Questions tagged [greeks]

Greeks are named quantities representing sensitivity of option price to change in underlying parameters. Use of [greeks] tag should relate to one more named quantities, such as delta or gamma.

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Are Black-Scholes Greeks bounded?

For time to maturity greater than zero, has it been proved somewhere that the Black-Scholes greeks $$ \frac{\partial^n BS}{\partial x^n} $$ are bounded, where $x := \log S$ and $S$ is the current spot ...
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Is there a closed form solution to calculate Fugit for stock options?

I am trying to find a quick and dirty way to estimate fugit for a basket of American options real time. Is there a quick way to provide a proxy? I know one can do binomial tree or monte carlos ...
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When is the gamma of an iron butterfly spread positive? (Assuming stock price at t=0 is equal to the highest strike price)

I know the Gamma of a butterfly using calls is $$\Gamma_{butterfly} = \Gamma_{C_{K_3}}-2\Gamma_{C_{K_3}}+\Gamma_{C_{K_3}}$$ Where K3-K2 are the same as K2-K1 and S=K1, But under what condition is the ...
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Showing that pnl from gamma and theta cancel

I've seen a few questions state without proof that $0.5 \Gamma S^2 \sigma^2 = \Theta$. That is, the gamma and theta pnls cancel out. For example: Relationship between time decay and gamma My question ...
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The Wikipedia formulas for Vanna differ by a factor of 100x, why is that?

For a given: Stock price ${\displaystyle S\,}$ Strike price ${\displaystyle K\,}$ Risk-free rate ${\displaystyle r\,}$ Annual dividend yield ${\displaystyle q\,}$ Time to maturity ${\displaystyle \...
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Quantlib: Greeks of FX option in Python

I'm using Quantlib in Python to price an FX option. I'm comparing the result to Bloomberg, to make sure the code is working correct. I also want to calculate all the Greeks, and eventually use those ...
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How can you compare Vega between strikes?

Given a specified maturity is there a way to compare Vegas between different strikes? Surely the Vega of an ATM option will be very different from the same Vega of an OTM option
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Dollar gamma formula and its derivation

I am seeing two formulas: $gamma = 0.5 * gamma * (stock price ^ 2) $gamma = gamma * (stock price ^ 2) Not sure where this 0.5 term is coming from. And also, what is the correct definition of ...
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How do we hedge option vega practically?

Suppose I’m a market maker, and I collect some spread buying an option due the flow I get. In this example, I must always quote. I want to hedge as much of the risk as possible over the lifetime of ...
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Should you compute the greeks on realized or implied volatility?

I am reading Trading Volatility by Collin Bennett and he says that you should compute the Greeks using realized volatility rather than implied volatility? Is this actually true? As far as I know the ...
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Finite Differences Vega calculation - confirmation on proper approach

I have a MC simulation that uses finite differences to calculate the Greeks. It's for baskets and calendar spreads mostly. Now the logical (to me anyway) approach to calculate Vega is to increase the ...
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Delta Hedging with a Different Underlying

In Bouzoubaa and Osseiran page 68 equation 5.3, the authors discuss delta hedging a call written for asset $S_1$ using a different but correlated underlying asset $S_2$. The authors provide the ...
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How does $(d_2/\sigma) = (1-d_1)$ while deriving the Vanna Formula from BSM? [closed]

Just realized there was a quant finance board, so I figured I'd post it here instead. I'm trying to derive Vanna from the Black-Scholes Model (BSM) equation, but had a hook up on one of the ...
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Why Do I Need to Scale Options Vega w.r.t T (Time till Expiration)

In the book that I am using, it said that I need scale vega according time with this formula: $\sqrt{90/T}$ to get the weight of the vega w.r.t t. The reasoning it offered is as follows: "...
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How does an Options Market Maker (OMM) deal with an asymmetric inventory?

