source('../Chapter12/utils.R')

sigma = 0.03 * 12 ## from per month to per year
delta_t = 1/12 ## monthly timesteps

## Parameters of the stock:
##
u = exp(sigma*sqrt(delta_t))
u_wrong = exp(sigma*delta_t)
##u = u_wrong ## test the books value of u
d = 1/u
r = 0.05
R = 1 + delta_t*r # total return over the next month
q = (R - d - delta_t*0.08)/(u - d)
print(c(u, u_wrong, d, R, q))

S0 = 0.625
K = 0.6

T_months = 6 ## time to expiration

## Build the stock price grid:
##
SSpot = make_spot_table(S0, u, d, T_months)
print('Spot lattice=')
print(round(SSpot, 3))

P_European = evaluate_put_option(SSpot, K, q, R, type='American')
print('American put option value=')
print(round(P_European, 3))