Sensitivity Analysis of Option Pricing: Impact of Volatility and Barrier Conditions

University Loughborough University (LU)
Subject Finance

Course Work

  • 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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