Binomial Option Pricing Model || Theory & Implementation in Python
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- čas přidán 8. 07. 2024
- Today I will introduce the Theory of the Binomial Asset Pricing Model and show how you can implement the binomial tree model to price a European call option in Python. The theory section of this video is long (sorry) and aims at giving you the absolute basics for understanding why and how to derive the discounted expectation of future payoffs under risk-neutral probabilities given the Binomial Model.
For those who just want to code, please skip ahead to the Python Implementation section. I will take you through two implementations of a simple binomial tree model in Python, one that will use ‘for loops’ to step through each node at each time step (a function I have defined as binomial tree slow), and the other (binomial tree fast) will vectorize these steps using numpy arrays, improving overall computation time as N time steps increase. Although not necessary for the example today, using numpy arrays and vectorizing our calculations will improve computations as we delve deeper into financial mathematics and implementation heading forward.
In this tutorial series we will be breaking down the theory described and published in Steven Shreve’s book’s Stochastic Calculus for Finance I & II. As a guide for implementing these concepts in Python, we will refer to the numerical methods and practices outlined in Les Clewlow & Chris Strickland’s book Implementing Derivatives Models.
00:00 Intro
00:50 Theory || What is Arbitrage? - Type I & II
04:20 Theory || No Arbitrage Pricing - The Law of One Price
05:47 Theory || One-period Binomial Model
11:00 Theory || Deriving the discounted expectation of future payoffs under risk-neutral probabilities
20:10 Theory || No Arbitrage Conditions
24:10 Theory || Multi-period Binomial Model
29:50 Python Implementation || Binomial Tree Slow
41:12 Python Implementation || Binomial Tree Fast
46:55 Python Implementation || Comparing the Slow vs Fast Implementation
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You are beyond skilled in both teaching and QF!
Thank you so much
I get it now. You explained everything in 30min very clear, and there is our teacher taking weeks and I got nothing.
Good job!!!
Brilliant channel. Keep it up!
It is an amazing video!
Well done!
Thank you for the video
great video, simplicity at its best :)
Hey I think it's great work here and now that I've started my financial engineering masters I can finally understand this. Just one thing tho - in the risk-neutral probabilities coding part, I think it should be u = np.exp(sigma * np.sqrt(T / N)), d = 1 / u, qu = (R - d) / (u - d)... I think there was a mixup somewhere
I am on my way study financial engineering master too :), so good to see another person in manadarin name
Fantastic lesson mate., really like this approach.
Didn"t understand any of it, but I did enjoy the 49 minutes anyways
Why does the bank account not decrease in value when going to the down state
At 32:49 -- won't you get a recombining tree even if ud is not 1 since if the stock price goes up then down the price will be udS_0 whereas if it goes down then up you'll get duS_0 which are the same thing? In these cases it's just not true that S_2 = S_0 but I don't see why that's an issue.
I understand it but what is it good for? How to apply it?
hey this was so great, I actually am using this to help me secure a quant position at a trading desk... I am just confused on one part, can i schedule a one on one?
Did you get the job?
@@benardkiplimo3508 nah, I wasn’t advanced enlugh
In 15:36 you say "bank account (Su-Sd)". I think it should be "stock units" not "bank account units" for your beta, no?
Hey, thanks for your video.
But shouldn't type 2 arbitrage (3:36) be defined as P(V_T>=V_0) = 1, since your definition allows for losing money by having V_0 > 0.
Greetings and stay healthy
Marcel
How does the coding change for American options?
If you have a 4 step time tree the number of nodes does not equal N+1
Hi very nice video but I think you have forgotten to take the max between the expectation and the payoff for each node.
That’s the pricing formula for American style options not European style
@@jonathonemerick2084 For European you never need to take the max. I mean exactly for the US kind the author forgot to take the max for each node.
This video was for European pricing only. No max required for each node?
Please check another video for American style option pricing czcams.com/video/K2Iy8bCmXjk/video.html
@@jonathonemerick2084 ok I got it because that's for European pricing. I thought it's for American kind. Thanks for your response.
@@QuantPy Yes I get it now since I was working on American side so I thought this example too. Thanks for the response.
You flipped the meaning of alpha and beta right on the middle and got a little bit confused there, didn't you? Or is there a meaning behind using beta for the weighting of stock and calling it bank account weighting?
The alpha and beta terms are just constants. In the video I've assigned Beta as the number of Shares and Alpha as the number of bank account units. Feel free to use your own constants and go through the math 👍