Computational Finance & Geospatial Computing

By the end, you can

• State the European call payoff formula and explain why the future price makes direct valuation impossible.
• Name all five Black–Scholes inputs and identify the most common confusion (σ = volatility, not expected return).
• Trace the Monte Carlo pricing algorithm: simulate paths, compute payoffs, average, discount.
• Apply the 1/√N convergence rule to determine how many extra samples are needed to achieve a target accuracy improvement.
• Explain why haversine is needed instead of Pythagorean distance for geographic coordinates.
• Describe how geohash encodes a location and why a shared prefix implies spatial proximity.
• Identify the geohash boundary gotcha and explain the 8-neighbor fix.
• Explain how an R-tree prunes bounding boxes to reduce spatial query complexity from O(n) to O(log n).
• Articulate the unifying principle: simulate to approximate, index to prune.