Reference no: EM132345828

Dan is trying to use Monte Carlo simulations with 6,000 trials to price a package of two exotic options. The first option is the so-called cash-or-nothing call option that delivers a fixed cash amount Q if the European counterpart is in the money and zero otherwise. The second option is the so-called asset-or-nothing call option that delivers the asset if the European counterpart is in the money and zero otherwise. The underlying stock is Apple Inc. with the current share price of $356.00 apiece. The options have identical strike price of $360, and will expire in six months. The risk-free rate is 2% per annum and the stock volatility is fixed at 39%. Moreover, the fixed cash amount Q is set to be $360 for the cashor-nothing call.

(1) What is the price of the cash-or-nothing call option?

(2) What is the price of the asset-or-nothing call option?

(3) The package consists of a short position on the first exotic option and a long position on the second exotic option. What is the price of this package? What do you find from comparing the package price to the price of a non-exotic European call option? Please provide an intuitive account on why this is the case.