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I am currently a senior in high school who has been tasked with writing a research paper on a math topic of our choice. I knew I wanted to research some sort of financial model but I was told most company models such as the DCF and CAPM were not advanced enough to research.

Que the Black-Scholes Option Pricing Equation. I started researching derivative equations and one of the most widely used models that I could find was the BS. I just have a couple questions regarding this model for anyone who has experience working with it.

  1. From my research I've gathered that the BS is used to find the appropriate price of a call premium, is this correct?

  2. What do d1 and d2 represent in the equation, I believe I have found that d2 represents the risk-free rate of the option but I could use some clarity here.

3.I have to set up a series of examples that apply the BS equation. I have read that the BS reflects the theoretical price of a call premium and not that practical one, would it be wrong to set up an example solving for the call premium using the BS, what other processes does this value have to go through to accurately reflect the market value of a call option?

I've only been reading over this topic for a couple of days now but it is quite interesting and I apologize if I incorrectly used some of the terminology or do not fully have a grasp of this concept.

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closed as off-topic by lehalle, LocalVolatility, noob2, Bob Jansen Mar 29 '17 at 14:13

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – lehalle, LocalVolatility, noob2, Bob Jansen
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1) If all the assumptions of Black-Scholes held in nature, then yes.

2)The answer to this can be rather long, so I found someone who already wrote something about it. It can be found at https://financetrainingcourse.com/education/wp-content/uploads/2011/03/Understanding.pdf

3) Black-Scholes assumes log-normality. This is not even remotely true. It also assumes infinite liquidity, that is the bid-ask spread is zero, always. There is also an assumption that the markets are in equilibrium inherited from the Capital Asset Pricing Model from which it can be derived. As such, when markets are not in equilibrium the model is silent about appropriate pricing. In the immediate future, you need to solve for a risk-free rate, but it is quite possible that Congress will close the government next month due to an inability to decide on spending. It is not impossible that it will default on the national debt. You would need an alternate asset, one likely not denominated in dollars. The only US companies with nearly risk-free status is Microsoft and Johnson & Johnson, but the debt has maturity risk and inflation risk because it is not immediately due.

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