- The Black-Scholes Formula - Tim Worrall
- Black Scholes Option Pricing Model Definition, Example
- Pricing Power Options in the Black-Scholes Model - Wolfram
- Black-Scholes Options Pricing Model — Indicator by SegaRKO
- Option Pricing Models - How to Use Different Option

First -

The holder of the call option contract is the person that buys the option. The writer of the contract is the seller. The buyer (or holder) pays the premium. The seller (or writer) collects the premium.

As an XYZ bag holder, the covered call may help. By writing a call contract against your XYZ shares, you can collect premium to reduce your investment cost in XYZ - reducing your average cost per share. For every 100 shares of XYZ, you can write 1 call contract. Notice that that by selling the contract, you do not control if the call is exercised - only the holder of the contract can exercise it.

There are several online descriptions about the covered call strategy. Here is an example that might be useful to review Covered Call Description

The general guidance is to select the call strike at the price in which you would be happy selling your shares.

One more abstract concept before getting to what you want to know. The following link shows the Profit/Loss Diagram for Covered Call Conceptually, the blue line shows the profit/loss value of your long stock position. The line crosses the x-axis at your average cost, i.e the break-even point for the long stock position. The green/red hockey stick is the profit (green) or loss (red) of the covered call position (100 long stock + 1 short call option). The profit has a maximum value at the strike price. This plateau is due to the fact that you only receive the agreed upon strike price per share when the call option is exercised. Below the strike, the profit decreases along the unit slope line until the value becomes negative. It is a misnomer to say that the covered call is at 'loss' since it is really the long stock that has decreased in value - but it is not loss (yet). Note that the break-even point marked in the plot is simply the reduced averaged cost from the collected premium selling the covered call.

As a bag holder, it will be a two-stage process: (1) reduce the average cost (2) get rid of bags.

It is easier to describe stage 2 "get rid of bags" first. Let us pretend that our hypothetical bag of 100 XYZ shares cost us $5.15/share. The current XYZ market price is $3/share - our hole is $2.15/share that we need to dig out. Finally, assume the following option chain (all hypothetical):

DTE | Strike | Premium | Intrinsic Value | Time Value |
---|---|---|---|---|

20 | $2.5 | $0.60 | $0.50 | $0.10 |

20 | $5.0 | $0.25 | $0 | $0.25 |

20 | $7.5 | $0.05 | $0 | $0.05 |

50 | $2.5 | $0.80 | $0.50 | $0.30 |

50 | $5.0 | $0.40 | $0 | $0.40 |

50 | $7.5 | $0.20 | $0 | $0.20 |

110 | $2.5 | $0.95 | $0.50 | $0.45 |

110 | $5.0 | $0.50 | $0 | $0.50 |

110 | $7.5 | $0.25 | $0 | $0.25 |

According to the table, we could collect the most premium by selling the 110 DTE $2.5 call for $0.95. However, there is a couple problems with that option contract. We are sitting with bags at $5.15/share and receiving $0.95 will only reduce our average to $4.20/share. On expiration, if still above $2.5, then we are assigned, shares called away and we receive $2.50/share or a loss of $170 - not good.

Well, then how about the $5 strike at 110 DTE for $0.50? This reduces us to $4.65/share which is under the $5 strike so we would make a profit of $35! This is true - however 110 days is a long time to make $35. You might say that is fine you just want to get the bags gone don't care. Well maybe consider a shorter DTE - even the 20 DTE or 50 DTE would collect premium that reduces your average below $5. This would allow you to react to any stock movement that occurs in the near-term.

Consider person A sells the 110 DTE $5 call and person B sells the 50 DTE $5 call. Suppose that the XYZ stock increases to $4.95/share in 50 days then goes to $8 in the next 30 days then drops to $3 after another 30 days. This timeline goes 110 days and person A had to watch the price go up and fall back to the same spot with XYZ stock at $3/share. Granted the premium collected reduced the average but stilling hold the bags. Person B on the other hand has the call expire worthless when XYZ is at $4.95/share. A decision can be made - sell immediately, sell another $5 call or sell a $7.5 call. Suppose the $7.5 call is sold with 30 DTE collecting some premium, then - jackpot - the shares are called away when XYZ is trading at $8/share! Of course, no one can predict the future, but the shorter DTE enables more decision points.

