Hull: Options, Futures, and Other Derivatives Summary and Cheat Sheet
21 views 0 purchase
Course
Derivatives and Risk Management (FN3206)
Institution
London School Of Economics (LSE)
Book
Options, Futures, and Other Derivatives, Global Edition
A summary of 'Options, Futures, and Other Derivatives summary' by John C. Hull with focus on the UoL LSE Derivatives and Risk Management syllabus. A handy cheat sheet is included at the end.
Save yourself the time of having to sift through the textbook- It is done very concisely here in this do...
All chapters necessary for the fn3206 module (see description for topics)
December 9, 2024
7
2024/2025
Summary
Subjects
ftap
derivatives
binomial tree model
black scholes
risk
forwards
futures
interest rates
swaptions
hedging
exotic options
yield curves
cheat sheet
the greeks
pricing
Connected book
Book Title:
Author(s):
Edition:
ISBN:
Edition:
More summaries for
Solution Manual for Options, Futures, and Other Derivatives Global Edition, 11th Edition By John Hull, All 36 Chapters Covered, ISBN: 9781292410654 & Verified Latest Edition
Financial Risk Management - All exercises/ problem sets solved - 18/20!!!
All-in-one Summary, notes and lecture commentary on Derivative Instruments
All for this textbook (8)
Written for
London School of Economics (LSE)
Unknown
Derivatives and Risk Management (FN3206)
All documents for this subject (1)
Seller
Follow
LSEmattUoL
Content preview
Options, Futures, and Other Derivatives summary
3rd Party summary of John C. Hull’s textbook
Financial Derivatives Overview
Key Concepts:
• Derivatives are financial instruments whose value depends on an underlying asset (e.g., stock, bond, com-
modity).
• They are used for hedging, speculation, and arbitrage.
• Types of derivatives: forwards, futures, options, and swaps.
• Equity derivatives (like call/put options) and interest rate derivatives (like swaps) are key areas in your
course.
• Arbitrage-free pricing, replication, and risk-neutral pricing are foundational concepts in derivative
pricing.
Example Question: - What is the payoff of a forward contract on a stock with a forward price of
$50?
Answer: The payoff of the forward contract at maturity is:
• Long position payoff: 𝑆𝑇 − 50 (where 𝑆𝑇 is the spot price at maturity).
• Short position payoff: 50 − 𝑆𝑇 .
Fundamental Theorem of Asset Pricing (FTAP)
Key Concepts: - The Fundamental Theorem of Asset Pricing (FTAP) states that in a no-arbitrage
market, there exists a risk-neutral measure under which all securities are priced.
• It links no arbitrage to the existence of a risk-neutral world where the discounted expected value of the
future cash flows is equal to the current price.
• Replication means creating a portfolio of the underlying asset and a risk-free bond that replicates the payoffs
of the derivative.
Example Question:
Given a call option with a strike price of $50, a stock price of $52, a risk-free rate of 5%, and a
1-year maturity, show how the absence of arbitrage can lead to the existence of a risk-neutral pricing
measure.
Answer:
Using the FTAP, the price of a derivative is the discounted expected payoff under the risk-neutral probability
measure.
For a call option with strike 𝐾, the price 𝐶0 is:
𝐶0 = 𝑒−𝑟𝑇 𝔼𝑄 [max(𝑆𝑇 − 𝐾, 0)]
1
, Binomial Tree Model
Key Concepts: - The binomial tree model is a discrete-time model used for option pricing. It approximates
the underlying asset’s price movements over discrete intervals.
• The model assumes that at each step, the asset price either up or down by a fixed factor.
• The risk-neutral probabilities are used to calculate the option’s price by working backward from expiration.
Formula: The price of a derivative at time 𝑡 = 0 is given by:
𝐶0 = exp(−𝑟 ⋅ Δ𝑡) ⋅ (𝑞 ⋅ 𝐶𝑢 + (1 − 𝑞) ⋅ 𝐶𝑑 )
where:
• 𝐶𝑢 and 𝐶𝑑 are the option prices at the up and down nodes,
• 𝑞 is the risk-neutral probability,
• 𝑟 is the risk-free rate
• Δ𝑡 is the time step.
Example Question:
A stock price is $50. The stock can either go up by 10% or down by 10% over one period. The risk-free rate is 5%.
What is the value of a European call option with a strike price of $52 using a one-period binomial tree?
Answer:
Up move: 𝑆𝑢 = 50 × 1.10 = 55
Down move: 𝑆𝑑 = 50 × 0.90 = 45
Option payoffs:
Black-Scholes Formula
Key Concepts: - The Black-Scholes model is a continuous-time model used for pricing European options. It
assumes constant volatility, no dividends, and a lognormal distribution of asset prices.
• The model uses stochastic calculus and provides a closed-form solution for European options.
2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller LSEmattUoL. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.67. You're not tied to anything after your purchase.
