Financial Engineering Course: Lecture 2/14, part 1/3, (Understanding of Filtrations and Measures)

Financial Engineering: Interest Rates and xVA
Lecture 2- part 1/3 Understanding of Filtrations and Measures
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This course is based on the book:
"Mathematical Modeling and Computation in Finance: With Exercises and Python and MATLAB Computer Codes", by C.W. Oosterlee and L.A. Grzelak, World Scientific Publishing, 2019.
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0:00 Introduction
7:14 Filtration
28:40 Conditional Expectations
39:32 Conditional Expectations in Python
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CONTENT OF THIS COURSE:
Lecture 1- Introduction and Overview of the Course
*** Lecture 2- Understanding of Filtrations and Measures
Lecture 3- The HJM Framework
Lecture 4- Yield Curve Dynamics under Short Rate
Lecture 05- Interest Rate Products
Lecture 06- Construction of Yield Curve and Multi-Curves
Lecture 7- Pricing of Swaptions and Negative Interest Rates
Lecture 8- Mortgages and Prepayments
Lecture 9- Hybrid Models and Stochastic Interest Rates
Lecture 10- Foreign Exchange (FX) and Inflation
Lecture 11- Market Models, Convexity Adjustments and Beyond
Lecture 12- Valuation Adjustments- xVA (CVA, BCVA and FVA)
Lecture 13- Historical VaR, SVaR and Expected Shortfall
Lecture 14- Summary of the Course
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#ComputationalFinance, #Python, #QuantitativeFinance, #FinancialMathematics, #MonteCarloSimulation, #OptionPricing, #Finance, #DerivativePricing, #BlackScholes, #FreeCourse, #FinancialEngineering, #Hedging, #Simulation, #Options, #xVA
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[bleacherz]

Thanks. I studied this material with prof sauer at gmu. I now see the value of the Tower Law. Thanks for being so generous.

[tedegooday]

Hi Lech,
Thank you for sharing your knowledge with us. I am a petroleum Engineer with an MS but I am interested in doing a MS in Financial Engineering instead of doing an MBA, I want to convert myself in Quant.

[MathFinGuy]

On slide 9, shouldn't it be that sigma algebra generated by X be a sub sigma algebra of the sigma algebra generated by Y instead of the other way round, for the last equation E[Y] = E[E[Y|X]] to hold?

[simoneserafini]

Hi Lech, when will the remaining parts of the lesson be available? Thank you again for the content, your channel is the best online resources on Quant Finance.

[MytabRealme]

Sir i have completed my+2 recently and i want to break into quantum trading by blending my major in computational engineering with financial engineering does that gonna be a good way?? If yes can i learn financial engineering by your videos ? And the book you have suggested❤❤

[romainp.]

Thank you for the classes! Shouldn’t it be t >= T for the first bullet point of the 23:59 slide? Thanks

[Itzcgs]

Thanks Lech
for a fab course and that too online with full access to all. I'm really liking the content and the way it's been explained.

I hv one question though on this lecture at 42:41 you mentioned two applications in python. I'm interested in second one and how we can apply LSMC or kernel regression techniques in such cases wherein we don't want to run multiple inner scenarios.

Example- i want to compute Initial Margin which is the percentile of the change in portfolio value i.e., delta of Value at T and Value at T+MPOR and both these time periods are in future.
Any guidance pls?

[Kokso.]

Lech can you please explain?
1. Xt1 is Ft1 measurable = known and constant at t1?
2. Xt1 is not Ft0 measurable = unknown and stochastic at t0?
3. Is measurable = known = constant?

[apocalypsebx]

Great content! I have a question: on 29:40 >> filtration in t1 is usually contained in filtration t2, so we can assume that filtration in T is the cumulative filtration of t1, t2, t3... T. Am I correct? Thank You!

[dipanjanbiswas]

Goldmine it is. Hi Prof, just to reconfirm - X(t+1) is not adapted to F(t+1), where t is current time

[Maximus]

Hi Lech, one question about the simulation of second problem. Why is the term E(W(t)) -W(s) called an "error" ? Is it because W(t) is a martingale and we do not expect the expectation to change from s to t ? Thank you.

[PhilipTheDuke]

Hi Lech,

thank you for posting this! I know what I'm doing in the summer.
Can you tell me if you have a pdf version of your book? I like the physical book and all, but I pdf is more versatile and save physical space.

[evgeniytitov]

Hi Lech, thank you for the lectrues! I subsiscbed on your channel and see that periodically you reload some of previously loaded leсtures.
Does it mean some new info added and it is good seeing once more?
Thank you

[fatinelbouhssini]

Thank you very much your videos are very helpful! I would like to ask you a practical question: How can I test if a stock price process is a martingale? (ie how can I prove it's not)

[chesterngwenya]

Hi Lech, where can we get solutions for the exercises?

[eaaepro]

Hi sir, thank you for this wonderful lesson. Is it preparation class? Or is it full class for financial engineering? Thank you in advance

[MytabRealme]

Sir i had completed my+2 recently and i want to break into quantum trading by blending my major in computational engineering with financial engineering does that gonna be a good way?? If yes can i learn financial engineering by your videos ? And the book you have suggested!❤