risk free arbitrage

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h21

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I know i may am been an idiot
But can someone take me through the whole calculation of risk free arbitrage, I simply can not make clear sense of it, how do you all memorize it?
1. decide what to buy sell - buy cheap, if the option under priced buy option, if the option over priced buy asset
2. calculate hedge ratio (can someone explain me the logic behind the hedge ratio? I am not clear with this at all)
3. calculate investment and return on expiration
I think i am mostly confused by hedge ratio, is it for each unit of instrument we are trying to hedge we buy this amount of hedging instrument? how should I think about it?
 
There are many, many arbitrage transactions; going through all of them is probably a waste of time.
It appears that you’re concerned primarily with option arbitrage. If so, the formula of interest is put-call parity: if the put and call prices violate the parity formula, there is an arbitrage opportunity.
Hedge ratios have nothing to do with arbitrage.
And, for whatever it’s worth, arbitrage is, by definition, risk-free.
 
There is no need to memorize specific transactions. Just understand parity conditions (formulas) and if in a particular case the left side is not equal to the right side then you act accordingly, i.e. sell higher side and buy lower side. The good thing about it is that mathematics helps even if you are confused with long/short terms. Lets look at put-call parity.
X/(1+r)^t+c-p=S
I reshuffled a bit to make you think about it because this is a crucial formula.
Now imagine left hand side is smaller than right hand side. You would long left hand side (buy bond, buy call, sell put) and short righ hand side (sell stock).
Now imagine left hand side is bigger than right hand side. You would short left hand side (sell bond, sell call, buy put) and long right hand side (buy stock).
Note how the command word long/short is equivalent to buy/sell, except when there is a minus sign. The minus sign reverses your action.
Now apply this to all parity conditions but there is no shortcuts to formulae. You must memorize them.
 
Hedge ratio you are probably referring to delta hedge. Option delta is option price sensitivity to stock price movement. A higher delta means you need fewer options to cover a stock position. The formula can’t be simpler
Number of options =number of stocks/delta
Since delta is a nuber between 0 and 1 you can deduce the math and the implications behind the formula.
 
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