Beyond Black-Scholes: A New Option for Options Pricing - WorldQuant (2023)

In 1973,Fischer Black,Myron ScholesandRobert Mertonpublished their now-well-knownoptions pricing formula, which would have a significant influence on the development of quantitative finance.1In their model (typically known as Black-Scholes), the value of an option depends on the future volatility of a stock rather than on its expected return. Their pricing formula was a theory-driven model based on the assumption that stock prices follow geometricBrownian motion. Considering that the Chicago Board Options Exchange (CBOE) opened in 1973, the floppy disk had been invented just two years earlier and IBM was still eight years away from introducing its first PC (which had two floppy drives), using a data-driven approach based on real-life options prices would have been quite complicated at the time for Black, Scholes and Merton. Although their solution is remarkable, it is unable to reproduce some empirical findings. One of the biggest flaws of Black-Scholes is the mismatch between the model volatility of the underlying option and the observed volatility from the market (the so-calledimplied volatility surface).

Today investors have a choice. We have more computational power in our mobile phones than state-of-the-art computers had in the 1970s, and the available data is growing exponentially. As a result, we can use a different, data-driven approach for options pricing. In this article, we present a solution for options pricing based on an empirical method using neural networks. The main advantage of machine learning methods such as neural networks, compared with model-driven approaches, is that they are able to reproduce most of the empirical characteristics of options prices.

Introduction to Options Pricing

With the financial derivatives known as options, the buyer pays a price to the seller to purchase a right to buy or sell a financial instrument at a specified price at a specified point in the future. Options can be useful tools for many financial applications, including risk management, trading and management compensation. Not surprisingly, creating reliable pricing models for options has been an active research area in academia.

One of the most important results of this research was the Black-Scholes formula, which gives the price of an option based on multiple input parameters, such as the price of the underlying stock, the market’s risk-free interest rate, the time until the option expiration date, the strike price of the contract and the volatility of the underlying stock. Before Black-Scholes, practitioners used pricing models based on the put-call parity or an assumed risk premium similar to the valuation of investment projects. In corporate finance, one of the most frequently used models for the valuation of companies is thediscounted cash flow model(DCF), which calculates the present value of a company as the sum of its discounted future cash flows. The discount rate is based on the perceived risk of investing capital in that company. The revolutionary idea behind Black-Scholes was that it is not necessary to use the risk premium when valuing an option, as the stock price already contains this information. In 1997, the Royal Swedish Academy of Sciences awarded theNobel Prize in economic sciencesto Merton and Scholes for their groundbreaking work. (Black didn’t share in the prize.He died in 1995, and Nobel Prizes are not awarded posthumously.)

If all option prices are available in the market, Black-Scholes can be used to calculate the so-called implied volatility based on option prices, as all the other variables of the formula are known. Based on Black-Scholes, the implied volatility should be the same for all strike prices of the option, but in practice researchers found that the implied volatility for options is not constant. Instead, it is skewed or smile-shaped.

Researchers are actively seeking models that are able to price options in a way that can reproduce the empirically observed implied volatility surface. One popular solution is the Heston model, in which the volatility of the underlying asset is determined using another stochastic process. The model, named after University of Maryland mathematicianSteven Heston, is able to reproduce many empirical findings — including implied volatility — but not all of them, so financial engineers have used different advanced underlying processes to come up with solutions to generate empirical findings. As the pricing models evolved, the following difficulties arose:

• The underlying price dynamics got more complex mathematically and became more general — for example, using Lévy processes instead of Brownian motions.

•The pricing of options became more resource intensive. Though the Black-Scholes model has a closed-form solution for pricing European call options, today people usually use more computationally intensive Monte Carlo methods to price them.

(Video) Black-Scholes Option Pricing Model -- Intro and Call Example

•It takes deeper technical knowledge to understand and use the pricing models.

Applying machine learning methods to options pricing addresses most of these problems. There are different algorithms that are able to approximate a function based on the function’s inputs and outputs if the number of data points is sufficiently large. If we see the option as a function between the contracted terms (inputs) and the premium of the option (output), we can simply ignore all of the financial questions related to options or stock markets. Later we will see how adding some financial knowledge back into the model can help improve the accuracy of the results, but on the basic level no finance-related information is needed.

