 These strategies adopted in two state model may not work well in the real world, say for one year model, because in real, there are more than many possibilities that stock prices can take other values. Now, to overcome this difficulty, the black skull or the BS model well serves the purpose, because through this model, the possibilities of multiple values can be reduced as this BS model helps in shorten the period. This black skull model has a insight back because it shortens the period involved in the strategies. As the stock price changes over first instant, another combination of the stock and boring needs to duplicate the call over the second instant and it goes on. Now, adjusting the combination from moment to moment can continually duplicate the call. The basic or fundamental intuition behind the BS model is that it helps in determining the duplicating combination at any moment and then it helps in valuing the option based on this duplicating strategy. In BS model, there are certain variables in the quantitative formulation where the in the model S stands for the current stock price, E is the exercise price of the call and R is the annual risk free of rate and that is continuously compounding. For sigma square, it is the variance per year in the return of the stock and T is the time in years to expiry. Then we have other two variables D1 or the delta and the D2. Additionally, there is a statistical variable that is in D. This states the possibility that a standardized normally distributed random variable will be less than or equal to D. Now, to understand the BS model, we have an example at the time 0 of October 4, the call option of April 49 has a value of price of dollar 4. Now, we assume that the stock price at time 0 is 0 and the stock price is 50 dollars, exercise price is 49 dollars, risk free rate is 7 percent. This call has 199 days to expire or the maturity date is 21st April of the year 1. The time to maturity in terms of ratio to the year is 199 over 365. So, this is equal to the variable T. The variance for the sigma square is 0.09 per year. Then using these variables, we can determine the value of this call with the help of the BS formula. Now, this BS formula works in three steps. At first step, we need to determine the value of D1 and DQ. Then we need to determine the value of ND1 and ND2. And in the last step, we need to determine the value of the call. Step 1, calculate the value of D1 and D2. Now, putting the values of variables relating to D1, we compute the value as 0.3742. And using this value of D1 in the model of D2, we can determine the value of D2 which is 0.1527. And in the second step now, we need to determine the value of ND1 and ND2. These two values can be found using the functions of normality distribution through the help of Excel. And using this function, we have the value of ND1 equal to 0.6459 and the value of ND2 as 0.5607. And at the step 3, using these variables, we can determine the value of a call through the model of BS. And the value of call is $5.85. The intuition from BS formula is that the value of call is basically the value of the call value. In which we have a stock price to multiply with the delta and getting the value deducted from our borrowing gives the value of call. That is the intuition behind the value of the black-skull model. We see that in our model, the value of ND is equal to the value of D1 which is equal to basically delta and it is 0.645. This delta states that we need to buy almost 65% of the share of the stock. And to duplicate the call, then we need to borrow an amount equal to $26.45. So this way we can duplicate the call.