A barrier option is a path-dependent option whose payoff depends on whether the underlying asset price traverses a barrier. A knock-out call is a call option that ceases to exist when the underlying price falls below a given barrier level H. Thus the payoff is given by where ST is the underlying price at expiry date T, and K is the exercise price. Suppose that a knock-out call is written on the FTSE 100 Index. The current index value, S0 = 5000, K = 5100, time to maturity = 1 year, H = 4900, IV = 25%, risk-free rate =

5%, dividend yield = 2%.

Design a Monte Carlo simulation to determine the fair price to pay for this option. Using the same set of random draws, what is the value of an otherwise identical call without a barrier?