Estimate Greeks and hedging PnL
Company: Morgan Stanley
Role: Data Scientist
Category: Software Engineering Fundamentals
Difficulty: medium
Interview Round: Technical Screen
Consider a vanilla European option under the Black-Scholes framework.
1. Without using a calculator, explain how you would mentally estimate the option's **delta**, **gamma**, and **vega**.
2. Suppose you do not remember exact values of the Gaussian CDF. What approximations or rules of thumb can you use to estimate the Greeks quickly and judge their order of magnitude?
3. Now assume the true market volatility is **not constant**, but you still price and delta-hedge the option using a **constant-volatility Black-Scholes model**. Describe the approximate PnL of the delta-hedged position, when the hedge tends to make or lose money, and how this depends on **realized volatility** versus **implied volatility**.
Overview: This question evaluates understanding of option Greeks (delta, gamma, vega), mental approximation of Gaussian probabilities, and the ability to reason about delta-hedged profit-and-loss under Black-Scholes model misspecification, categorized under Software Engineering Fundamentals for a Data Scientist role.
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