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

S0 = 12
mu = 0.15
sigma = 0.2
r = 0.10

delta_t = 1/12

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))

K= 14

n_months = 10

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

## Part (a): Price the European call:
##
C_European = evaluate_call_option(SSpot, K, q, R, type='European')
print('European call option value=')
print(round(C_European, 2))


## Part (b): Price the Pay-Later option:
##
pay_later_present_value = function(C, SSpot, K, q, R, type='European'){
    ##
    ## Working backwards evaluate a call option.
    ##
    n_steps = dim(SSpot)[2] # = number of columns = number of time units + one column for the initial spot value
    n_rows = n_steps

    V = matrix(NA, nrow=n_rows, ncol=n_steps)
    for( jj in seq(n_rows, 1, -1) ){
        for( ii in 1:jj ){
            if( jj == n_steps ){ ## the final column/timestep
                if( SSpot[ii, jj]>K ){
                    V[ii, jj] = SSpot[ii, jj]-K-C
                }else{
                    V[ii, jj] = 0.
                }
            }else{
                if( type=='European' ){
                    V[ii, jj] = (q*V[ii, jj+1] + (1-q)*V[ii+1, jj+1])/R
                }
                if( type=='American' ){
                    pv_option = (q*V[ii, jj+1] + (1-q) *V[ii+1, jj+1])/R
                    early_exercise_value = max( c(SSpot[ii, jj]-K, 0) )
                    V[ii, jj] = max( c(pv_option, early_exercise_value) )
                }
            }
        }
    }
    return(V)
}

##PL = pay_later_present_value(2.0, SSpot, K, q, R) ## how to call this function

## For a sequence of C values ca1culate the present value of the pay-later option:
##
ns = 100
PV = rep(NA, ns)
cs = seq(1.5, 2.5, length.out=ns)
for( ci in 1:ns ){
    PL = pay_later_present_value(cs[ci], SSpot, K, q, R)
    PV[ci] = PL[1, 1]
}

## Plot this present value:
##
##postscript('../../WriteUp/Graphics/Chapter13/chap_13_ex_11_pay_later_pricing.eps', onefile=FALSE, horizontal=FALSE)
plot(cs, PV, type='l', pch=19, xlab='Estimated Premium', ylab='Expected Present Value')
abline(h=0, col='red')
grid()
##dev.off()

mi = which.min(abs(PV))
print(sprintf('C= %f; min(PV)= %f', cs[mi], PV[mi]))

## Print the lattice:
##
PL = pay_later_present_value(cs[mi], SSpot, K, q, R)
print(round(PL, 2))