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Questions tagged [options]

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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Why would you take a Loan when trying to Illustrate a Riskless Hedge?

I'm reading an article trying to derive option pricing with a simple approach, but I got stuck. In the second paragraph of this article (Name – Options Pricing: A Simplified Approach), which takes ...
Telefondemonen_se's user avatar
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Could Delta hedging performance be worsening with increased frequency past a certain point?

Im currently trying to recreate the delta hedging results found in Chapter 19 of "Options, Futures and other Derivatives" by John C. Hull (2021) shown in the picture below. When trying to ...
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why shouldn't you exercise this american option early? [closed]

I know there's many questions of this vein, but I'm still confused why for American call options on non-dividend-paying stocks, early exercise options never make sense. Suppose I had purchased a 100 ...
APerson's user avatar
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time value of option proportional to sqrt(time)

I'm reading Natenberg's Options Pricing and Volatility, and in Chapter 18, he mentions this about an example: We can further refine our approximation if we note that an at-the-money option is made up ...
APerson's user avatar
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3 votes
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Relationship between Open Interest and Implied Volatility

Reference Request for any papers/articles that test the relationship between options open interest and its implied volatility. E.g. I would assume that a high market maker short interest on a strike ...
volquant's user avatar
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Proof of the value of an option using hedging and no-arbitrage [ Paul Wilmott Chapter 3.12.2]

I encounter a difficulty in understanding the proof of finding the value of an option. Before going into the proof, let's talk above the assumptions and parameters of the model. Assume that we know ...
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Options on Futures Historical tick data [duplicate]

Where can I find historical tick by tick data for E Mini S&P 500 Options on Futures by CME? I am looking for level 1 tick data with bid ask quotes.
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Pricing a custom option in terms of simpler instruments

I have the following custom European Option $F$ on the underlying $S$ whose pay-off at expiry $T$ follows: $$ F(T) = \min{[B, \max{[K_1-S(T), S(T)-K_2,0]}]} $$ where $B$ is a cash position and $0<...
Sid's user avatar
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2 votes
3 answers
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How to calculate overnight implied volatility?

I am trying to workout how to calculate the implied volatility of the overnight movement from market close to open. That is, the volatility of the from the closing price $S_t$ to the opening price $S_{...
Xerium's user avatar
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Preferred Option pricing model [closed]

I am at Uni studying mathematical finance and wanted to know which is most preferred /widely used model by Finance Industry Practitioners from the list below. Fourier Transform for option pricing ...
dijoney J's user avatar
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Zero-coupon call in CIR model

In an excellent textbook Brigo & Mercurio, I have a difficulty to derive a zero-coupon call option (3.26). What I did here didn't follow a stream of the main text. I assumed (3.28) and derived (3....
9 on 2's user avatar
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What are $\mu$ and $a$ in $ \mu = a + \frac{\sigma^2}{2} $

Considering GBM: \begin{equation} S(t_i) = S_0 \exp(a \cdot t_i + \sigma \cdot W(t_i)) = S_0 \exp\left((\mu - \frac{\sigma^2}{2}) \cdot t_i + \sigma \cdot W(t_i)\right) \end{equation} I am interested ...
Marlon Brando's user avatar
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How to solve special ATM case for Hagan approximation?

In Hagan et al's original SABR paper (https://www.next-finance.net/IMG/pdf/pdf_SABR.pdf), how do we reduce (2.17a) to (2.18) for the special ATM case? Could someone help walk me through the algebra? ...
user72283's user avatar
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P/L table for a delta hedged position

I am trying to replicate the table at pag. 119 of Dynamic Hedging by N. Taleb with no success. In the example called "A misleading delta" an operator has the following position: long \$1 ...
Enrico's user avatar
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Market Making in practice

I read some of the papers in the market making literature such as: Avellaneda - Stoikov market making model but was wondering if these types of models are actually use in pratice? It seems that when ...
confucius_is_confused's user avatar
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How does delta adjustment relate to skew stickiness ratio (SSR)?

