A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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1answer
192 views

Exotic option pricing

I'm trying to price an option with payoff $\max\{a\cdot S_t - K,0\}$ where $a$ is a known constant. Ideally I'm looking for a closed form, continuous-time solution. Where should I begin?
6
votes
1answer
191 views

Prove or disprove “If at least 10% of an option's value is time value, it has a delta less than 90”

"If at least 10% of an option's value is time value (ie. time value >= 0.1*call price), it has a delta less than 90". In practice and after doing many tests with an option pricing calculator, this ...
3
votes
1answer
602 views

Science behind options pricing into Earnings event

I am wondering about studies regarding the uncanny options pricing into public company's earnings reports. The phenomenon being that the price of a straddle before earnings costs near exactly the ...
2
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0answers
92 views

Option symbol conversion [closed]

Maybe more of a programming question, Is there a Ruby gem to facilitate conversion of an option symbol notation from one form to another? For example, one source provides TZA1220J18 but an API for ...
3
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0answers
132 views

Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative

Let $X_t$ be an american style financial derivative with random exercise time $T$ where $t$ and $T$ belongs to some finite set $A$. Buying this derivative requires the buyer to pay $p_t$ up to time ...
3
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1answer
126 views

Do Bond Put Dates always fall on Coupon Dates (for non-zero coupon bonds). Calculation rules for Coupon Dates

This may not be the most appropriate SE site to ask this question, but I can't seem to find a better place to ask, so here goes: Do Puttable Bonds' put dates always fall on Coupon Dates? When they ...
6
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3answers
1k views

What really drives option implied volatility?

A common and oft repeated belief regarding options volatility is that implied volatility increases due to people bidding up a contract, usually related to anticipation of the outcome of an expected ...
0
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4answers
272 views

What is the Benefit of holding a short option?

i am new to corporate finance and ask myself why a investor is interested in being short on a Option? The only he can win is a premium but he can loose much more. I understand with being a short I can ...
1
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1answer
311 views

Calculate historical (ATM) option prices with public data

I just saw the question How to calculate the most realistic historical option prices with additional publicly available parameters and I am interested in the step before that. How can I calculate ...
2
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0answers
73 views

Any thoughts on how Warren Buffet's B of A warrants might be “marked-to-market” by either counterparty?

It's not too long since Berkshire Hathaway got its 10-year warrants in Bank of America alongside its \$5 billion purchase of preferred stock. At the time I saw some discussion about the value of ...
2
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5answers
6k views

Why do some people claim the delta of an ATM call option is 0.5?

I am looking for a mathematical proof in terms of differentiating the BS equation to calculate Delta and then prove it that ATM delta is equal to 0.5. I have seen many books quoting delta of ATM call ...
7
votes
1answer
2k views

What is the best live options data API?

What is the best/cheapest service to get real-time (as real-time as you can get) on stock options? I'm looking for the fastest update on the ENTIRE market, with a few stocks prioritized, so I need ...
2
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0answers
120 views

How to find the upper bound of a digital option given some market data?

Given the price of a call equals to 5 with Strike 100, please find the upper bound (sup) of the digital option with strike 105. I am not sure about the solution, but I write the condition like this, ...
10
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5answers
623 views

Is it ever possible that---because of illiquidity---exercising an out-of-the-money option is better than directly buying the stock?

Is there a case, where due to illiquidity, exercising out-of-the-money options could be better than directly buying the stock? When a stock is too illiquid, there are some costs because of this ...
9
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3answers
865 views

Implementing a Fast Fourier Transform for Option Pricing

So, I'm in need of some tips regarding a small project I'm doing. My goal is an implementation of a Fast Fourier Transform algorithm (FFT) which can be applied to the pricing of options. First ...
7
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1answer
293 views

When pricing options, what precision should I work with?

I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and ...
4
votes
1answer
635 views

Can American options with no dividends and zero risk-free rate be treated as European?

Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the ...
2
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0answers
143 views

What is the highest frequency greek for options on futures on bonds?

I'm considering exchange traded options of futures on bonds. Options on bond futures are usually American, thus the Black model is out of question. Which is the most imporatant Greek with respect to ...
5
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1answer
318 views

What are VIX back-month futures based on?

The VIX calculation is a weighted average of prices for front-month out-the-money options on the S&P index. So for VIX futures, this makes sense for the front month vix futures (being based on a ...
5
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2answers
2k views

Implied Volatility from American options (binomial)

I am trying to get the implied volatility from options on commodity futures and I know it's possible to get it from the binomial american options (on an non-dividend paying stock). I believe it is ...
7
votes
2answers
1k views

How to calculate the most realistic historical option prices with additional publicly available parameters

This is a follow up question of this one. My aim is to create the most realistic historical option prices possible with publicly available data. I want to do this for backtesting purposes. The ...
4
votes
2answers
440 views

Does put-call parity hold for a compound option with underlying American option?

Say there is an American put option that expires $N$ months from today. A call-on-put (CoP) option provides the owner the right to buy the American put option in exactly $M < N$ months (but no ...
3
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0answers
169 views

How companies choose earnings release dates, & effect on Implied Volatility

A company's earnings release date significantly affects weekly or monthly option prices/implied volatility. For companies that typically release earnings on the cusp of monthly options expiration, ...
5
votes
2answers
973 views

Constructing an approximation of the S&P 500 volatility smile with publicly available data

Besides of the VIX there is another vol datum publicly available for the S&P 500: the SKEW. Do you know a procedure with which one can extrapolate other implied vols of the S&P 500 smile with ...
3
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1answer
213 views

Eurodollar Options Stike Price > 100 bps

Looking at Eurodollar IR options market data coming down from CME, I can see a whole host of options where the strike is > 100 bps. My understanding in this case is that puts will always be in the ...
5
votes
1answer
429 views

Modified bisection formula for deriving implied volatility for a dividend paying american option

I am trying to work out the formula for calculating the implied volatility of an american option on a stock paying dividends (discrete payments or annualized yield). On page 171 of Haug The ...
3
votes
2answers
791 views

How to calculate COMPOSITE underlying implied volatility from ATM (near month) option prices?

