When you performed the homework assignment, how did you compute the delta?

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BlackTom AI · Accepted Answer

The question asks about how delta was computed for a homework assignment. 
Option 1: 'Enter the AMZN price and the call price. The delta = % change in the call price vs. the previous day divided by % change in the stock price vs. the previous day. If the stock price did not change, use the previous calculated delta.' This describes a finite-difference approach to approximate delta by comparing changes in the option price to changes in the underlying price, including a rule for when the underlying price hasn’t moved. In many practical settings, this is a reasonable numerical method for delta estimation. 
Option 2: 'Enter the AMZN price and the call price and solve for the implied volatility. Then take the derivative of the Black-Scholes call price with respect to the stock price.' Here the process starts by implied volatility estimation, then differentiates the Black-Scholes price with respect to stock price. However, the stated sequence is inconsistent with standard delta calculation: delta in Black-Scholes is the partial derivative with respect to the stock price, assuming volatility is fixed; solving for implied volatility first would change the model input, and the result would not be the delta under a fixed-vol assumption. This makes the approach conceptually misaligned for a straightforward delta computation. 
Option 3: 'Enter the AMZN price and compute the standard deviation of the logarithm of the stock price. Then insert this into the Black-Scholes. Then take the derivative of the Black-Scholes call price with respect to the stock price.' This option describes a step that yields the parameter sigma (volatility) from the log returns and then uses Black-Scholes with that sigma. While delta in Black-Scholes is the derivative with respect to S, simply plugging a computed sigma into Black-Scholes and differentiating would still conceptually be a Black-Scholes delta computation, but the explicit instruction to compute the standard deviation of log prices as a standalone step is not the standard delta calculation method; it confuses parameter estimation with the delta definition. 
Overall, Option 1 provides a direct and commonly used finite-difference method for estimating delta that matches the notion of assessing how the option price changes with the underlying, including a rule for unchanged underlying. The other options mix in volatility estimation steps that are not required for the direct delta calculation and introduce conceptual misalignments with how delta is defined in option pricing.

IFEPIA7022_001_2025_3 - Economics of Finance EOF Final - Dec 16, 2025

When you performed the homework assignment, how did you compute the delta?

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