It is somewhat the same process as previously described, but you need to do your homework a little more diligently. What is your forecast on the stock movement? Since $7.5 is the closest strike to your average, when do you expect XYZ to rise from $3/share to $7.5/share? Without PR, you might say never. With some PR then maybe 50/50 chance - if so, then what is the outlook for PR? What do you think the chances of going to $5/share where you could collect more premium?

Suppose that a few XYZ bag holders (all with a $8/share cost) discuss there outlook of the XYZ stock price in the next 120 days:

Person | 10 days | 20 days | 30 days | 40 days | 50 days | 100 days | 120 days |
---|---|---|---|---|---|---|---|

A | $3 | $3 | $3 | $3 | $3 | $4 | $4 |

B | $4 | $4 | $5 | $6 | $7 | $12 | $14 |

C | $7 | $7 | $7 | $7 | $7 | $7 | $7 |

Person B appears to be the most bullish of the group. This person might sell the $5 call with 20 DTE then upon expiration sell the $7.5 call. After expiration, Person B might decide to leave the shares uncovered because her homework says XYZ is going to explode and she wants to capture those gains!

Person C believes that there will be a step increase in 10 days maybe due to major PR event. This person will not have the chance to reduce the average in time to sell quickly, so first he sells a $7.5 call with 20 DTE to chip at the average. At expiration, Person C would continue to sell $7.5 calls until the average at the point where he can move onto the "get rid of bags" step.

In all causes, each person must form an opinion on the XYZ price movement. Of course, the prediction will be wrong at some level (otherwise they wouldn't be bag holders!).

Note that if you are unfortunate to have an extremely high average per share, then you might need to consider doing the good old buy-more-shares-to-average-down. This will be the fastest way to reduce your average. If you cannot invest more money, then the approach above will still work, but it will require much more patience. Remember there is no free lunch!

This post has probably gone too long! I will stop and let's discuss this matter. I will add follow-on material with some of the following topics which factors into this discussion:

- Effect of earnings / PR / binary events on the option contract - this reaction may be different than the underlying stock reaction to the event
- The Black-Scholes option pricing model allows one to understand how the premium will change - note that "all models are incorrect, but some are useful"
- The "Greeks" give you a sense about how prices change when the stock price change - Meet the Greeks video
- Position Management - when to adjust, close, or roll
- Legging position into strangles/straddles - more advanced position with higher risk / higher reward

Hey all,

Still getting used to working on TT and had a question regarding the IVx number listed next to each set of contracts. I've read the TastyWorks definitely of IVx but was hoping somebody could ELI5 it for me.

Using AMZN as an example:

On Tastytrade it shows an IVx for 2/1 Options Contracts of: 51.3%(+/-115.54)

On Schwab (my other broker) they break down Imp Vol. on a strike by strike basis for the contracts expiring 2/1 and each strike has an Imp Vol of <50.

Can anyone explain the difference and how I can use it as I become more familiar with how options pricing drives IV?

submitted by Xayde26 to wallstreetbets [link] [comments]
Still getting used to working on TT and had a question regarding the IVx number listed next to each set of contracts. I've read the TastyWorks definitely of IVx but was hoping somebody could ELI5 it for me.

Using AMZN as an example:

On Tastytrade it shows an IVx for 2/1 Options Contracts of: 51.3%(+/-115.54)

On Schwab (my other broker) they break down Imp Vol. on a strike by strike basis for the contracts expiring 2/1 and each strike has an Imp Vol of <50.

Can anyone explain the difference and how I can use it as I become more familiar with how options pricing drives IV?

Hi everybody. Hopefully this post doesn't sound too rant-y but I'm pretty frustrated by the amount of info out there that I'm not able to pick up on. There just seems to be a million ways to do calculated expected move. Here's what I've gathered so far.

There seems to be two general methods:

First Method: IV-Based

This means that there is a 68% probability that the stock in question will be between -1 and +1 sigma at the date of expiration, a 95% probability between -2 and +2, and a 99% probability between -3 and +3.

