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.