# 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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### Stochastic vs. local volatility model choices for greeks

As a follow-up of another question (which is I feel slightly separate, hence a new question). Assume we want to fit a volatility surface with the goal of calculating good greeks, not prices. We can ...
331 views

### If two models imply the same volatility surface, do their greeks still differ?

Well, question is in the title. Assume I have two different models (for example a local volatility model and a stochastic volatility model such as a Dupire model and a SABR model for example) and I am ...
225 views

### Vanna vs volga and vega

So the bloomberg article that I'm referring to (Bloomberg. Variations on the Vanna-Volga Adjustment. Travis Fisher. Quantitative Research and Development, FX Team. January 26, Version 1) states that ...
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### Option pricing Greeks in Python - incorrect Gamma with MC option pricing (Black) using AAD autograd / JAX libraries - but works with closed form?

I am attempting to use AAD (Adjoint Algorithmic Differentiation) with a simple Black MC pricer, and found that the Gamma is incorrect. The output was compared to Black analytical Greeks, as well as ...
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### Swaption risk bucketing

In the IR swaption market, we have 24Expire10Tenor instruments(like a 2410 Matrix). Now I have the Vega number for each instrument, and I want to reduce the matrix size with the same total vega risk. ...
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### Why the sign of RHO in BSM and Black76 Model is opposite?

I find the formula of RHO using Black76 model (Source, alternatively see Wikipedia and scroll to "Under the Black model"): $$RHO_{call} = -t*c$$ $$RHO_{put} = -t*p$$ which means the sign ...
1 vote
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### Combine standard error in finite difference with Monte Carlo

I'm using Montecarlo to estimate the value of an option, $$\overline V(S_T, r, \sigma, T;N)=\mathbb{E} \left[V(S_T, r, \sigma, T)\right]$$ which comes with a standard error $SE$. I'm using "bump-...
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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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1 vote
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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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### 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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### 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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### 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 ...
1 vote
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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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