source('utils.R')

sigma = 0.2
S0 = 62
K = 60
delta_t = 1/12
r = 0.10

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))

n_months = 5

## Build the stock lattice:
##
SSpot = make_spot_table(S0, u, d, n_months)
print('Spot 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))

## Build the call and put lattices:
##
P_European = evaluate_put_option(SSpot, K, q, R, type='European')
print('European put option value=')
print(round(P_European, 2))

## Price the "as you like it" option by working backwards:
##
n_months = 3
n_steps = n_months+1
asYouLikeIt = matrix(NA, nrow=n_steps, ncol=n_steps)
for( jj in seq(n_months+1, 1, -1) ){
    for( ii in 1:jj ){
        if( jj == (n_months+1) ){ ## the final column/timestep
            asYouLikeIt[ii, jj] = max( c(C_European[ii, jj], P_European[ii, jj]) )
        }else{
            asYouLikeIt[ii, jj] = (q*asYouLikeIt[ii, jj+1] + (1-q)*asYouLikeIt[ii+1, jj+1])/R
        }
    }
}
print(round(asYouLikeIt, 2))