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hello this is David Harper a banach turtle with an illustration of the intuition behind the black-scholes Merton option pricing model certainly one of the most popular and famous pricing models in all of Finance what Iamp;#39;d like to do is build up to the black Scholes Merton so when we see the final formula itamp;#39;s not a total stranger to us the idea the intuition behind the black Scholes is that if we write a call option that we can hedge against that obligation with this portfolio in two parts and this portfolio is a replicating portfolio such that is if we dynamically rebalance it itamp;#39;s going to always match the payoff on the call that we write and therefore this the present value of this portfolio equals the present value of the call option so what I mean is with this replicating portfolio what we have here on the left is a long position in the stock but not an entire share of stock a fractional share of the stock signified by Delta so we have Delta times th