Analyze whether the resulting profile makes sense and explain why. Ensure that a separate function is used to handle this sensitivity analysis task. Explain in your report any precautions taken to minimize noise in the sensitivity analysis.

• Produce about 10 selected numerical scenarios to illustrate the impact of varying volatility.
• Analyze whether the resulting profile makes sense and explain why.
• Ensure that a separate function is used to handle this sensitivity analysis task.
• Explain in your report any precautions taken to minimize noise in the sensitivity analysis.
• Determine what the option approximately becomes when B is much, much larger than S₀.
• Determine what the option becomes when B < S₀.
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• Use your program to derive the probability that the payoff of the option exceeds $5, given the following numerical example:
  • The underlying asset is a stock that pays no dividends.
  • Spot price S₀ = 100$
  • Volatility = 20%
  • Time to maturity = 2 years
  • Discount rate = 2%
  • Barrier B = 150$
• Consider an approach or trick in implementing mainPricer that may reduce the computational/simulation effort compared to a brute-force approach.
• Discuss whether this pricing-efficient approach has any downsides when applied to sensitivity analysis.

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