How do we model for stock, bond prices and then value an option considering

Figure 10.3: Upward and downward price fluctuation of typical stock

Here is the rate of interest for the stock market price increase, which more generally can be described as the average price increase on a continuous compounding case.

Figure 10.4: Price movement of a typical bond

Here  is the rate of interest for the bond market price increase, which more generally can be described as the average price increase on a continuous compounding case.

In case we have such n time periods, i.e.,  then the corresponding calculations will be as shown as below with the help of Figure 15.

Figure 10.5: Price fluctuation of a typical stock for three time periods, and three states of price movement

At time  let the state of the system be , then we have