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Hello all,

I am starting a new thread for greeks. I shall discuss all the greeks in coming days. So lets start with the delta.

Delta is the rate of change of option price with respect to the underlying asset.

Delta hedging is maintaining delta neutral portfolio. delta=dC/dS so delta hedging assumes that option price change linearly w.r.t. the underlying without considering the convexity of the option price w.r.t. the underlying. As delta keeps on changing with the price of the underlying in order to maintain a delta neutral portfolio the hedge position must be re-balanced continuously.

If portfolio is currently x dollars of stocks and we wish to hedge it against negative movement of stock prices than we can take (1/delta) position in put options. If portfolio position changes negatively to x-k where k is the downward movement of portfolio than the corresponding payoff for put options position is -delta*change in portfolio position(delta=-dP/dS) or equal to delta*-(-k)=delta*k.So net payoff is total position in put options*delta*k=(1/delta)*delta*k=k. so overall change in position of combination of put options and portfolio is zero(k+(-k)=0).

The delta neutral hedging is ideal for very small changes in the value of the underlying but for good changes in underlying value the hedge position needs to be maintained continuously.

The delta of a European call with on a non dividend paying stock is N(d1) and delta of the European put on the stock is N(d1)-1.

thanks

I am starting a new thread for greeks. I shall discuss all the greeks in coming days. So lets start with the delta.

Delta is the rate of change of option price with respect to the underlying asset.

Delta hedging is maintaining delta neutral portfolio. delta=dC/dS so delta hedging assumes that option price change linearly w.r.t. the underlying without considering the convexity of the option price w.r.t. the underlying. As delta keeps on changing with the price of the underlying in order to maintain a delta neutral portfolio the hedge position must be re-balanced continuously.

If portfolio is currently x dollars of stocks and we wish to hedge it against negative movement of stock prices than we can take (1/delta) position in put options. If portfolio position changes negatively to x-k where k is the downward movement of portfolio than the corresponding payoff for put options position is -delta*change in portfolio position(delta=-dP/dS) or equal to delta*-(-k)=delta*k.So net payoff is total position in put options*delta*k=(1/delta)*delta*k=k. so overall change in position of combination of put options and portfolio is zero(k+(-k)=0).

The delta neutral hedging is ideal for very small changes in the value of the underlying but for good changes in underlying value the hedge position needs to be maintained continuously.

The delta of a European call with on a non dividend paying stock is N(d1) and delta of the European put on the stock is N(d1)-1.

thanks

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