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Programming and financial model including option value move

Here is what what caught my attention today, This inlcude Machine learning books, modeling notes, C++ memory handling, and  option value move

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Python for Finance: Gathering and Visualizing Stocks Data

CppCon 2014: Mike Acton “Data-Oriented Design and C++”

Machine Learning and Data Sciences for Financial Markets: A Guide to Contemporary Practices 1st Edition This has been considered good according to the NYC Contact

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CFA L1 Important Formulas

In order for a financial model to be a powerful communication tool, certain criteria must be met. This ePaper offers a detailed breakdown of the key attributes needed for financial models as well as guidance on how to effectively plan & design a financial model.

Bayesian statistics and modelling often spark debates, but remain valuable. Despite controversies, they excel at handling uncertainty and have applications across domains. It’s crucial to approach these discussions with an open mind, embracing the mix of skepticism and usefulness they offer.

If you don’t understand options & greeks, you don’t understand markets

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5 points:

1) Basics

An option is the right to buy or sell a stock at a pre-specified price.

So if a stock is trading at $10, and you own a call option with an exercise price of $12 and 1 year to expiration –

That clearly is worth something.

But how much?

2) Black-Scholes Equation

The primary answer to that is Black-Scholes.

It describes two competing forces in an option’s value:

The negative force is the decay of the option’s value over time (its “Theta”)

The positive force is the growth in option value as the stock moves (its “convexity” – #2 attached multiplying Gamma by vol & price).

Leaving aside risk free return, the core insight of the Black-Scholes math is this:

The negative impact of time decay at every moment must exactly offset the positive impact of price convexity.

You can watch that change function (PDE) balance precisely in cell N21.

3) Black-Scholes Formula

But the most practical form is the solution to this PDE calculating the exact value of call/put options.

Simplifying a bit, that formula says the following:

What is the probability that this option ends up profitable –

And then multiplies that probability by the difference between the expected value of the stock in that scenario and the exercise price.

This math reconciles exact Black-Scholes to the expected value approximation in cell V29.

4) Greeks

The Greeks show how options move with changes in their inputs:

Delta = option value move per change in the stock price

Gamma = how much delta itself moves with the stock

Vega = option value move per 1% change in volatility

Theta = option value move per day that passes

The other less frequently used Greeks generally capture rates of change of those above (higher order derivatives).

Math & sensitivities attached.

5) Strategies, Extensions, & Limitations

There are as usual two camps of investors:

Those expressing directional views on fundamentals or events; and then those matching, servicing, & trading against the first group.

The second includes market makers, vol surface traders, carry & dispersion traders, and others.

But options also serve as a metaphor for almost any payout structure in finance:

Credit investors and merger arbs sell puts

VC and biotech buy calls

Distressed varies by cap table position

Options describe a wide range of outcomes in ways other vehicles can’t.

And in equities, despite other methods like binomial trees, and Black-Scholes assumptions that are often wrong –

The essential framework

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Is identifying how asset volatility interacts with finite time and changing market conditions.

There is further depth in every direction here

But as always, the key is a firm grasp of the principles,

Clarity around the math,

And intellectual honesty about the limitations.

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That’s all for now

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