33. Consider a more complex form of barrier option, the double barrier knock-out call. In this case, the option gets knocked out if either barrier is breached during the option's life. For this option, using any method of your choosing, price the option for the following parameters: S = 100, K = 100, lower barrier 80, upper barrier 120, maturity 0.25 years, risk-free rate of 6% p.a., zero dividends, and volatility of 35%. Answer the following questions:
(a) What is the price of this option?
(b) What is the price at S = 95 and at S= 105?
(c) What is the price at a volatility of 50%? What does this tell you about the sign of the vega?
(d) What is the delta of the option at stock prices 95, 100, and 105?
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