The Black-Scholes-Merton Model (FRM Part 1 2023 - Book 4 - Chapter 15)

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After completing this reading, you should be able to:
- Explain the lognormal property of stock prices, the distribution of rates of return, and the calculation of expected return.
- Compute the realized return and historical volatility of a stock.
- Describe the assumptions underlying the Black-Scholes-Merton option pricing model.
- Compute the value of a European option using the Black-Scholes-Merton model on a non-dividend-paying stock.
- Compute the value of a warrant and identify the complications involving the valuation of warrants.
- Define implied volatilities and describe how to compute implied volatilities from market prices of options using the Black-Scholes-Merton model.
- Explain how dividends affect the decision to exercise early for American call and put options.
- Compute the value of a European option using the Black-Scholes-Merton model on a dividend-paying stock.

[@syeedmohammeduzzalhossain5452]

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I would have failed all my units if I didn't have these videos to teach me, I sincerely thank you.

[@henrynguyen6756]

Thank you Professor Forjan. We need more videos from you.!

[@CAGauravVerma]

Great explaination! Always grateful.

[@JoshMolina]

Great work! Thank you for sharing!

[@analystprep]

You're welcome!

[@dhruthij7430]

Great class so nicely explained sir

[@ahmadhilal2417]

very simplified and helpful.
thank you!!

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[@fatemakhatunfayza7089]

Nicely explained! Lot of thanks.

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[@idrisstalbi2785]

Wonderful !!! THANK YOU SO MUCH !!!

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Glad you like it!

[@RandyVee733]

amazing help. thank you so much

[@linaelmoutaki5610]

Thank you very much Professor Forjan

[@netexponent6217]

Great one! I just have one question Black-Scholes model uses constant volatility. What do you mean by this? Because volatility changes when we apply iteration.

[@davidgavan7921]

What a man!!!

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[@ron3252]

Thank you!

[@pranav1394]

You simplified that so well! Thank you!

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You're welcome!

[@Ninax280899]

Why is return on time value different in d1 and d2?

[@j.l.5461]

5:55 "Since lnSt is log-normally distributed". Isn't this wrong? lnSt is normally distributed as St is log-normally distributed.

[@parnzpanuz]

This should be the nobel prize. Thx.

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[@Disney124ddd]

in the textbook the the black scholes model variance is SD• root of T, but here it’s using SD^2

[@analystprep]

Hi Venus. Could you give us a timestamp?

[@lfeng0766]

@@analystprep 4:25 , it is different way of writing normal distribution. Written as N(u , variance) is the formal way, Written as N(u , Stdev) in the textbook is understood. At 6:09 the confidence interval is calculated correctly with stdev

[@rutammokashi2146]

(SD) x (Root of T) which is given in the textbook is just the root of (SD²) x (T) which is shown in this video.
so, the textbook one gives you the standard deviation and the one here gives you the variance.
it's basically the same thing.

[@ishankjain2393]

@@rutammokashi2146 Its not the same thing. Here it is sigma square * square root of T but textbook, it is sigma square * T

[@Mdigi1982]

@@ishankjain2393 I think its an error.

[@yvesprimeau6031]

Well done

[@analystprep]

Thank you!

[@n1kosv750]

@@analystprep I wanna ask something. Why when you add one more step on the binominal tree the option value increase??

[@lifewithnasha]

Why do we use the model to price option

[@benitaezeala4654]

thank you, prof J

[@CC-vt5ev]

The lognormal the return not simply stock price