source('utils.R')

T = 5/12
sigma = 0.2
r = 0.1
K = 60
t = 0

## Ca1culate the call prices:
##
C_62 = BS_Call(62, t, r, K, T, sigma)
print(sprintf('c(S=62)= %f', C_62))

C_63 = BS_Call(63, t, r, K, T, sigma)
print(sprintf('c(S=63)= %f', C_63))

DeltaS = 63 - 62
DeltaC = C_63 - C_62
print(sprintf('DeltaC= %f', DeltaC))

print(sprintf('Delta approximation= %f', DeltaC/DeltaS) )

## Increment time:
##
C_tprime = BS_Call(62, t+0.1, r, K, T, sigma)
print(sprintf('C_tprime= %f', C_tprime))

DeltaC = C_tprime - C_62
print(sprintf('DeltaC= %f', DeltaC))
print(sprintf('Theta= %f', DeltaC/0.1))