Equities Project

Give me a 30-second overview of your project.

An equity options dashboard: Python/FastAPI calculates volatility, Black-Scholes prices, and Greeks; Next.js displays them.

Walk me through the data flow.

Ticker → Next.js → FastAPI → Yahoo price history → Python calculations → JSON → dashboard.

Why did you choose Python and FastAPI?

Python is strong for numerical work; FastAPI makes the calculations accessible through typed API endpoints.

What does the frontend do versus the backend?

Frontend handles inputs and charts. Backend handles market data, validation, and calculations.

What are the four dashboard sections?

Overview: prices. Volatility: HV20/HV30. Pricing Lab: theoretical options and Greeks. Option Chain: planned.

Where does your market data come from?

Yahoo Finance historical daily data. Useful for learning, but unofficial and not live option quotes.

Is the spot price in your app live?

No. It uses the latest available daily close, not an intraday executable quote.

What does the Pricing Lab actually calculate?

European call/put price, intrinsic and time value, Delta, Gamma, Vega, Theta, and sensitivity charts.

What does your project NOT do yet?

No live option chain, implied volatility solver, backtesting engine, or persistent database.

How does your news feature work?

Shows up to four matched ticker-related Yahoo headlines with links, not AI-written summaries.

What is a call option?

Right to buy stock at strike K. Expiry payoff: max(S − K, 0).

What is a put option?

Right to sell stock at strike K. Expiry payoff: max(K − S, 0).

What's the difference between payoff and profit?

Payoff is expiry value. Profit = payoff − premium paid (before fees).

Explain ITM, ATM, and OTM.

Call ITM: S > K. Put ITM: S < K. ATM: S ≈ K. OTM: no immediate exercise value.

What are intrinsic value and time value?

Intrinsic = immediate exercise value. Time value = option premium − intrinsic value.

European versus American options?

European: exercise only at expiry. American: exercise any time before expiry.

What is a bid-ask spread and why does it matter?

Bid = best buy offer; ask = lowest sell offer. Their spread is a trading cost and liquidity signal.

Explain put-call parity.

European parity: C − P = S·e^(−qT) − K·e^(−rT). It checks call/put consistency.

What is Black-Scholes used for in your project?

It estimates a European option's theoretical price from spot, strike, time, volatility, rates, and dividends.

What inputs go into Black-Scholes?

Spot S, strike K, time T, volatility σ, interest rate r, dividend yield q, and call/put type.

State the dividend-adjusted Black-Scholes call formula.

Call: C = S·e^(−qT)N(d1) − K·e^(−rT)N(d2). N = normal CDF.

What are d1 and d2?

d1 = [ln(S/K) + (r−q+σ²/2)T]/(σ√T); d2 = d1 − σ√T.

What are the key Black-Scholes assumptions?

European exercise, constant volatility/rates, frictionless trading, and lognormal stock returns.

Why does option value generally rise with volatility?

Greater uncertainty increases upside potential while a long option's downside stays limited.

What happens to an option's value at expiry?

Time value goes to zero. Call payoff: max(S−K,0); put: max(K−S,0).

Why does the risk-free rate matter?

It discounts the strike and changes risk-neutral carry; higher rates usually help calls and hurt puts.

Why include dividend yield q?

Dividends reduce expected stock carry: higher q usually lowers calls and raises puts.

What is Delta, with an example?

Sensitivity to a $1 stock move. Delta 0.60 ≈ option gains $0.60 if stock rises $1.

What is Gamma, with an example?

Change in Delta per $1 stock move. Gamma 0.03 ≈ Delta rises by 0.03.

What is Vega, with an example?

Sensitivity to volatility. Vega 0.40 ≈ option gains $0.40 for a 1-percentage-point vol rise.

What is Theta, with an example?

Daily time decay. Theta −0.02/day ≈ option loses $0.02 after one day, all else equal.

What is Rho? Is it shown in your app?

Sensitivity to interest rates. Not displayed among the app's four Greeks.

Why are Delta and Gamma important to hedging?

Delta estimates hedge shares; Gamma indicates how quickly that hedge needs rebalancing.

Where are Gamma and Vega often largest?

Gamma tends to peak near ATM close to expiry; Vega is often highest near ATM with more time.

Why can Greeks be wrong for large market moves?

Greeks approximate small moves. Large moves change Greeks, so reprice the whole option.

Simple returns versus log returns?

Simple: Pₜ/Pₜ₋₁ − 1. Log: ln(Pₜ/Pₜ₋₁). Log returns add across periods.

How do you calculate HV20 or HV30?

Sample standard deviation of 20/30 daily log returns × √252. Needs 21/31 prices.

Why multiply daily volatility by sqrt(252)?

Assuming stable, independent daily returns, variance grows with time; standard deviation with √time.

Why use adjusted close for realized volatility?

Adjusted close avoids split/dividend distortions in returns; the spot proxy uses daily Close.

Historical volatility versus implied volatility?

Historical vol measures past moves; implied vol backs out σ from market option prices. App uses historical.

How does a rolling volatility window work?

Move the return window forward one day, adding the newest and dropping the oldest.

How did you test the Black-Scholes engine?

Put-call parity, monotonic behavior, expiry edge cases, and Greeks versus finite differences.

What is a finite-difference check of Delta?

Approximate Delta by [V(S+h) − V(S−h)]/(2h); compare with the analytical result.

Why use central rather than forward differences?

Central differences usually reduce approximation error, but h must not be too small or large.

What edge cases can break option calculations?

Near-zero expiry/volatility, bad prices, or extreme strikes. Validate inputs and handle limits.

How do you prevent bad market data from creating fake outputs?

Sort and validate dates, reject duplicates, preserve missing values, and surface provider errors.

Why separate pure analytics functions from data fetching?

Pure math functions are reproducible, easier to unit-test, and independent of API failures.

How would you productionize this for a quant team?

Add licensed point-in-time data, storage, quote validation, monitoring, and repeatable testing.

How would you add implied volatility?

Use a valid market option quote; numerically solve Black-Scholes(σ) = market price.

What is the biggest limitation, and what would you build next?

Main gap: no live quotes/IV. Next: validated option chain and IV for market comparisons.