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))

## Price the European call (this duplicates the numbers in Figure 12.7 in Example 12.3)
##
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))

## Price the American put (this duplicates the numbers in Figure 12.8 in Example 12.4)
##
P_American = evaluate_put_option(SSpot, K, q, R, type='American')
print('American put option value=')
print(round(P_American, 2))