Some pointers on Derivatives

• Delta is always positive for Call and negative for Puts. Delta exposure is negative for Short Call and Long put.
• Everything else staying constant, the premium for a Call option keeps reducing as we approach the expiry. This is because of reducing Time value.
• When we short a call we have a positive pay off only when the option is Out of the money
• An easier way to understand Delta, is to think of it as an approximate possibility of the option being exercised.
• For delta hedging short positions we have to buy/sell options. You always "lock in a loss" trying to delta hedge a short call(short gamma) if we use only underlyings. This is because of the convexity, of the short call payoff. So only way to delta hedge in this case is to buy gamma by buying options.
• Call Deep ITM - Delta =1, Gamma= 0 ; Deep OTM - Delta =0, Gamma =0 ; ATM - Delta =0.5, Gamma=1