source('../Chapter13/utils.R') ## load in functions to compute the Black-Scholes call price

t = 0 ## the current time 
T = 0.25 ## time in years till August expiration

r = 0.07 ## yearly interest rate

strikes = c(1600, 1700)/100.

market_prices = c(1.29, 0.70) ## from Figure 16.8

S0 = mean(strikes) ## initial guess at the spot and the volatility 
sigma = 0.4

min_fn = function(x){
    S = x[1]
    sigma = x[2]

    predictions = BS_Call(S, t, r, strikes, T, sigma)
    res = mean((market_prices - predictions)^2)
    return(res)
}
## Test our function once: 
##print(min_fn(c(S0, sigma)))

res = optim(c(S0, sigma), min_fn, method='Nelder-Mead')
S = res$par[1]
sigma = res$par[2]
predictions = BS_Call(S, t, r, strikes, T, sigma)
print(sprintf('S= %f; sigma= %f; C(K=16)= %f; C(K=17)= %f', S, sigma, predictions[1], predictions[2]))