One of these approximation techniques usesartificial neural networks, which have a number of useful properties. For example, some members of artificial neural networks are universal approximators — meaning that if the sample is large enough and the algorithm is complex enough, then the function that the network learned will be close enough to the real one for any practical purpose, as showed byGeorge Cybenko(1989)2andKurt Hornik,Maxwell B. StinchcombeandHalbert White(1989).3Artificial neural networks are suitable for large databases because the calculations can be done easily on multiple computers in parallel. One of their most interesting properties is duality in calculation speed: Although the training can be quite time-consuming, once the process is finished and the approximation of the function is ready, the prediction is extremely fast.

Neural Networks

The essential concept of neural networks is to model the behavior of the human brain and create a mathematical formulation of that brain to extract information from the input data. The basic unit of a neural network is a perceptron, which mimics the behavior of a neuron and was invented by American psychologistFrank Rosenblattin 1957.4But the potential of neural networks was not unleashed until 1986, whenDavid Rumelhart,Geoffrey HintonandRonald Williamspublished their influential paper on the backpropagation algorithm, which showed a way to train artificial neurons.5After this discovery, many types of neural networks were built, including themultilayer perceptron(MLP), which is the focus of this article.

The MLP is made up of layers of perceptrons, each of which has an input: the sum of the output of the perceptrons from the previous layer multiplied by their weights; it can be different for each perceptron. The perceptrons use a nonlinear activation function (like the S-shaped sigmoid function) to transform the input signals into output signals and send these signals into the next layer. The first layer (the input layer) is unique; perceptrons in this layer have just an output, which is the input data. The last layer (the output layer) is unique in the sense that in regression problems it usually consists of a single perceptron. Any layers between these two layers are usually called hidden layers. For an MLP with one hidden layer, the visualization is as follows in Figure 1.

Beyond Black-Scholes: A New Option for Options Pricing - WorldQuant (1)

Figure 1 can be written mathematically between the hidden layer and the input layer as:

Beyond Black-Scholes: A New Option for Options Pricing - WorldQuant (2)

(Video) How to interpret N(d1) and N(d2) in Black Scholes Merton (FRM T4-12)

and between the final output and the hidden layer as:

Beyond Black-Scholes: A New Option for Options Pricing - WorldQuant (3)

wheref1andf2are activation functions, α and β contain weight matrices between layers, and ε is an error term with 0 mean.

The first step of the calculation is to randomly initialize the weight matrices; this process will be used to transform the input variables to the forecasted output. Using this output, the value of the loss function can be calculated, comparing the real and the forecasted results using the training data. The backpropagation method can be used to calculate the gradients of the model, which then can be used to update the weight matrices. After the weights have been updated, the loss function should have a smaller value, indicating that the forecasting error on the training data has been decreased. The previous steps should be repeated until the model converges and the forecasting error is acceptable.

Although the previous process may seem complicated, there are many off-the-shelf programming packages that allow users to concentrate on the high-level problem instead of the implementation details. The user’s responsibility is to convert the input and output data to the correct form, set the parameters of the neural network and start the learning phase. Typically, the most important parameters are the number of neurons in each layer and the number of layers.

Pricing Options with Multilayer Perceptrons

As shown previously, the classical options pricing models are built on an underlying process that reproduces the empirical relationship among option data (strike price, time to maturity, type), underlying data and the premium of the option, which is observable in the market. Machine learning methods do not assume anything about the underlying process; they are trying to estimate a function between the input data and premiums, minimizing a given cost function (usually the mean squared error between the model price and the observed price on the market) to reach good out-of-sample performance.

There is an evolving literature applying other data science methods, such as support vector regression or tree ensembles, but neural networks like multilayer perceptrons generally fit well for options pricing. In most cases, the option premium is a monotonic function of the parameters, so only one hidden layer is needed to deliver high precision and the model is harder to overtrain.

Using machine learning for pricing options is not a new concept; two of the relevant early works were created in the early 1990s to price index options on the S&P 100 and the S&P 500.6,7These methods are convenient nowadays thanks to the availability of several software packages for neural networks. Although pricing options became easier, it is still slightly more complicated than loading the input data (options characteristics, data of the underlying asset) and target data (premiums) and pressing “enter.” One problem remains: designing the architecture of the neural network and avoiding overfitting the model.

(Video) The Black-Scholes Model EXPLAINED

Most machine learning methods are based on an iterative process to find the appropriate parameters in a way that minimizes the difference between the results of the model and the target. They usually start by learning meaningful relationships, but after a while they are minimizing only the sample-specific error and reducing the general performance of the model onunseen out-of-sample data. There are many ways to handle this problem; one of the popular ones is early stopping. This method separates the original training data into training and validation samples, instructing the model only on the training data and evaluating it on the validation sample. At the beginning of the learning process, the error of the validation sample decreases synchronously with the error of the training sample, but later the training and validation samples start to diverge; the error decreases only in the training sample and increases in the validation sample. This phenomenon signals the overfitting of the parameters, and the process should be stopped at the end of the synchronously decreasing phase.