Sometimes 250-252 is used instead of 365, which seems to be the case when DTE refers to market days until expiration. Is that correct?

There are a number of ways to calculate IV. I would appreciate it if somebody could elaborate on which might be best and the differences between them:

Second Method: Straddle-Based

My understanding is that this is more used for binary events like earnings, but in general I've found two methods:

In the end, I'm just trying to be as accurate as possible. Is there a**best, preferred** method to calculating the expected move of a stock in a given timeframe? Is there a best, preferred method to calculating IV (I'm inclined to go with ToS's model simply because they're large and trusted). Is there some **Python library** out there that already does this? For a retail trader like me, **does it even matter**??

Any help is appreciated. Thanks!

submitted by hatitat to options [link] [comments]
There seems to be two general methods:

First Method: IV-Based

- One Standard Deviation Move = (P) (IV) (DTE/365)^0.5

This means that there is a 68% probability that the stock in question will be between -1 and +1 sigma at the date of expiration, a 95% probability between -2 and +2, and a 99% probability between -3 and +3.

Sometimes 250-252 is used instead of 365, which seems to be the case when DTE refers to market days until expiration. Is that correct?

There are a number of ways to calculate IV. I would appreciate it if somebody could elaborate on which might be best and the differences between them:

- ThinkOrSwim uses the
**Bjerksund-Stensland**Model [1] - I assume this is the "annualized" implied volatility aforementioned, because it is an IV value assigned to the stock as a whole ... what does that mean? I thought IV values were only calculated for a specific option contract??- As an aside, ToS in particular confuses me because none of the IVs seem to correlate - Exhibit A

- I thought I might look into how
**VIX was priced off of SPY**[2], as an analog, and use it as a basis for finding IV for any other stock as a whole. I don't know where they got their formula from - Backsolve for IV using
**Black-Scholes**[3]. This would only gives one value for IV, which I think only applies to that specific option contract and not to the stock as a whole?? - Some websites say to use the IV given that is closest to the desired time period [4] - of course I have no idea how the IV is calculated in the first place (Bjerksund-Stensland again? Black-Scholes?) What's the difference between using the IV of a weekly or a yearly option?
- Brenner and Subrahmanyam [5] - understood that this seems to be just an approximation. Should I be looking at formulas from 1988, however?

Second Method: Straddle-Based

My understanding is that this is more used for binary events like earnings, but in general I've found two methods:

- Expected Move = (0.85) (Front Month Straddle) [6] OR
- Expected Move = (Price of Straddle close to Desired Time Period) / (Price of Underlying) [7]

In the end, I'm just trying to be as accurate as possible. Is there a

Any help is appreciated. Thanks!

Hi everyone,

I've been working on a project for my Bachelor Thesis in Finance with Python for quite a while now and I'd love to have some feedback from you.

The project focuses on Option Pricing using the Black Scholes Model for Plain Vanilla and Binary Options. It allows the user to perform a series of tasks like computing and plotting greeks, option payoffs and the implied volatility surface and skew.

The script requires Chrome and quite a few modules to properly work, and the code is macOS native, meaning that it may not work on other operating systems (sorry for that).

My go-to IDE is PyCharm, but I guess any other IDE will work fine.

Here you can find the link to the GitHub repository where the project is located.

I will leave also some links to resources about all the theory behind the computations I do in the project for the ones that are not familiar with this topic.

Options Theory)

Black-Scholes Model

Binary Options

Greeks)

Options Strategies

Implied Volatility

Volatility Smile (Skew)

If you have any question let me know.

Thank you!

submitted by rcrmlt to learnpython [link] [comments]
I've been working on a project for my Bachelor Thesis in Finance with Python for quite a while now and I'd love to have some feedback from you.

The project focuses on Option Pricing using the Black Scholes Model for Plain Vanilla and Binary Options. It allows the user to perform a series of tasks like computing and plotting greeks, option payoffs and the implied volatility surface and skew.

The script requires Chrome and quite a few modules to properly work, and the code is macOS native, meaning that it may not work on other operating systems (sorry for that).

My go-to IDE is PyCharm, but I guess any other IDE will work fine.

Here you can find the link to the GitHub repository where the project is located.

