Fundamentals of Futures and Options Markets by John C. Hull

Brian Lee
Jul 29, 2025

Bibliography

Hull, John C. Fundamentals of Futures And Options Markets. 9th ed. Upper Saddle River, NJ: Pearson, 2016. ISBN 978‑0‑13‑408324‑7.

Reading Notes

Stock Returns Are Normal (Hull 2016, 294)

Black-Scholes-Merton … assumes that the return on the stock in a very short period of time, \(\Delta t\), is normally distributed.

In contrast, future stock prices are assumed to follow a lognormal distribution (Hull 2016, 295).

See Mathematics for the relationship between normal and lognormal distributions.

Stock Prices Are Lognormal (Hull 2016, 295)

Future stock prices are assumed to follow a lognormal distribution.

In contrast, stock returns are modeled using a normal distribution (Hull 2016, 294).

See Mathematics for the connection between normal and lognormal distributions.

Historical Volatility (Hull 2016, 299)

Number of Trading Days (Hull 2016, 300)

Hull uses 252 as the average number of trading days in a year. However, Passarelli uses 256 instead of 252; see (Passarelli 2012, 62).

See Number of Trading Days for the reasons for discrepancies.

Assumptions Underlying Black-Scholes-Merton (Hull 2016, 301)

Black-Scholes-Merton Equations (Hull 2016, 304)

Because the American call price, \(C\), equals the European call price, \(c\), for a non-dividend-paying stock, equation (13.5) also gives the price of an American call.

(13.5) is the call price question from Black-Scholes-Merton (BSM).

Black-Scholes-Merton is the same as Black-Scholes.

Implied Volatility (Hull 2016, 307)

More in-depth than (Passarelli 2012, 62). Introduces a simple iterative method for estimating implied volatility. Includes a footnote mentioning that more advanced techniques exist.

Greek Letter Calculation (Hull 2016, 362)

Calculating Greeks require choosing an option-pricing model.

• European options: Black-Scholes-Merton (BSM)
• American options: Binomial tree.
  May use Black-Scholes for American calls for stocks without dividends; see (Hull 2016, 304).

Use Implied Volatility (\(IV\)).

Stop-loss Strategy for Hedging (Hull 2016, 362)

Not recommended.

Delta Hedging Example (Hull 2016, 365)

Ex 17.1

Delta Calculation Example (Hull 2016, 365)

Ex 17.2