Let us use an example of a market maker quoting the ATM straddle. Under Black-Scholes: S = 100 K = 100 DTE = 3 IV: 20 r = 0 q = 0 No rates or dividends for ...
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Aggregating greeks to portfolio level

I have been asked to calculate/aggregate certain Greeks (delta, gamma, and vega) up to portfolio level for a portfolio consisting of a range of (long and short) equities, convertible bonds, and ...
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Distribution of total delta of option portfolio

We know the delta of a portfolio of options is simply the sum of deltas of the individual options. But are there any additional known properties about the total delta (or other greeks) of a portfolio ...
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Generating Greeks with American Options

Investor and Software Engineer but very new to quant finance here... I have the below code (which I'm sure will be helpful for some) and have some questions regarding the function parameters! Is RF ...
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No Probability in Greeks

In an interview, I was once told that I should not consider probability when talking about option greeks since from a mathematical point of view greeks have nothing to do with probability. That is of ...
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Greeks of portfolio in response to underlying price change

I'm trying to wrap my head around Greeks, and I'm getting a little bit confused. For example, let's say my portfolio holds a long 5 month ATM call with strike \$20, and short 2 month OTM call with ...
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Can gamma of an option be greater than its delta?

I have a currency pair usdinr put option with strike price at 73.5 INR, risk free rate 0, underlying price of 75.4025, days to expiry is 15 and iv is 5.9%. Delta of this option is -0.019 and gamma is ...
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What is the greatest theoretical delta value?

In a few options positions I'm currently holding I noticed delta values of ~0.6 while gamma is ~1.0 which surprised me as I thought delta can never be greater than 1 - meaning for every 1\$ move in ...
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How to attribute daily options P&L between Greek sensitivities [duplicate]

When building a P&L attribution system for options, what is the market convention for attributing daily P&L between delta, gamma, vega, and theta Greeks? I'm particularly interested in how ...
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The greeks, vanillas and digitals

Question 1: I know website’s like: https://optioncreator.com/ display the pricing and payoff graphs of regular plain vanilla puts and calls. I would like to know if there is any website that displays ...
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Vega of derivative when volatility is stochastic?

What is Vega for a derivative when the volatility of the underlying asset stochastic process itself? When the value of the derivative is $V_d$ vegais $\partial V_d/\partial\sigma$. Consider for ...
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Deriving Bachelier Greeks

I am working on the Bachelier Model with r not equal to 0 as described in the first and most upvoted answer in following link: Bachelier model call option pricing formula This is fairly easy to code ...
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Mixed greeks in Python - How plot the following

I am interested about greeks with Black-Scholes. In this case, I have the python formula to compute the greek called "Vanna", that is: $\frac{\partial^2 P}{\partial \sigma \partial S}$ the ...
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What is the intuition behind a positive theta for European long puts?

I've googled extensively for an answer to this question. Very similar (if not identical) questions have popped up in this same website (example) but I never find the answers to be clear and/or precise....
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Risk-managing vanilla books (sell-side)

I am interested in learning more about how traders risk-manage books of vanilla options. I presume there should be a fairly standard list of facts. For the moment, the area of interest is FX, as ...
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What is delta of an option signaling?

In an interview I was once asked what the delta of an option was and my answer started from the fact that it is the first derivative of the option with respect to the price, and then I concluded ...
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Monte Carlo Greeks for Fixed Strike Asian Call

I am interested in pricing an European-style fixed strike asian call with payoff $\max(A(S)-K;0)$, where $A(S)=\frac{1}{n}\sum_{i=1}^nS(t_i)$ is a discrete arithmetic average and $K$ is the strike ...
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Using delta as probability of an option expiring in the money

I understand that delta can be seen as a probability proxy for an option expiring in the money, as well as deltas for call options ranging from 0 to 1 and deltas for put options ranging from 0 to -1. ...
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what is option zeta?

Is this an option greek? I've come across this term in some option book, and also online definition e.g. HERE: A measure that captures the premium difference between the value of an option calculated ...
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How to derive the relationship between gamma and theta?

