Binomial Lattice

Choose a lattice specification (e.g., Cox, Rubinstein, and Ross, or Jarrow and Rudd) to implement a binomial model to value European Call and Put options. Provide the relevant lattice values including the risk-neutral probability and up-and-down moves. Use Word's Equation Editor for all formulaic expressions. Briefly discuss how one obtains the values for the risk-neutral probability and up-and-down moves so that the lattice produces option values which converge to that of the Black-Scholes closed form solution. You will then value European Call and Put options for the following inputs:

S_0=75,100,125

X=100

r=.05

=.20

T=1,0.5,.0001

nsteps=10,25,50,75,100,200,...,1000

Using the above inputs, plot the value of the European Call and Put options (two separate graphs) for stock prices of 75, 100, and 125 and the number of time-steps to illustrate convergence of the lattice to the Black-Scholes closed for solution. That is, you will have 6 graphs (stock prices of 75, 100, and 125, European Call, European Put) where you can see how the value obtained from the lattice model converges to that of the Black-Scholes model for the same set of inputs. Briefly discuss what you see and how the values comport with the Black-Scholes model and your knowledge of option values.