Models that have more parameters can be overfitted more easily, so the number of the perceptrons and layers should be balanced between learning the important features and losing some precision because of overfitting. The learning rate determines how much to modify the parameters in each iteration; it is an important setting and must be set manually. Sometimes these metaparameters are decided based on validation errors; choosing them is more art than science. Picking the “best” parameters can yield better results, but the accuracy gained during fine tuning usually diminishes, so the trained model is good enough to use after just a few trials.

Improving Performance

The above-mentioned methods can be generally used for improving neural network models. In many cases, adding problem-specific knowledge (in this case, financial knowledge) can improve the performance of the model. At this point, the MLP has already learned a good approximation of the options pricing formula, but the precision is determined by the sample size (which is usually fixed) and the input variables. From here, there are three ways to further improve performance:

1. Add more input variables that help the model to better understand the options pricing formula.

2. Increase the quality of the input variables by filtering outliers.

3. Transform the function in a way that it is easier to approximate.

The first approach is quite straightforward. Introducing a new variable into the model increases its complexity and makes it easier to overfit. As a result, each new variable has to increase the predictive power of the model to compensate for the increased number of parameters. And because option prices are dependent on the expected volatility of the underlying security in the future, any variable that acts as a proxy for the historical or implied volatility usually makes the MLP more precise. To improve the accuracy, Loyola University Chicago professors Mary Malliaris and Linda Salchenberger suggested adding the delayed prices of the underlying security and the option.

The second method is to increase the quality of the input variables. Because the prices of less liquid options typically contain more noise than do more-liquid ones, filtering out those options should improve the accuracy of the pricing model. But if we would like to estimate the premium for deep-in-the-money or out-of-the-money options, this cleaning method could eliminate a significant part of the used dataset. Thus, it is important for researchers to choose filtering criteria that are the optimal choice between dropping outliers and keeping the maximum amount of useful information.

(Video) T3 - C3: Black-Scholes and beyond. Interview with Myron Scholes

The third approach — where art takes over methodology — raises an open question: If the neural network can approximate any function, then what should we forecast? This is the point at which there is the least amount of consensus among practitioners.

The problem is clear: We need a final output from the neural network that says how much an option with the input parameters is worth. That, however, does not mean the final price is the best target to aim for. The question is less relevant when we have a large sample size. When the dataset is small, choosing the best way to measure a function can increase the precision further. The most frequently chosen solutions are the following:

Predict the premium of the option directly, potentially using the information we have from mathematical models — for example, adding implied volatility to the input variables.Even if we successfully minimize the error for the function of the premium, that does not mean that after transforming it to the final prediction the errors will still be the best achievable for the premium. By predicting the premium directly, we are forcing the best result.

Predict the implied volatility of the option, and put it back into the Black-Scholes formula.That should make the premium readable. The big advantage here is that the different target variable is in the same range of values even if the premium of the option is different in magnitude. Other Black-Scholes variables can be used to try to predict options premiums, but implied volatility is the most popular among them.8

Estimate the ratio between the option premium and the strike price.If the underlying options prices behave like geometric Brownian motions, that property can be used to reduce the number of input parameters. In this case, the researcher would use the ratio between the underlying price and the strike price as one of the input parameters instead of using the underlying and strike prices separately. This solution can be very useful if the size of the dataset is small and you are more exposed to overfitting problems.

While there is disagreement about which function researchers should try to predict, there is a second debate about whether the dataset should be split into subsets based on various qualities. Malliaris and Salchenberger argue that in-the-money and out-of-the-money options should be split into different datasets. From a practical point of view, this approach can be useful because the magnitude of the option premiums can be very different in the two groups. Sovan Mitra, a senior lecturer in mathematical sciences at the University of Liverpool, contends that if the data are split into too many parts, the chance of overfitting increases and the model’s precision on out-of-sample results is reduced.9

The world has come a long way since Black, Scholes and Merton published their seminal papers on options pricing in 1973. The exponential growth in computational power and data, particularly over the past decade, has allowed researchers to apply machine learning techniques to price derivatives with a precision unforeseen in the ’70s and ’80s. Back then, options pricing was driven mainly by theoretical models based on the foundation of stochastic calculus. In this article, we provide an alternative method that uses machine learning, in particular neural networks, to price options with a data-driven approach. We believe that this approach could be a valuable addition to the tool set of financial engineers and may replace traditional methods in many application areas.

