Questions tagged [black-scholes]

Black-Scholes is a pricing model used to determine the fair price or theoretical value for a call or put option based on six variables such as volatility, type of option, underlying stock price, time, strike price, and risk-free rate.

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Black Scholes PDE vs closed form

What is the difference between the 2 formulas below, how and why we choose what to use? Does PDE simulate option price through time, therefore we can use it for American options as well? Black Scholes ...
Skittles's user avatar
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why volatility increases price for ITM call options?

Similar questions have been asked here, but I'm not able to find this exact question. For a European call option, if it's very in-the-money, wouldn't a higher volatility decrease the probability it ...
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On the meaning of Delta hedging

Basically, I'd really like to give a natural interpretation of as prescribed by the Black-Scholes model for European derivatives, where O(t) is the option price and S(t) is the price of the ...
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What are alternatives to Black-Scholes model that doesn't assume random walk behavior?

I've recently started binary options trading as a hobby and I want to know how brokers decide the return rates on binary options. I asked this Question and I tested the model proposed in the answer. ...
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What effects does a change in IV on the call side have on the put side?

In a European type options market, consider this scenario, where someone starts to buy call options very aggressively which increases call IV rapidly. At the same time, the underlying price remains ...
Vaibhav Sharma's user avatar
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Why do implied volatility changes at different strike prices exactly coincide with one another?

Please see the image of the Implied volatility of different strike prices separated by 100 points. This is the recorded data of the actual market. As it can be clearly observed that the Implied ...
Vaibhav Sharma's user avatar
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Option strategy, Black, Scholes and Merton Model and Lognormal distribution

The Black, Scholes and Merton option pricing model assumes the stock price changes are lognormally distributed. Then, How to show graphically How this distribution changes when 1a)an investor or/and ...
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Option pricing model: Black-Scholes-Merton model

Suppose, that a stock is priced at $ 400 and a volatility of 0.39. I buy a call option with an exercise price of $ 400 that expires in 3 months. The risk-free rate is 8%. Now, The theoretical value ...
Win_odd Dhamnekar's user avatar
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Pricing of options on a non-total return market index

I'm looking at ITM call options for the ESTX50 price(not total return) index. I notice that they gradually become cheaper for the same strike price, the further the expiration date is. The prices per ...
Nikolay Rys's user avatar
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Price of a Call Option as you Increase the time periods

I'm pricing call options at the moment and seeing how call option prices change depending solely on the periods of volatility. In one case the stock changes every month, the other it changes every ...
J0fClubz's user avatar
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What causes option prices to differ from Black-Scholes model so vastly?

I have tested Python and pre-defined web implementations of the Black-Scholes options pricing model. From these tests I've observed pricing differences between the model's output and real options ...
cardycakes's user avatar
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Calculate OTM premium from implied volatility?

ThinkOrSwim, IBKR, and others reports the implied-volatility (IV) for a given expiration. If I know the current underlying price and IV for that expiration, can I compute a rough estimate of the call ...
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Would a call option with one strike price be worth more than a call option with two different strike prices?

For example, say there is a call option with a strike price of $50 for a stock. Now, say there is another call option for the same stock with a strike price of $50 if the stock price is below $60, but ...
Jonathan's user avatar
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Is it important to understand option pricing models before trading options?

Options seem to be one of the most complex financial instruments generally available to retail investors. The common advice given to beginners (at least on this site) is that beginners "must ...
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Index Options + Options calculator [closed]

I noticed that even though SPX and SPY track the S&P Index (I realize latter is an ETF and 10x lower), the options prices for a particular chain that I observed today are not exact. They're ...
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Is there intuition behind asymmetry in call and put prices?

There is a certain asymmetry in (European) call/put prices, even with negligible interest and dividend rates. For example, assume current price $100, interest rate 0.01%, dividend 0, volatility 25%, ...
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does bid and ask volume affect option price

I have been trying to figure out how option pricing works and so far my understanding is as follows: There are few methods to determine the option price, Black-Scholes method is one of them. However,...
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What do the d's in this financial derivatives equation mean?

In my financial derivatives class, I am confused by the meaning of the d's in the following equation. Are they derivatives? What are they? dLt = mdt + σdBt Where L = log(St), log return
democrenes's user avatar
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How do I know what option on a particular stock X will move the most?

Say for instance I have a view that MSFT in the coming 3 months is going to come out with a big upgrade to their full year guidance. Let's assume in the event that this happens the stock goes up a lot ...
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Crash O Phobia and the reason for higher pricing of out of the money puts

In my stochastic finance course we are currently talking about Implied Volatility and Crash O'Phobia. According to Rubinsteins Crash O'Phobia, put-sellers attach a higher probability to the left tail ...
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Difference between deltas of American vs European Call options

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? Also, is there any way to determine the price of an ...
Chia Zhi Hao's user avatar
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Does sigma in Black-Scholes attempt to take into account future events?

