Patrick Boyle

These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. https://amzn.to/2WIoAL0
Check out our website http://www.onfinance.org/

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In finance, the binomial options pricing model provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein in 1979, six years after the Black Scholes model. Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument.

The Binomial options pricing model approach has been widely used since it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the model is based on a description of an underlying instrument over a period of time rather than a single point in time. As a consequence, it is used to value American options that are exercisable at any time in a given interval as well as Bermudan options that are exercisable at specific instances of time. Being relatively simple, the model is readily implementable in computer software or even in spreadsheets like Excel.

Although computationally slower than the Black–Scholes formula, it is more accurate, particularly for longer-dated options on securities with dividend payments. For these reasons, various versions of the binomial model are widely used by practitioners in the options markets.

The Risk-Neutral Binomial Tree Approach
The concept of a portfolio made up of some portion of stock and some portion of a derivative on that stock gives rise to the ability to generate equivalent cash flows at end nodes of binomial trees, and this certainty of cash flows allows us to discount the cash flows at the risk-free rate. The ability to discount cash flows in the future at a known risk-free rate gives us the concept of risk-neutral valuation.

Risk neutral valuation is a powerful concept in derivatives pricing which enables valuation of assets based on their expected payoffs at different points in time and with different scenarios of underlying asset price movements.

Risk-neutral valuation is applicable whenever you can create a portfolio including the underlying plus a derivative on the same underlying. It cannot be extrapolated to find the value of derivatives on other underlyings. It relies on the portfolio instruments having a level of dependency on one another.
This model is very flexible and powerful because we don’t need to know the real probability of the upside scenario, or the real likelihood of the downside economic scenario—it is not required to maintain our certainty of cash flows at the end point.

An easy mistake to make is to confuse this constructed probability distribution with real-world probability. They will be different, but the method of risk-neutral pricing is, like many other useful computational tools, convenient and powerful. The approach of risk-neutral valuation makes sense for valuation purposes but only works when all of the instruments included in the valuation model depend on the same underlying and thus are exposed to the same risks, though held in different proportions. We are pricing the option in terms of the underlying stock, thus risk preferences are taken into account in the pricing of the underlying.

The risk-neutral binomial tree approach is mathematically equivalent to the portfolio approach previously covered, and gives us the exact same valuation. The risk neutral binomial tree valuation approach to value the derivative, f, is as follows.

With some algebra, you can show that the risk-neutral formula is mathematically equivalent to the portfolio approach where  of shares is calculated to generate riskless outcomes at maturity, T.

Although we are not making any assumptio

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All slides are available on my Patreon page: https://www.patreon.com/PatrickBoyleOnFinance

Fixed income refers to any type of investment under which the borrower or issuer is obliged to make payments of a fixed amount on a fixed schedule. For example, the borrower may have to pay interest at a fixed rate once a year, and to repay the principal amount on maturity. Fixed-income securities can be contrasted with equity securities – often referred to as stocks and shares – that create no obligation to pay dividends or any other form of income.

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What Is Portfolio Management?
Portfolio management is the art and science of selecting and overseeing a group of investments that meet the long-term financial objectives and risk tolerance of a client, a company, or an institution.

Portfolio management requires the ability to weigh strengths and weaknesses, opportunities and threats across the full spectrum of investments. The choices involve trade-offs, from debt versus equity to domestic versus international and growth versus safety.

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Marc Andreessen appeared on the Joe Rogan podcast this week arguing that the Consumer Financial Protection Bureau (CFPB) should be shut down as it debanks conservatives.

In today's video we use the example of the finfluencer promoted fintech bank Yotta - look at its ties to another fintech - synapse to try to understand if the CFPB should be defunded or if savers need to be protected from fintech firms that are mostly unregulated.