Balazs Mezofi is a Quantitative Researcher at WorldQuant and has an MSc in Actuarial and Financial Mathematics from Corvinus University in Budapest.

(Video) CRR convergence to Black Scholes

Kristof Szabo is a Senior Quantitative Researcher at WorldQuant and has an MSc in Actuarial and Financial Mathematics from Eötvös Loránd University in Budapest.


What is the most accurate options pricing model? ›

The Black-Scholes model is perhaps the best-known options pricing method. The model's formula is derived by multiplying the stock price by the cumulative standard normal probability distribution function.

What is the limitation of Black-Scholes model? ›

Limitations of the Black-Scholes Model

Assumes constant values for the risk-free rate of return and volatility over the option duration. None of those will necessarily remain constant in the real world.

Is there an equivalent of Black-Scholes for futures contract pricing? ›

The Black formula is similar to the Black–Scholes formula for valuing stock options except that the spot price of the underlying is replaced by a discounted futures price F. and N(.) is the cumulative normal distribution function.

How are options priced in the real world? ›

Options prices, known as premiums, are composed of the sum of its intrinsic and time value. Intrinsic value is the price difference between the current stock price and the strike price. An option's time value or extrinsic value of an option is the amount of premium above its intrinsic value.

What is the most commonly used option pricing model? ›

Key Takeaways

Some commonly used models to price options include the Black-Scholes model, binomial tree, and Monte-Carlo simulation method.

What is the most profitable pricing strategy? ›

Pricing Strategy

Most popular: Cost Plus Pricing – Calculate your costs then slap a profit margin on top of it! Second Most Popular: Match Competitors Pricing Pick a price similar to your competitors and run with it!

Why is the Black-Scholes model inaccurate? ›

In summary, the Black-Scholes model is wrong qualitatively, rather than quantitatively. This is because its fundamental components, namely the Geometric Brownian Motion and the continuous-time limit of the portfolio replication approach, are both qualitatively wrong.

What assumptions does the Black-Scholes model make that are wrong? ›

Assumptions of the Black-Scholes-Merton Model

No dividends: The BSM model assumes that the stocks do not pay any dividends or returns. Expiration date: The model assumes that the options can only be exercised on its expiration or maturity date. Hence, it does not accurately price American options.

How accurate is Black-Scholes model? ›

Regardless of which curved line considered, the Black-Scholes method is not an accurate way of modeling the real data. While the lines follow the overall trend of an increase in option value over the 240 trading days, neither one predicts the changes in volatility at certain points in time.

What is Black 76 pricing model? ›

Black's Model, also known as the Black 76 Model, is a versatile derivatives pricing model for valuing assets such as options on futures and capped variable rate debt securities. The model was developed by Fischer Black by elaborating on the earlier and more well-known Black-Scholes-Merton options pricing formula.

Which model is used for pricing futures contract? ›

The Expectancy Model of futures pricing states that the futures price of an asset is basically what the spot price of the asset is expected to be in the future. This means, if the overall market sentiment leans towards a higher price for an asset in the future, the futures price of the asset will be positive.

How is binomial option pricing model different from Black-Scholes? ›

In contrast to the Black-Scholes model, which provides a numerical result based on inputs, the binomial model allows for the calculation of the asset and the option for multiple periods along with the range of possible results for each period (see below).

Why is option pricing difficult? ›

Option pricing is a difficult aspect of derivative trading. Due to the number of factors influencing the price of an asset and the difficulty of predicting the final price of an asset, the price of an option is very hard to determine.

What does an option pricing model tell us about option prices? ›

Option Pricing Models are mathematical models that use certain variables to calculate the theoretical value of an option. The theoretical value of an option is an estimate of what an option should be worth using all known inputs. In other words, option pricing models provide us a fair value of an option.

Why are options priced differently? ›

Like most other financial assets, options prices are influenced by prevailing interest rates, and are impacted by interest rate changes. Call option and put option premiums are impacted inversely as interest rates change: calls benefit from rising rates while puts lose value.

What is the most successful option strategy? ›

A Bull Call Spread is made by purchasing one call option and concurrently selling another call option with a lower cost and a higher strike price, both of which have the same expiration date. Furthermore, this is considered the best option selling strategy.