I will leave also some links to resources about all the theory behind the computations I do in the project for the ones that are not familiar with this topic.

Options Theory)

Black-Scholes Model

Binary Options

Greeks)

Options Strategies

Implied Volatility

Volatility Smile (Skew)

If you have any question let me know.

Thank you!

Hi all, was doing searching for some research papers like I do every few months, and decided I'd throw them up here if anyone is interested in them.

Most of these link directly to pdfs (view, not instant-download).

**bolded** = you should read them

If anyone else reads these, I'm sure lots of the guys here would appreciate a quick review, summary points, or just your thoughts on any of them.

submitted by ObviousTwist to thewallstreet [link] [comments]
Most of these link directly to pdfs (view, not instant-download).

If anyone else reads these, I'm sure lots of the guys here would appreciate a quick review, summary points, or just your thoughts on any of them.

**Forecasting Volatility in Financial Markets: a Review**(60 pages)- Option Strategies: Good Deals and Margin Calls (40 pages)
- Option trading strategies based on semiparametric implied volatility surface prediction (30 pages)
- Short Term Variations and Long-term Dynamics in Commodity Prices (20 pages)
- Success and failure of technical trading strategies in the cocoa futures market (40 pages)
- The Information Content of the S&P 500 Index and VIX Options on the Dynamics of the S&P 500 Index (45 pages)
- The Performance of Model Based Option Trading Strategies (25 pages)
**evidence on the efficiency of index option markets**(15 pages)- OPTIONS EVALUATION - BLACK-SCHOLES MODEL VS. BINOMIAL OPTIONS PRICING MODEL (10 pages)
**ECB: risk, uncertainty, and monetary policy**(40 pages)- TIMING STRATEGY PERFORMANCE IN THE CRUDE OIL FUTURES MARKET (30 pages)
**An Anatomy of Futures Returns: Risk Premiums and Trading Strategies**(40 pages)- Roll strategy efficiency in commodity futures markets (40 pages)
**Spread trading strategies in the crude oil futures markets**(35 pages)**Commodity Strategies Based on Momentum, Term Structure and Idiosyncratic Volatility**(20 pages)- AN EXAMINATION OF MOMENTUM STRATEGIES IN COMMODITY FUTURES MARKETS (30 pages)
**understanding crude oil prices**(45 pages)**BONUS BOOK: The Bond and Money Markets: Strategy, Trading, Analysis**(1150 pages): a comprehensive textbook on bonds, interest-rate derivatives, money markets, credit derivatives, yield curve analysis, structured products, CDOs

This is how messed up my mind is (and why the title works):

Vibrator -> "Good Vibrations" -> The Beach Boys -> "Smile" Album -> Volatility Smile

Why Taylor Swift? She is innocent and naive just like most retail.

Now that we have that out of the way let's talk options....

So one of things that came out of the 87' crash was what we call the volatility smile which is simply the skew of puts and calls relative to their moniness. So what the fuck does that mean? Prior to the crash a modified black scholes model was used to price options; the problem is that black scholes assumes that volatility is constant - it isn't. When the black swan event occurred vol shot up and everyone lost their asses as both puts and calls were not skewed and thus always under priced.

The smile name is derived because the volatility surface resembles a smile or smirk where OTM puts and calls are skewed higher than ATM puts and calls. Here is an example:

http://www.optionsideacentral.com/wp-content/uploads/2013/10/AAPL-Skew.gif

You can also see the vol skewness on think or swim or ib under the "implied vol" section and see how as you get closer and closer to the ATM vol contracts and then goes up again.

the "smirk" (or the look I give a chick after I am caught looking at here clevage)

You will see that most smiles are askew to the downside (google volatility smile mother fucker can't do everything for you) - why is this? Isn't it wrong? Max loss to the downside is zero and max loss to the upside is infinity so why is it like this?

