Problems of binomial options pricing Model

If we want to find the price of the option using Binomial Model,We need

1)Risk-free rate of interest
2)The possible share-price moves

3)Time period

->Risk free rate is the market interest rate,

->Time period is depending on option expiry,, either 1month,3 month or 6 months.

->But the most crucial is possible share price moves,  it is very difficult to predict the change of price volatility.

To overcome this, we need to divide time up into many small steps.

As steps in time become shorter and shorter, discrete time will tend towards

continuous time and the jumps or falls in share prices in each period will become

infinitesimally small. For reasonably accurate results, the time to maturity should be divided into at least 50 steps.

As we move along the binomial tree hedge ratio changes i.e. dynamic hedge

needs to be rebalanced.

To overcome these difficulties, we go for

 The Black-Scholes Equation

•Because it is an analytical solution (I.e. one-step) and therefore more elegant and

computationally much more efficient.

•Black-Scholes makes one additional assumption that returns on assets are normally distributed.