What are the 3 option pricing model? ›

What is Three-Tiered Pricing? A three-tiered pricing model is a business method of laying out three different service solutions to your customers at three different pricing points, no matter if you use fixed pricing, value pricing or a volume pricing model.

What are the 4 types of pricing methods? ›

There are many different pricing strategies, but Competitive Pricing, Cost-plus Pricing, Markup Pricing and Demand Pricing are four common methods for small business owners to use.

What are the 4 pricing strategies? ›

What are the 4 major pricing strategies? Value-based, competition-based, cost-plus, and dynamic pricing are all models that are used frequently, depending on the industry and business model in question.

What are the 5 pricing methods? ›

The Five Most Common Pricing Strategies
  • Competitor-based Pricing. Competitor-based pricing, also known as competitive pricing or competition-based pricing, is more like plagiarism. ...
  • Value-based Pricing. ...
  • Cost Plus Pricing. ...
  • Dynamic Pricing. ...
  • Key-value item Pricing.

What volatility to use for Black-Scholes? ›

Implied volatility is derived from the Black-Scholes formula, and using it can provide significant benefits to investors. Implied volatility is an estimate of the future variability for the asset underlying the options contract.

What model is used to price American options? ›

The Bjerksund-Stensland model is a closed-form option pricing model used to calculate the price of an American option. It is designed specifically to determine the American call value at early exercise when the price of the underlying asset reaches a flat boundary.

What is the difference between Black model and Black-Scholes? ›

The major difference between these two models that that Blacks model uses forward prices to value futures option while the Black-Scholes model uses spot prices.

Which of the following is not an assumption of Black and Scholes model? ›

It can not be exercised before the expiration date. In the light of above discussion, the correct option is 3) the option being valued can be exercised anytime before the expiration date.

What is not directly observable in the Black-Scholes option pricing formula? ›

The Black–Scholes formula has only one parameter that cannot be directly observed in the market: the average future volatility of the underlying asset, though it can be found from the price of other options.

What is the simple explanation of Black-Scholes? ›

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

What is risk-free rate in Black-Scholes? ›

The risk-free rate of return is positively correlated with the value of an option. One component of the Black-Scholes Model is a calculation of the present value of the exercise price, and the risk-free rate is the rate used to discount the exercise price in the present value calculation.

What is the simplified Black-Scholes formula? ›

The Black-Scholes formula expresses the value of a call option by taking the current stock prices multiplied by a probability factor (D1) and subtracting the discounted exercise payment times a second probability factor (D2).

Who is the most popular black model? ›

Perhaps the most famous Black supermodel, Naomi Campbell was officially discovered at age 15 while shopping in London, though she had appeared in a Bob Marley music video as a child. After she was scouted, she became a top supermodel of the late '80s and '90s, and remains a major figure in the industry today.

How does the Black-Scholes option pricing model work? ›

What is the Black-Scholes Model For? The model is used to find the current value of a call option whose ultimate value depends on the price of the stock at the expiration date. Because the stock price keeps changing, the value of this call option will change too.

How do you choose a pricing model? ›

How to choose your pricing strategy
  1. Determine your value metric. ...
  2. Evaluate pricing potential. ...
  3. Review your customer base. ...
  4. Determine a price range. ...
  5. Review competitors' pricing. ...
  6. Consider your industry. ...
  7. Consider your brand. ...
  8. Gather feedback from customers.
Sep 22, 2022

Which are two option pricing models? ›

Black-Scholes Pricing Model (BSM)

These two option pricing models (BSM and Binomial pricing model) are mathematical models to calculate the theoretical value of an option. They provide us with a fair value estimate of an option.

How many models are there future pricing? ›

Two types of future pricing models are given below: Cost-carry model.

Which pricing strategy is used to enter a new market? ›

Price skimming

This type of pricing is ideal for businesses that are entering emerging markets. It gives companies the opportunity to capitalize on early adopters and then undercut future competitors as they join an already-developed market.

Why is the binomial option pricing model used to price options? ›

The binomial option pricing model is a risk-free method for estimating the value of path-dependent alternatives. With this model, investors can determine how likely they are to buy or sell at a given price in the future.

Why do most options traders lose money? ›

3) Over trading

Reflecting the problem of frequent trading, the Sebi report found out that loss-making traders expended an additional 28% of net trading losses as transaction costs which includes brokerage, clearing fee, exchange fee, SEBI turnover fee, STT and GST.