Volatility on the downside skew is greater than the upside because:

What's happening with options prices on SPY? looking at sep 26 calls $202 strike. options price was trading higher today when SPY was 200.60 than it is now, when it's 201.21. will things normalize after this volatility? I'm red on my calls when i feel like i should be well in the money

Skew is the reason - with a binary event volatility is raised significantly more on the wings (further OTM options) then the ATM (regardless the whole vol surface moves) so when the market doesn't move the skew flattens taking out the higher vol component even though the stock delta may be rising.

saavy???

submitted by midgetginger to options [link] [comments]
Vibrator -> "Good Vibrations" -> The Beach Boys -> "Smile" Album -> Volatility Smile

Why Taylor Swift? She is innocent and naive just like most retail.

Now that we have that out of the way let's talk options....

So one of things that came out of the 87' crash was what we call the volatility smile which is simply the skew of puts and calls relative to their moniness. So what the fuck does that mean? Prior to the crash a modified black scholes model was used to price options; the problem is that black scholes assumes that volatility is constant - it isn't. When the black swan event occurred vol shot up and everyone lost their asses as both puts and calls were not skewed and thus always under priced.

The smile name is derived because the volatility surface resembles a smile or smirk where OTM puts and calls are skewed higher than ATM puts and calls. Here is an example:

http://www.optionsideacentral.com/wp-content/uploads/2013/10/AAPL-Skew.gif

You can also see the vol skewness on think or swim or ib under the "implied vol" section and see how as you get closer and closer to the ATM vol contracts and then goes up again.

the "smirk" (or the look I give a chick after I am caught looking at here clevage)

You will see that most smiles are askew to the downside (google volatility smile mother fucker can't do everything for you) - why is this? Isn't it wrong? Max loss to the downside is zero and max loss to the upside is infinity so why is it like this?

Volatility on the downside skew is greater than the upside because:

- They are insurance of a black swan event
- If the skew is noticeably higher then they are getting pounded by buyers
- Puts are more expensive to trade

What's happening with options prices on SPY? looking at sep 26 calls $202 strike. options price was trading higher today when SPY was 200.60 than it is now, when it's 201.21. will things normalize after this volatility? I'm red on my calls when i feel like i should be well in the money

Skew is the reason - with a binary event volatility is raised significantly more on the wings (further OTM options) then the ATM (regardless the whole vol surface moves) so when the market doesn't move the skew flattens taking out the higher vol component even though the stock delta may be rising.

saavy???

On Black-Scholes Equation, Black-Scholes Formula and Binary Option Price Chi Gao 12/15/2013 Abstract: I. Black-Scholes Equation is derived using two methods: (1) risk-neutral measure; (2) - hedge. II. The Black-Scholes Formula (the price of European call option is calculated) is calculated Definition of the Option Pricing Model: The Option Pricing Model is a formula that is used to determine a fair price for a call or put option based on factors such as underlying stock volatility, days to expiration, and others. The calculation is generally accepted and used on Wall Street and by option traders and has stood the test of time since its publication in 1973. examining digital or binary options which are easy and intuitive to price. We shall show how the Black-Scholes formula can be derived and derive and justify the Black-Scholes-Merton partial di erential equation. Keywords: Black-Scholes formula, Black-Scholers-Merton partial di eren-tial equation, replication, self- nancing portfolio, martingale This is an updated version of my "Black-Scholes Model and Greeks for European Options" indicator, that i previously published. I decided to make this updated version open-source, so people can tweak and improve it. The Black-Scholes model is a mathematical model used for pricing options. From this model you can derive the theoretical fair value of an options contract. History. The Black Scholes pricing model is named after the American economists Fischer Black and Myron Scholes. In 1970 Black, a mathematical physicist, and Scholes, a professor of finance at Stanford University, wrote a paper titled “The Pricing of Options and Corporate Liabilities.”

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An Binary option's quality is The mixture of its intrinsic value and time value. The possible house buyer would reap the benefits of the Binary options trading of buying or not. forex trading strategies, day trading, etf trading, binary options, currency trading, futures trading, binary options trading, binary options brokers, option pricing, binary options demo account ... Now that we have a working Monte Carlo simulation model we extend it to price a number of exotic contracts such as Asian options, barrier options, binary options and lookback options. We take a ... FIN 438 Investment Theory Ch 16. Option Valuation. Pricing Options with Mathematical Models Introduction to the Black-Scholes-Merton model and other mathematical models for pricing financial derivatives and hedging risk in financial markets. About ...

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