The correct delta hedging of a derivative $V$ in a model where volatility $\sigma$ is a function of the underlier $S$ requires a stock holding of an amount $$ \frac{dV}{dS}=\frac{\partial V}{\partial ...
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Hope you can recommend me some books about building mechanical options trading systems

I have some basic understanding of CTA and am quite familiar with options pricing theory. I am interested in learning about books that discuss the use of options tools to construct mechanical trading ...
BearSpread's user avatar
1 vote
1 answer
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FX Strangle Market Conventions

Info on Risk Reversals for context In the FX vanilla options market buying risk reversal involves selling a lower strike put and buying a higher strike call. The price of such a structure is a ...
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Confusion about how price of a contingent claim at time 1 could give arbitrage

I have been reading the book Tomas Bjork's Arbitrage Theory in Continuous Time and could not understand how there could be arbitrage if the price of a contingent claim is not $X$. To give some ...
KMR's user avatar
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Describing the volatility skew with a set of options

Say you have a set of options data, and you filter the dataset based on certain criteria such as the bid-ask spread, open volume etc. and you end up with a set of liquid options based on said criteria....
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Synthetic replication of a spread option payoff

I have two assets, $S_1$ and $S_2$, and a European exchange-one-asset-for-another call option, such as those introduced by Margrabe (1978). So my payoff at expiration is the difference between the ...
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Interpolation of IV based on delta

I have a dataset with options, all the same date and time to maturity but different IV and delta. Now, I want to find the IV for certain delta values (e.g 0.5) through interpolation. Do you think that ...
Masmar's user avatar
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What is the P&L

I have a question about the P&L calculation, please. If we sell a call option on a stock with a volatility of 16%. Theta is worth 100€/day. Let's assume that the spot moves by 2% in one day. What ...
Raphael Morel's user avatar
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What to predict in delta-gamma hedging?

I am working in delta-gamma hedging with machine learning. I guess I have to predict gamma (since predicting gamma tells you how delta will behave) but I don't know why is it needed. I think that a ...
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Change in price of underlying impact on delta gamma and vega

I am working my way through Natenberg's book as well as the accompanying workbook, and there is a question I cannot figure out (p86). Futures price = 149.65 time to August expiration = 8 weeks annual ...
nickhealy's user avatar
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Summarizing the Volatility Skew as a Single Number

Related questions to this topic/subject: Expressing Volatility Smile as One Number Volatility skew and how to capture it? In both posts, the authors/respondents recommend using the second derivative ...
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Barrier Reverse Convertible Coupon

I want to ask regarding Barrier Reverse Convertible, I got this from https://bookdown.org/maxime_debellefroid/MyBook/barrier-reverse-convertibles.html "The price of this barrier reverse ...
testingBRC's user avatar
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pricing option with two volatility regimes

How would I price a 1-year ATM European call option, given I know that for the first 6 months, the realized volatility will be 20% and the latter six months, the realized volatilty will be 90%? One ...
Sameer Lal's user avatar
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Heston model calibration to option prices and implied volatility

I hope that you are having a great day, I am trying to write a research paper on the Heston model deep calibration. I noticed during my literature review that the most common approach is to calibrate ...
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Market Making in ETF, how the hedging is typically done

I was wondering how Market Makers in ETF hedge themselves. I believe that they don't buy the underlying basket because some of the stocks could be extremely illiquid. So my guess is that they buy CALL/...
option_vol's user avatar
2 votes
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What is the impact of the rollover of VIX futures contracts on VIX options?

I am inquiring about the potential impact of futures rollover on VIX options prices. I am currently exploring diagonal and calendar spreads on VIX options, and I need to modelize this. Your insights ...
Samuel Dana's user avatar
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Leveraged ETF construction

It says that leveraged ETF are constructed using options/swaps, but I didn't see any example of how you can replicated a leveraged index using options and swaps. For example taking the S&P500 ...
missing_name's user avatar
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How to access the Black Sholes Formula through the Distributive Law?

Recently I read a comment on how to interpret the Black Sholes Formula and more specifically how to wrap your head around the d1/d2. Although there were many good comments, this one stood out when one ...
Telefondemonen_se's user avatar
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2 answers
179 views

How to conclude which option is overpriced (by using implied volatility)

I have a small question regarding how to conclude which option is more overpriced? See the following table Option Theoretical Value Option Price Option Implied Volatility 7.00 8.00 26% 6.00 6.75 28%...
bigstreet's user avatar
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2 answers
115 views

Why do ATM options intuitively have higher Time Value (Extrinsic Value) than Out- and In-The-Money options?

