When we replicate a portfolio of cash and stock for a call option, shouldn't the replicating portfolio's greeks be equal to options greeks?

Is that true? If it is, how is it that a portfolio of cash and stock has same vega as the option, since the vega of stock and cash is 0. What am I missing here?

Do the weights on cash and stock change in such a way with time such as to mimic the greeks, but at any single point the greeks of the portfolio aren't equal to options?


1 Answer 1


The pricing of options is married with the concept of a hedging strategy that replicates the effect of the option. If you can only long or short a stock that will not replicate the greeks, it only creates delta. It is the commitment to the strategy that achieves it.

For example if the price goes up and you are committed to buying more to increase your delta then you have simulated gamma. And if volatility increases then your expected activity under your hedging strategy also increases hence you have simulated vega, but it doesn't inherently exist in your portfolio of just owning a stock.


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