I am trying to derive this formula Θ = –0.5 × Γ × S^2 × σ^2 to see where it comes from. My thinking is that PnL = delta dS + Vdσ + 0.5Γ(dS)^2 + Θdt. Assume we delta hedged and vega hedged, first and ...
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Speculation with quanto option - how to see the realized correlation

From this question, on vanilla option vol speculation, we can gain intuition on the impact of realized vol on the gamma, and consequently on the efficiency of the speculation trade. Asuming long ...
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Black-Scholes Call Portfolio: Bond Weight Interpretation

$$C - \frac{P(z_{1})}{k(y, \tau)} \cdot S + \frac{P(z_{2})}{k(r,\tau)} \cdot F = 0$$ $$C - \Delta \cdot + w_{2} \cdot F = 0$$ OK, so with $\Delta$ I am hedging my directional risk, but what is $w_{2}$?...
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Finite Difference Method in Greeks (Options)

I need a way to approximate the analytical formula of Greeks of a generic call option using the Finite Difference Method. For example, the FD method for Delta/Gamma is the following one: Now, I am in ...
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2 votes
2 answers
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Numeraire explanation on currency greeks

Would it be possible to help understand the numeraire of certain currency options? Derivations from the Black Scholes models for Delta and Gamma, $Delta = e^{-r_f T} N(d_1)$ $Gamma = \frac{e^{-r_f T}}{...
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Effect of Implied volatility on option delta

I am currently hedging a short put option where strike is 6027 and expiry is 30th Mar 2023. As per my understanding when option is ITM increase in volatility will decrease the delta and decrease in ...
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Calculation of SABR delta

I have a relatively simple question on the calculation of the SABR delta. I consider the Bartlett's delta (although my question remains the same for the unadjusted SABR delta from Hagan (2002) ). The ...
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Volatility targeting / sizing for option strategies

I am trying to work out how to properly size an option strategy to a given target volatility. Assuming I have \$100 capital and I would like to have a strategy's long-run daily volatility to be \$1 (e....
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How to parameterising Greek Surfaces?

I'm currently working on my master thesis, where I have data on option trading volume and flow (number of shares bought minus sold; i.e., net position), divided among three kinds of market ...
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How to compute (the sign of) Gamma?

If I have historical prices of a stock at the market close and 10 minutes before the market close over a long period of time, how can I infer the sign of the Gamma of the stock? I read something about ...
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Delta-Gamma VaR approximation and cross-gamma

Suppose we have a portfolio of say two vanilla options (e.g. on two index futures). One option A with underlying X and a second option B with underlying Y. I'm trying to calculate the delta-gamma ...
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How are the greeks defined for the two legs or more strategies with regards to options?

I am to figure out something, and can't find any reference. I wonder: does it make sense to talk of a delta or other greek of a strategy? It seems that you can't put a price exactly on a call spread ...
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1 answer
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Why does the price of an option increase with increasing Rho?

I was wondering why the price of an option increases with Rho (price change for a derivative relative to a change in the risk-free rate of interest). I found this explanation on a website: "Each ...
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2 votes
1 answer
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How to approximate a delta using monte carlo methods and finite differences via Higham's book?

I'm currently taking a Mathematical Finance module at University and one of the recommended texts is “An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation” by D.J. ...
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Finding optimal calendar spreads and diagonals

I am looking for some pointers on risk/return profiles of calendar spreads and diagonals with different strikes and expiration dates, preferably based on historical backtests with SPY options. Please ...
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What is the relationship between Vanna and Gamma?

I'm trying to build a crude model for the effects of delta hedging on major indices like the S&P 500. My background is more in pure mathematics so a lot of this stuff is new to me. That said I ...
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6 votes
2 answers
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Relationship between Vega and Gamma in Black-Scholes model

my question is the following one: I don't manage to prove that, in Black-Scholes model, single-signed Gamma options have values that are monotonic in the volatility. I am looking for an exhaustive and ...
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