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Patrick's Books:
Statistics For The Trading Floor: https://amzn.to/3eerLA0
Derivatives For The Trading Floor: https://amzn.to/3cjsyPF
Corporate Finance: https://amzn.to/3fn3rvC

Ways To Support The Channel
Patreon: https://www.patreon.com/PatrickBoyleOnFinance
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Business Inquiries ➡️ [email protected]

Patrick Boyle On Finance Podcast:
Spotify: https://open.spotify.com/show/7uhrWlDvxzy9hLoW0EYf0b
Apple: https://podcasts.apple.com/us/podcast/patrick-boyle-on-finance/id1547740313
Google Podcasts: https://tinyurl.com/62862nve

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Additional Reading:
CNBC Article: https://www.cnbc.com/2024/11/22/synapse-bankruptcy-thousands-of-americans-see-their-savings-vanish.html
How Safe are Online Banks & Fintechs?: https://www.bloomberg.com/news/articles/2024-10-09/how-safe-is-your-money-really-in-online-banks-and-fintechs
Andreessen-Backed Fintech's Meltdown Shows Bank Middlemen Risks: https://news.bloomberglaw.com/banking-law/andreessen-backed-fintechs-meltdown-shows-bank-middlemen-risks
Rob Copeland - How To Keep Your Money Safe: https://www.nytimes.com/2024/08/10/business/online-lending-banking-money-risks.html
CFPB Debanking Press Release: https://www.consumerfinance.gov/about-us/newsroom/cfpb-finalizes-rule-on-federal-oversight-of-popular-digital-payment-apps-to-protect-personal-data-reduce-fraud-and-stop-illegal-debanking/
a16z Investment list: https://a16z.com/investment-list/
Joe Rogan - Marc Andreessen Interview: https://www.youtube.com/watch?v=ye8MOfxD5nU

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Tello Mobile offers flexible & affordable phone plans with prices up to $25/month! Check out Tello using my link → https://tello.com/?utm_source=partner&utm_medium=cpc&utm_campaign=PatrickBoyle&src=partner&mdm=cpc&cmg=PatrickBoyle

AI chatbots are replacing search engines—and in the process, they’re gutting the economics of journalism, reviews, and the open internet. In this video, we explore how tools like ChatGPT, Claude, and Google’s AI Overviews are intercepting audiences, scraping content without compensation, and threatening the viability of independent news and trusted information. From collapsing traffic to lawsuits and poisoned training data, this is a story about what happens when the web’s information economy starts to eat itself.

Patrick's Books:
Statistics For The Trading Floor: https://amzn.to/3eerLA0
Derivatives For The Trading Floor: https://amzn.to/3cjsyPF
Corporate Finance: https://amzn.to/3fn3rvC

Videos Mentioned:
@BennJordan Poisonify: https://www.youtube.com/watch?v=xMYm2d9bmEA
Benn Jordan on AI Cameras: https://www.youtube.com/watch?v=Pp9MwZkHiMQ
Angela Collier on Vibe Physics: https://www.youtube.com/watch?v=TMoz3gSXBcY
My Video on Blitzscaling: https://www.youtube.com/watch?v=p7Lo0sZfdHE

Ways To Support The Channel
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Business Inquiries ➡️ [email protected]

Patrick Boyle On Finance Podcast:
Spotify: https://open.spotify.com/show/7uhrWlDvxzy9hLoW0EYf0b
Apple: https://podcasts.apple.com/us/podcast/patrick-boyle-on-finance/id1547740313
Google Podcasts: https://tinyurl.com/62862nve

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These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. https://amzn.to/2WIoAL0
Check out our website http://www.onfinance.org/

Follow Patrick on twitter here: https://twitter.com/PatrickEBoyle

What is Rho in Options?
Rho is the rate at which the price of a derivative changes relative to a change in the risk-free rate of interest. Rho measures the sensitivity of an option or options portfolio to a change in interest rate. Rho may also refer to the aggregated risk exposure to interest rate changes that exist for a book of several options positions.

If an option or options portfolio has a rho of 1.0, then for every 1 percentage-point increase in interest rates, the value of the option (or portfolio) increases 1 percent. Options that are most sensitive to changes in interest rates are those that are at-the-money and with the longest time to expiration.