I am trying to calculate the implied volatility of an underlying given observed prices of call and puts. There are two scenarios: The ATM strike is pinned by the market (i.e. underlying level == ...
6
votes
2answers
3k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
9
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1answer
304 views

What drives changes in implied volatility on ETFs/ETNs?

I thought implied volatility, as well as the VIX, primarily increase due to increases in the underlying asset's volatility, as well as the options themselves being bid up because more people were ...
7
votes
4answers
2k views

How to obtain true probabilities from Black-Scholes?

How to obtain true probabilities from Black-Scholes option pricing equation? Suppose, that we know risk adjusted discount rate for the underlying asset (the drift term in the physical measure) and ...
0
votes
1answer
901 views

what is the best way to calculate the probability of an equity option ending in the money?

Given historical implied volatility and all other know variables (stock price, option strike price, option expiration date, dividend rate, interest rate) what is the best way to calculate the ...
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2answers
658 views

Can we replicate a call option without borrowing and make it cheaper in this way?

I learned how to price a European call option using this video lecture. The considered case is very simple. The call option gives the right to buy 100 Euros for 100 Dollars in one month from now. The ...
11
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3answers
562 views

What benchmark/index to use for backtesting a portfolio of stock options?

What benchmark should I use for backtesting a model for when I should buy an option of a particular stock? For equities, one could say their portfolio outperformed the S&P 500. I would like to ...
12
votes
2answers
678 views

Can you fully hedge an option in the presence of counterparty risk?

The derivation of the Black-Scholes model assumes no counterparty risk. Does the presence of counterparty risk invalidate the argument behind the model? EDIT: The question is about options in ...
6
votes
4answers
2k views

How does an option's time value depend on moneyness?

How does an option's time value (also known as extrinsic or instrumental value) depend on how far it is in the money or out of the money? In other words, how does the time value change as the ...
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votes
4answers
1k views

True or False? An option's price will always be greater than or equal to its intrinsic value

Since if the option's price is lower than its intrinsic value (eg. strike price - current stock price for puts), then an arbitrage opportunity arises from buying the option at bargain and then ...
2
votes
5answers
670 views

how expected moves are priced into options

I understand that expected price changes of underlying assets are usually priced into options, but I don't understand how. For instance, before upcoming earning reports the option values are inflated ...
3
votes
1answer
278 views

Which approach is better for modeling option exercise strategies, rational or behavioral?

This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some ...
5
votes
1answer
519 views

How to apply quasi-Monte Carlo to path-dependent options?

Following up on my recent question on variance reduction in a Cox-Ingersoll-Ross Monte Carlo simulation, I would like to learn more about using a quasi-random sequence, such as Sobol or Niederreiter, ...
3
votes
1answer
131 views

Analysis of Unbalanced Covered Calls

Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events. I couldn't find any reference to this strategy (unbalanced is ...
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2answers
133 views

Buying one company or index against another, is this readily possible with options, with an accurate return (also Alpha Indexes)

There's a relatively new product in the market / on the Nasdaq called Alpha Indexes. It lets one own a company -- e.g. Apple, GE, Google, etc -- as the difference between how that company does (the ...
5
votes
1answer
1k views

How would I value a perpetual bond with an embedded option?

I am trying to work out how to value the following transactions. It should be straight forward, since it breaks down into a series of well known instruments, yet I am not sure how to evaluate it: ...
4
votes
3answers
299 views

Given markets usually fall fast and rise slowly, are there trading mechanisms to take advantage of this?

Per a previous question on this topic -- markets generally fall fast and rise slowly: what options strategies or other strategies can one use to take advantage of this common occurrence?
0
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1answer
264 views

Does an option's price “ratio” with the underlying security price?

I'm trying to understand option pricing better. Let's say security ABC is \$40, and a 38 PUT option with 40% implied volatility (and 90 days till expiration) is priced at X. If security ABC then ...
7
votes
2answers
2k views

Are there comprehensive analyses of theta decay in weekly options?

Are there comprehensive analyses of how much theta a weekly options loses in a day, per day? I know what the shape of theta decay looks like, in theory, where the decay towards zero happens more ...
4
votes
1answer
239 views

What are good conditions to roll a leap further out in time?

If you're hedging with a back month / leap option, what are good underlying / market conditions to move this option out even further in time? For simplicity, let's say you own a call with 6 months ...
6
votes
1answer
380 views

How sensitive are vertical spreads to changes in implied volatility?

How sensitive are vertical spreads to changes in volatility / implied volatility in the money, at the money, and out of the money? I'm thinking for 1 point spreads this would be very small / neutral ...
9
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2answers
314 views

When is it rational to exercise a bond option early?

Consider american options on interest rate futures such as the 10-year treasury note. When is early exercise optimal?
5
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2answers
296 views

What changes to put-call parity are necessary when evaluating american options on non-dividend paying assets?

If an underlying doesn't pay dividends (for our purpose defined as any distribution to the underlying's holder) directly or indirectly (e.g. options on futures) how does put-call parity change from ...
4
votes
4answers
1k views

How to price a calendar spread option?

How do you price calendar spread options, that is, options on the same underlying and the same strike but different times to maturity? Clarification: I'm interested in the pricing of a a CSO ...