I am learning basic information about Black-Scholes wrt options pricing. I see that the standard deviation of the stock price is taken into account. This seems to only rely on existing (historical) ...
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How to calculate Black-Scholes using Google Sheets?

I'd like to calculate Black-Scholes using Google Sheets based on this formula: https://www.erieri.com/blackscholes. Here are the parameters I'm using in the form: Stock price = 60.89 Option strike ...
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What is the Meaning of the Black-Scholes Value?

We are currently learning about the Black-Scholes Merton Model. I understand the process of finding the call option. However, I'm wondering what the answer actually means. For example: Stock Price = ...
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For a gain of +$X on the underlying security, would the gains on a single LEAP be identical to the gains on 100 shares of that security? [duplicate]

I have 100 shares of stock X which I am very long-term bullish on, and lately I've been considering selling those 100 shares and buying a LEAP for as far out as possible instead. The furthest I can ...
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Black scholes, futures, and American vs. European options

After having taken a look at this question about American and European options I was under the impression that the main difference between American and European options in Black Scholes pricing was ...
ford prefect's user avatar
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Does Implied Volatilty factor in all known future events?

With regards to option pricing in the BS model, if there is an earnings announcement coming up or an anticipated product launch, will the IV be correspondingly high to account for these known events (...
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Does Black Scholes exhibit the volatility smile?

You often hear about the volatility smile. Is that something that occurs within a standard Black Scholes model, with the usual formula for the price of a call? If we were to observe some call price (...
Imp's user avatar
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In option pricing formulas, is the volatility and short rate a decimal or a percentage?

In the BS option pricing formula, when entering values for volatility and short rate, do we enter them as percentages or decimals? Take the time unit to be a year, i.e. if we want to price something ...
John's user avatar
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Effect of company issued options on share price

A company has 100,000 shares and 100,000 unexercised call options (company issued). Share price and strike price both at $1. I assume the fact that these options exist will slow any price increases ...
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Implied or historical volatility to calculate theoretical options price with black scholes?

According to the black scholes model, volatility is one of the variables to calculate the fair price of an option. However, it doesn't specify which volatility should I use. Should I take the ...
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If option prices are publicly quoted on an options exchange, why do people use Black-Sholes to estimate their price?

I always wondered why the Black-Sholes-Merton model was used to estimate the price of European-style options when their prices are available on quoted exchanges? I think I am missing something big ...
James Blanch's user avatar
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Calculating greeks from given option information

I have some software that spits out information about an option. Strike, underlying information, etc, but I cannot get the greeks using this software. Given that these are American options, is there ...
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How does a delta signify the probability of expiring in the money

I was watching this video on option greeks and the guy said (at 34 min): If an option has a delta of 34, it has a 34% probability of expiring in the money? Is it possible to understand it intuitively ...
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Why IV and stock price are inversely related

What is the reason that Implied Volatility and Stock Price are inversely related? Is it possible to understand this qualitatively without getting into the math of the Black-Scholes formula?
Victor123's user avatar
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How are stock options priced?

I was reading the Wikipedia article about the Black-Scholes model, and it says this: The key financial insight behind the equation is that one can perfectly hedge the option by buying and selling the ...
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Black & Scholes article : option pricing

I am currently reading the famous article by Fischer Black and Myron Scholes called 'The pricing of Options and Corporate liabilities'. Just at the beginning of the article, they go on and explain ...
Mathusalem's user avatar
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How to calculate the standard deviation of stock returns?

I'm trying to learn the the Black–Scholes option pricing formula and one of the elements of that formula (according to http://bradley.bradley.edu/~arr/bsm/pg04.html) is the "standard deviation of ...
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Difference between Black-Scholes, Binomial models and Market price in European index options?

Need some help! I have calculated the theoretical price of an index option using BS and Binomial models and are now comparing the three. While BS and Binomial have approximately the same value, ...
Nic Loogatev's user avatar
13 votes
6 answers
54k views

Does the Black-Scholes Model apply to American Style options?

After reading the Wikipedia article on the Black-Scholes model, it looks to me like it only applies to European options based on this quote: The Black–Scholes model (pronounced /ˌblæk ˈʃoʊlz/1) is ...
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Can the Delta be used to calculate the option premium given a certain target?

I’m struggling for a while now with a question about options, namely 'which is the best option to buy?'. I have various books on options, but I’m not an mathematician and don’t have (yet) any ...
Jura's user avatar
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Calculating fair value of an oanda.com box option

How do I calculate the theoretical "fair value" of an oanda.com box option? More specifically, how do I calculate the probability that a given FOREX parity will enter a given range in a given period ...
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