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## Finance and capital markets

### Course: Finance and capital markets>Unit 9

Lesson 7: Black-Scholes formula

# Introduction to the Black-Scholes formula

Created by Sal Khan.

## Want to join the conversation?

• I understood the maths perfectly, but I'm having trouble comprehending why do this in the first place? I don't understand what do you mean exactly by saying that we're using this to find the option value? If we use it today, do we compare the results with the actual numbers in play? So if it's lower than the actual price being traded, what should we do?
• Hello Sir,
Plz explain how the BS formula will change when storage cost and dividend is taken into consideration?
• This is a pretty advanced topic that Khan doesn't really cover right now. Maybe a future video will have these concepts outlined.

If you know anything about pricing basic futures and forwards, you know that if there is a dividend it's present value is subtracted from the underlying. The same concepts apply here, but you're just dealing with a more complicated formula.

Here's a good article that explains the concepts: http://www.vwl.unibe.ch/studies/3081_d/FMT_Handout_Extensions_BSM.pdf
• In the BS option pricing formula why do we add sigma squared/2 to r for calculating d1, but minus it for calculating d2. I am looking for an intuitive answer without the heavy math.
• Why is the standard deviation calculated on log returns not nominal returns? Is it because S.D. of log returns is closer to a normal distribution?
• Log returns have some mathematical properties, that make the calculations easier. For example, you can add them. If you have periods t1, t2, ... , tn, sum of the log returns is equal to the log return for tn and t1. It doesn't work for arithtmetical returns.

Also, at least in short periods, log returns are normally distributed and their sums are also normally distributed.

Also, it's easier to work in continous time when you have the returns in this form, because of all differentiation and integration
• Are options instruments that investors like to use in volatile markets? Can these be used in forex markets?
• So for the T where you mean time to expiration, is this in terms of years? Like if it's 6 months then my T will be 0.5
• Years would be the most common. As long as the volatility and interest rate are in terms of the same time periode, then it really doesnt matter.
• After we obtain the value of the European call from the Black Scholes model, do we call this the intrinsic value of the option? And do we compare the value we obtain to the prices of similar options which are currently traded on the market? Is this how it works?
• The intrinsic value of the option usually refers (for a call option, as an example) to the positive difference between the current share price and the strike price. If the call is "in the money", it has intrinsic value. If it is out of the money, there's still a chance that it will become in the money before expiration, and the value of that chance is the time value
• why the binomial model is not enough so that we need to have black scholes model, except that B-S can deal with log normal problem. ?
• The binomial model was created first.

The binomial model converges to the bs-model. So they give the same prices. The BS formula has analytical expresions so it is much quicker to calculate.
• can someone tell me more on the N() function? (A link to the video would be nice too)