Why do most people lose money on options? ›

Traders lose money because they try to hold the option too close to expiry. Normally, you will find that the loss of time value becomes very rapid when the date of expiry is approaching. Hence if you are getting a good price, it is better to exit at a profit when there is still time value left in the option.

Can option becomes worthless? ›

As an option approaches expiry, the contract holder must decide whether to sell, exercise, or let it expire. Options can be in or out of the money. When an option is in the money, it can be exercised or sold. An out-of-the-money option expires worthless.

How do you tell if an option is fairly priced? ›

When it comes to the price of an option, the amount of time that the option has until expiration and the level of its implied volatility are two of the main factors that play into whether the option's price is actually cheap or expensive.

Who determines options prices? ›

The price of an option is a function of the market: buyers and sellers. In other words, when more people want to own an option, there may be a rise in the price, as the forces of supply and demand become more pronounced. In times of large market movement, the secondary markets may experience some increased volatility.

What percentage of option traders make money? ›

However, the odds of the options trade being profitable are very much in your favor, at 75%. So would you risk $500, knowing that you have a 75% chance of losing your investment and a 25% chance of making a profit?

What are the six factors that determine an option's price? ›

There are six factors affecting the price of a stock option:
  • The current stock price, S 0.
  • The strike price, K.
  • The time to expiration, T.
  • The volatility of the stock price, σ
  • The risk-free interest rate, r.
  • The dividends that are expected to be paid.

Is the Black-Scholes model accurate? ›

Though usually accurate, the Black-Scholes model makes certain assumptions that can lead to predictions that deviate from the real-world results. The standard BSM model is only used to price European options, as it does not take into account that American options could be exercised before the expiration date.

Which option model is used for pricing options? ›

There are two important models for option pricing – Binomial Model and Black-Scholes Model. The model is used to determine the price of a European call option, which simply means that the option can only be exercised on the expiration date.

What are the 5 assumptions of Black-Scholes model? ›

What are the assumptions of Black-Scholes model formula? The assumptions are that stock prices follows a lognormal distribution, it cannot have negative value, no dividends are payed, frictionless market, constant volatility, riskless rate, and follows the European style option.

Why is Black-Scholes still used? ›

The BSM is considered the standard model for valuing options; a model of price variation over time of financial instruments such as stocks that can, among other things, be used to determine the price of a European call option.

What are the 4 types of options? ›

There are four basic options positions: buying a call option, selling a call option, buying a put option, and selling a put option. With call options, the buyer is betting that the market price of an underlying asset will exceed a predetermined price, called the strike price, while the seller is betting it won't.

What are the 4 pricing models? ›

What are the 4 major pricing strategies? Value-based, competition-based, cost-plus, and dynamic pricing are all models that are used frequently, depending on the industry and business model in question.

How many options pricing models are there? ›

There are two types of options: call options and put options. A call option gives the buyer of the option the right to buy the underlying asset at a fixed price, called the strike or the exercise price, at any time prior to the expiration date of the option. The buyer pays a price for this right.

What are the 8 types of pricing? ›

Great pricing strategies are essential for generating strong profit from the get-go, and sustaining growth over time.
  • 8 pricing strategies and why they work. ...
  • Cost-plus pricing. ...
  • Value pricing. ...
  • Penetration pricing. ...
  • Price skimming. ...
  • Bundle pricing. ...
  • Premium pricing. ...
  • Competitive pricing.

What is the safest option strategy? ›

The covered call strategy is one of the safest options strategies that you can execute. In theory, this strategy requires an investor to purchase actual shares of a company (at least 100 shares) while concurrently selling a call option.

Who is the best option trader ever? ›

1. Paul Tudor Jones (1954–Present) The founder of Tudor Investment Corporation, a $11.2 billion hedge fund, Paul Tudor Jones made his fortune shorting the 1987 stock market crash.

What is the easiest option trading strategy? ›

Buying Calls Or “Long Call”

Buying calls is a great options trading strategy for beginners and investors who are confident in the prices of a particular stock, ETF, or index. Buying calls allows investors to take advantage of rising stock prices, as long as they sell before the options expire.


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2. A Conversation with Myron Scholes
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3. Option Pricing | Black & Scholes Model | Option Trading
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4. Finance with Python! Black Scholes Merton Model for European Options
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5. BS Option Pricing Model Spreadsheet Tutorial
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6. Sie Hendrata Dharmawan - “Financial Engineering: What Is It? Why Is It Useful?“
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