
Which one is correct fair pricing of futures ?
PS: At the end of 3rd chapter J.C. Hull mentions about relation between $E[S_T]$ and $F_0$ using concept of systematic risk/ speculators and hedgers, which I did not completely understand.
PPS: Please forgive me if I used some wrong terminology. Hope with time I'll be able to learn the basics. Also forgive me if this question is really stupid, I could delete it if required.