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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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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 ...
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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 ...
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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 (...
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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 ...
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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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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?
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...