Check out our playlist on the Options Greeks to see more on this topic.

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The first two batches of the Epstein files have finally been released, and the revelations are explosive. For decades, the media and the justice system ignored the most basic question: Who helped him? Now, thanks to thousands of pages of newly released DOJ documents, we know that there were the co-conspirators.

In this video, we look through the latest evidence to expose the network of co-conspirators and high-powered enablers who made Jeffrey Epstein’s crimes possible. We go beyond the headlines to reveal the specific individuals—from Ghislaine Maxwell to banking titans like Jes Staley—who were far closer to Epstein’s operation than they ever admitted.

We break down the bombshell New York Times investigation that dismantles the myth of Epstein's "financial genius" and uncover the bipartisan cover-up that kept these files buried for 40 years. From Donald Trump’s newly revealed flight logs to Bill Clinton’s White House connections, we show how a "two-tier" justice system worked to protect the powerful at the expense of the truth.

@nytimes article: https://www.nytimes.com/2025/12/16/magazine/jeffrey-epstein-money-scams-investigation.html

Patrick's Books:
Statistics For The Trading Floor: https://amzn.to/3eerLA0
Derivatives For The Trading Floor: https://amzn.to/3cjsyPF
Corporate Finance: https://amzn.to/3fn3rvC

Ways To Support The Channel
Patreon: https://www.patreon.com/PatrickBoyleOnFinance
Buy Me a Coffee: https://www.buymeacoffee.com/patrickboyle

Visit our website: https://www.onfinance.org
Follow Patrick on Twitter Here: https://bsky.app/profile/pboyle.bsky.social

Business Inquiries ➡️ [email protected]

Patrick Boyle On Finance Podcast:
Spotify: https://open.spotify.com/show/7uhrWlDvxzy9hLoW0EYf0b
Apple: https://podcasts.apple.com/us/podcast/patrick-boyle-on-finance/id1547740313
Google Podcasts: https://tinyurl.com/62862nve

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According to the consumer advocacy group Public Citizen, almost half of all corporate money contributed to this year's US election campaigns has come from crypto backers and politicians are bending to their will with promises to reduce regulation and consumer protections.

Why do Trump and Kamala Harris suddenly support crypto? In today's video we follow the money.

Patrick's Books:
Statistics For The Trading Floor: https://amzn.to/3eerLA0
Derivatives For The Trading Floor: https://amzn.to/3cjsyPF
Corporate Finance: https://amzn.to/3fn3rvC

Ways To Support The Channel
Patreon: https://www.patreon.com/PatrickBoyleOnFinance
Buy Me a Coffee: https://www.buymeacoffee.com/patrickboyle

Visit our website: https://www.onfinance.org
Follow Patrick on Twitter Here: https://twitter.com/PatrickEBoyle

Zeke Faux Book - Number Go Up: https://amzn.to/4gMw5a2
Molly White Article - https://www.citationneeded.news/coinbase-campaign-finance-violation/
Public Citizen Report - https://www.citizen.org/article/big-crypto-big-spending-2024/

Business Inquiries ➡️ [email protected]

Patrick Boyle On Finance Podcast:
Spotify: https://open.spotify.com/show/7uhrWlDvxzy9hLoW0EYf0b
Apple: https://podcasts.apple.com/us/podcast/patrick-boyle-on-finance/id1547740313
Google Podcasts: https://tinyurl.com/62862nve

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All slides are available on my Patreon page: https://www.patreon.com/PatrickBoyleOnFinance

Todays class is all about investment asset classes. We examine the different types of investment an investor can put their savings in and try to work out the expected return of these asset classes, the drivers of these returns, and why an investor might be attracted to these different investments. We learn about portfolio construction and diversification.

The asset classes we discuss are, fixed income, equities and hybrid instruments like preferred stock and convertible bonds. We learn about real estate or property investments, commodities, foreign exchange and collectibles.
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