8

Just for clarification, delta and probability of expiring in the money are not the same thing. What the guy meant was that delta is usually a close enough approximation to the probability. One way to think about it is to look at the probabilities and deltas of In the Money, Out of the Money, and At the Money options. A deep in the money option has a really ...


7

Using the data, the call option is $2.34, but what exactly does that mean? Does that mean the buyer has the obligation to buy the stock for $2.34? No, a call option is when someone purchases the right to buy the stock at the exercise price. The obligation is on the seller to provide the stock. The buyer can just let the option go unexercised if the buyer ...


4

Black-Scholes is one of several pricing models that uses six variables to determine the theoretical value for an option. You mentioned five of them. You did not mention a dividend so it is assumed that there is none. What's lacking in your question is an understanding of what a call option is, namely the right to buy an asset an agreed price on or ...


3

Option pricing models used by exchanges to calculate settlement prices (premiums) use a volatility measure usually describes as the current actual volatility. This is a historic volatility measure based on standard deviation across a given time period - usually 30 to 90 days. During a trading session, an investor can use the readily available information ...


3

Just a few observations within the Black-Scholes framework: American calls have the same price as European calls on non-dividend paying assets. The Black-Scholes formula is applicable only to European options (and, by the above, to American calls on non-dividend paying assets). By the call-put parity, if you have European call prices for some expiry dates ...


3

One thing I would like to clear up here is that Black Scholes is just a model that makes some assumptions about the dynamics of the underlying + a few other things and with some rather complicated math, out pops the Black Scholes formula. Black Scholes gives you the "real" price under the assumptions of the model. Your definition of what a "real" price ...


3

Options pricing is related to game theory. In sports, you like the Reds, I like the Greens. We wish to bet on a game. We can choose points to give the lower team's final score in order to make such a bet 50/50. Or knowing my Greens are far superior, I offer you odds. "If your Reds win, I will pay you 10 times your bet." The B-S model does a good ...


2

The Black-Scholes model was based on assuming lognormal stock price fluctuations with a constant volatility. However, the modern practice is to use the Black-Scholes formula not as a prediction but merely as a parametrization of option prices, where the observed price of a given option at a given time translates to a "local" implied volatility (IV). Thus, ...


2

If we were to observe some call price (e.g., 15), and then derived implied volatilities from the BS formula depending on different strike prices but fixed maturity (i.e, maturity = 1, and strike goes from 80 to 140??), would we then see a smile? Yes. Market prices for various strikes and a given maturity often have higher implied volatilities from the Black-...


2

do we enter them as percentages or decimals? As a decimal. A "20%" annualized volatility would be entered as 0.2 in the Black-Scholes model I am not just looking for an answer, but also an explanation. The fundamental assumption of the Black-Scholes model is that the underlying price is a stochastic process which has a standard deviation of s (omega ...


2

A company has 100,000 shares and 100,000 unexercised call options (company issued). Share price and strike price both at $1. What country is this related to? I ask because, in the US, most people I know associate a "call" option with the instrument that is equivalent to 100 shares. So 100,000 calls would be 10,000,000 shares, which exceeds the number of ...


2

The answer to your question as asked is no. Call options, even those issued by the company, cannot create new shares unless they are employee stock options. Company-issued warrants, on the other hand, can create new shares.


2

Is there a difference in the value of Delta of American and European options with the same underlying asset price, strike price, time to maturity? Probably. The difference between American and European options primarily affects the expiration date - American have multiple expiration dates while European have one. As a result a different method is used to ...


1

With the disclaimer that I acknowledge that Bob (the member whom I consider our resident expert and author of the current answer) is a few levels above me in options knowledge, I'll offer a layman's answer - A stock has a volatility. BS (The options pricing equation) offers a 'fair value'. Since one can use BS to reverse-engineer the equation, an option ...


1

If you plot implied volatility (IV) against strike prices, several curves occur: Volatility Smile is a U-shaped curve Reverse Skew (aka Volatility Smirk) is where lower strikes have higher IV than higher strikes (ITM calls and OTM puts are more expensive than OTM calls and ITM puts). This is the pattern depicted in your link. The popular explanation ...


1

Black-Scholes is a classic case of "all models are wrong but some are useful". Black-Scholes is a formula that tells you what the price of an option would be if: The stock's returns are log-normally distributed You know the stock's volatility Dividends are continuous Trading is continuous and free of transaction costs Borrow is always available if ...


1

I'm not familiar with this form of Black-Scholes (d1, d2, C), but the original q was regarding NORMDIST, is there a chance that NORMDIST and NORMSDIST are being confused? NORMDIST - 4 arguments, the value of the norm distro. link NORMSDIST - 1 arguments, the value of the standard norm distro cumulative function. link


1

I don't use Google sheets nor am I very good with Excel so I'm not sure how much help this will be. I wrote the Black Scholes formula in a spreadsheet 25+ years ago, back in the days when BS software was in its infancy on the retail side. The call value from my calculation is $21.67 and the put value is $0.57 and they are almost identical to the output ...


1

The delta matters, how far in the money or out the money. you should really use a calculator that shows you projections. I'm a fan of Thinkorswim's platform for simulating options PnL


1

I don't think your understanding is correct. The main difference between American-style and European-style option is the timing of the right to exercise the option. In American-style options, the option can be exercised at anytime whereas it is a point-in-time for European-style options. Models used for those scenarios are different because the time horizon ...


1

It depends on the accuracy you require. Some of them are intuitive - e.g. the 'delta' is the likelihood the option will expire above or below the strike price of the option. For an at-the-money option, that will be 50%. For an out-of-the money option, that will be close to zero. An in the money option will be close to 100%. 'gamma' is how much the 'delta'...


1

What the other answers seem to miss is that there isn't just a vague or qualitative relation between delta and the probability of expiring in the money. Though the two are not equal in general, there is a precise limiting case in which they converge (and so in many practical cases they may be very close). This is the case where the Black-Scholes assumptions ...


1

The delta is the ratio between a price change in the underlying and price change in the derivative. So a delta of .5 means that if the stock price goes up $1, the option will go up $.50. The reason that the delta and the probability of being in the money are (roughly) equal is that an increase in stock price is useful to a holder of the option only if the ...


1

people are willing to pay higher premiums for options when stocks go down. Obviously the time value and intrinsic value and interests rates of the option doesn't change because of this so the miscalculation remainder is priced into the implied volatility part of the formula. Basically, anything that suggests the stock price will get volatile (sharp moves ...


1

For implied volatility it is okay to use Black Scholes but what to do with the historical volatility which carries the effect of past prices as a predictor of future prices? And then precisely the conditional historical volatility. I suggest that you go with the process like, for stock returns: 1) download stock prices into an Excel spreadsheet 2) take the ...


1

Congratulations! You've found what's known in the biz as "an opportunity". If you do invest in options based on Black-Scholes and binomial models, and assuming you've done your math right, then all you need do now is buy options, or set up an option strategy, such that you profit as the theoretical and the real move toward each other. Of course, that's ...


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