I'm trying to get some intuition concerning the Black Sholes Formula and in doing so I've come across these graphs: Trying to understand the intrinsic value relationship with Options Value was ...
Telefondemonen_se's user avatar
11 votes
2 answers
885 views

Why are Black-Scholes derived greeks used for risk management when alternatives exist?

To my understanding, it is still quite common for market makers of vanilla options to use Black-Scholes greeks. My concern with this is best expressed by Pat Hagan in the original SABR model paper: &...
mrdrralph's user avatar
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If an option is undervalued, how does shorting a portfolio generate profit?

I am reading Hull's Options book. He introduces a one-step binomial model and a no-arbitrage argument, using the example shown in the picture below: Consider a portfolio consisting of a long ...
user546106's user avatar
4 votes
1 answer
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What are the downsides of using Kim's integral equation (1990) to determine the exercise boundary of an American option?

I'm new to the industry and trying to wrap my head around American options pricing. The integral equation(1) from Kim (1990) doesn't seem to make any strong assumptions, and approximating the integral ...
Eashan Gandotra's user avatar
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Replicating power (electricity) options in US markets

For options on power (e.g. https://www.ice.com/products/6590519/Option-on-ERCOT-North-345KV-Real-Time-Peak-Fixed-Price-Future ), how would you replicate this? Vanilla options in equities can be ...
Sameer Lal's user avatar
3 votes
1 answer
178 views

How to estimate Dealers’ Gamma Positioning

I am new here so please forgive my basic question. There are many websites and experts out there that estimate dealer gamma positions, but I don't know what they are doing. I think I understand the ...
Suzume's user avatar
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2 votes
1 answer
230 views

Options related factors forecasting cross section of returns

I came across this research paper that shows that skewness derived from options surfaces can help explain the cross section of returns. https://pubsonline.informs.org/doi/10.1287/mnsc.2015.2379 Are ...
helloimgeorgia's user avatar
1 vote
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Real options: discount rate for the value of the underlying security

This is an example inspired by Chapter 3, sub-chapter "Combining decision trees with real options(DTRO)", sub-sub-chapter "Case 4 Part Two", of Boer, F.P., 2004. Technology ...
robertspierre's user avatar
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PnL of a delta-hedged straddle

On Twitter, this question has been making the rounds: If you sold a 30 vol for a one year out at the money straddle, have access to free, perfect, and continuous delta hedging, and stock realizes a ...
snoreBore's user avatar
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104 views

How do I calculate the implied dividend yield and/or the forward rate for an equity ETF?

I am interested in building an implied volatility surface for a given ETF given a set of option prices for several combinations of (call/put,strike,expiry). I am interested in different ways to arrive ...
quantypythonshow's user avatar
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1 answer
84 views

Up And Out, negative delta close to barrier

For Up And Out options, is there an intuition as to why delta becomes negative as spot approaches the barrier. Thinking in terms of replicating portfoliio I would have assumed delta is always non-...
Paul's user avatar
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1 answer
151 views

Most Accurate Method for Pricing crypto Options

I'm currently studying financial derivatives and I've become particularly interested in cryptocurrency options, specifically Bitcoin. Given the unique characteristics of Bitcoin and other ...
Maria Torres's user avatar
1 vote
1 answer
101 views

How should I go about computing the 30-day model free implied volatility (MFIV) daily?

As the title suggests, how can I calculate the MFIV daily (for a market index)? My MFIV follows the procedure described in DeMiguel et al. (2013) Improving Portfolio Selection Using Option-Implied ...
KaiSqDist's user avatar
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Setting Bid-ask for option forward-type strips

do you know if there is any methodology on how to define spreads when fx option market maker is trying to quote for exaple various fx forward strip strategies? From bbg ovml or software which we are ...
Kos3_'s user avatar
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1 vote
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Estimating dynamics of volatility surface?

I have a daily time series of volatility smiles for an option contract. How can i calculate whether the smile is sticky strike, sticky delta or something in-between!
David's user avatar
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Does it make sense to use Black Scholes greeks to attribute P/L given the Black Scholes assumptions don't hold?

I've seen some takes from experts in the industry (Benn Eifert for example) who say that we should treat Black Scholes as a translation mechanism for putting price into a more workable form (IV). They ...
mrdrralph's user avatar
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