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Consider an exchange option with a barrier clause in the following sense: the option is knocked-in (opposite of the knock-out feature we have seen so far) if the price of the asset that we currently do not hold (denoted V in the slides) crosses a barrier on its way up. The option premium is paid upfront but we do not hold the derivative until the knock-in event occurs. (In contrast, for a knock-out option, we get the option as soon as we pay the premium at time 0.) Use Monte Carlo to price this knock-in exchange option with the following parameters: V0 = 50; U0 = 50; sigmaV = 0.3; sigmaU = 0.6; rho = 0.7; T = 1; r = 0.03; and the barrier for the V price is 60.
Your price should be estimated with so-called “penny accuracy” (i.e.: the ratio of the length of the 95% confidence interval to the M.C. sample average should be less than 1%) and therefore you need to set the number of your replications accordingly.
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