1) Please produce about 10 selected numerical scenarios to illustrate the impact of varying the volatility. Does the resulting profile make sense to you? Why? Please make sure you’ve used a separate function that takes charge of this sensitivity analysis task. Please explain in your Report any precaution(s) that you took to minimize the noise in your sensitivity analysis.
2) What does this option approximately become when B is much much, much larger than S0?
3)What does this option become when B < S0?
4) Use your program to derive the probability that the payoff of the above option turns out to be > 5$, for the following numerical example: The underlying is a stock that pays no dividends, its spot S0 = 100$, its volatility = 20%, time to maturity = 2 years, discount rate =2%, B=150$.
5)Finally, can you think of an approach/trick in implementing mainPricer, that may shorten the computational/simulation effort involved in the pricing (compared eg to a brute-force approach)? But is there a downside to this (pricing) efficient approach when applied to sensitivity analysis?
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