09. Brownian motion calculations - probabilities by calculus

PRDTM2-787 AI Trading C4 L1 Vid9 Brownian Motion Calculations- Probabilities By Calculus

Applying Probability Concepts in Stock Valuation

Explore the process of determining the probability that a company's stock price will rise above a certain threshold, using a real-world scenario:

  1. Scenario: Calculate the chance that company ABC's stock price, currently at $80, will exceed $100 in six months at a hedge fund.

  2. Initial Parameters:

    • Constant A (15%): Estimate of stock return
    • Volatility (30%): Measure of price fluctuation
    • Timeframe: Six months expressed as 0.5 years

  3. Relative Return:

    • Formula: Normal distribution with mean as "A*t" (0.075) and standard deviation as "Sigma * sqrt(t)" (0.212)
    • Event Probability Calculation: Price increase above $100 means relative return > 0.25

  4. Analytical Approach:

    • Using cumulative distribution function (CDF) of the normal distribution
    • Result: Probability found to be 20.5% using Python's scipy.stats package

  5. Next Steps:

    • Verify results using Monte Carlo simulations in the subsequent discussion.

X has standard normal distribution. What is P(X > 3)?
SOLUTION: 0.0013

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