source('utils.R')

sigma = 0.3
S0 = 36
K = 40

r = 0.08

T_months = 5 ## time to expiration

print('Monthly timesteps:')
delta_t = 1/12 ## monthly timesteps

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

## Build the stock price grid:
##
SSpot = make_spot_table(S0, u, d, T_months)
print('Spot lattice=')
print(round(SSpot, 2))

P_European = evaluate_put_option(SSpot, K, q, R, type='European')
print('European put option_value=')
print(round(P_European, 2))

P_American = evaluate_put_option(SSpot, K, q, R, type='American')
print('American put option_value=')
print(round(P_American, 2))


print('Half-month intervals:')
delta_t = (1/12)/2 ## timesteps are every two weeks

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

## Build the stock price grid:
##
SSpot = make_spot_table(S0, u, d, 2*T_months)
print('Spot lattice=')
print(round(SSpot, 2))

P_European = evaluate_put_option(SSpot, K, q, R, type='European')
print('European put option_value=')
print(round(P_European, 2))

P_American = evaluate_put_option(SSpot, K, q, R, type='American')
print('American put option_value=')
print(round(P_American, 2))