source('utils.R')

S0 = 50
K = 50
sigma = 0.2
r = 0.1
D = 3 ## the dividend payment (per share)
delta = 3.5/12 ## of a year (when the dividend payment is made)

n_months = 6
T = n_months/12

delta_t = 1/12 ## monthly timesteps

## Parameters of the stock:
##
u = exp(sigma*sqrt(delta_t))
d = 1/u
R = 1 + r/12 # total return over the next month
q = (R - d)/(u - d)
print(c(u, d, R, q))

## Build the stock (S*) the random component stock lattice:
##
SStarSpot = make_spot_table(S0 - D*exp(-r*delta), u, d, n_months)
print('S* (random part) lattice=')
print(round(SStarSpot, 2))

## Compute the true stock price lattice (including the present value of the dividend):
##
n_steps = n_months+1
n_rows = n_steps
SSpot = matrix(NA, nrow=n_rows, ncol=n_steps)
for( jj in 1:n_steps ){
    ## Has the dividend been paid yet?
    ##
    t = (jj-1)/12
    if( t < delta ){
        div_part = D*exp(-r* (delta-t))
    }else{
        div_part = 0
    }

    for( ii in 1:jj ){
        SSpot[ii, jj] = SStarSpot[ii, jj] + div_part
    }
}
print('Stock Price lattice=')
print(round(SSpot, 2))

C_European = evaluate_call_option(SSpot, K, q, R, type='European')
print('European call option value=')
print(round(C_European, 2))

C_American = evaluate_call_option(SSpot, K, q, R, type='American')
print('American call option value=')
print(round(C_American, 2))