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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48 views

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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93 views

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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106 views

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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147 views

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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66 views

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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83 views

How to attribute daily options P&L between Greek sensitivities

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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87 views

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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56 views

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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116 views

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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2answers
103 views

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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97 views

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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125 views

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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60 views

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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73 views

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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51 views

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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119 views

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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230 views

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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101 views

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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439 views

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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61 views

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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60 views

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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109 views

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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48 views

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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121 views

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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69 views

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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156 views

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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1answer
72 views

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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115 views

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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91 views

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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838 views

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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101 views

Impact of correlation on greeks of a multi-underlying autocallable product

Please could someone explain how the greeks (especially the delta) of a multi-underlying autocallable product (i.e. an autocall on a basket) change when the correlation of the underlyings fluctuates? ...
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109 views

What does the theta curve of an american option look like?

Is the theta decay curve you see often given around the internet below in fact valid for American-style options? Often times, calculations for European-style options (Black-Scholes) are passed off as ...
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48 views

Calculation Option Greeks per day using Quantlib

I'm trying to calculate option greeks and impVol for a series of European index options (they are in a DataFrame) using QuantLib. Is there a way to get the Greeks and impVol on a daily basis? Thank ...
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162 views

How do you finance theta decay when replicating an option?

When constructing a replicating portfolio for a short position in a call option under Black Scholes, I am not able to pinpoint the source of gains from theta decay. When theta decay materializes, I ...
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132 views

Method of comparing two option pricing models?

I am currently writing a small paper comparing the Black-Scholes formula to the Bachelier model. However I am wondering how exactly I should compare the two models? Obviously I am comparing the prices ...
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89 views

VIX ATM Options Delta

VIX ATM options seem to have delta that is very far from .5 (.18/.82 for 60dte now) with .5 being in 30 territory. Why is this very different from stock options? Why is atm put much less sensitive to ...
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177 views

Greeks for Asian options on futures

I'm trying to get the Greeks for the PDB Option Contract (Crude Outright - Dated Brent (Platts) Average Price Option): https://www.theice.com/products/26535747/Crude-Outright-Dated-Brent-Platts-...
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52 views

How does a hedged portfolio account for other greeks?

So a classic delta-hedged portfolio on a call option is: $$-C - \Phi(d) \cdot B + \frac{d}{dS}C \cdot S = 0$$ How is risk of other Greeks hedged? Is it something like this? $$-C - \Phi(d') \cdot B + \...
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Greeks of caps,floors and swaptions

I will have an interview for a junior position as interest rates volatility trader. I would like ask you some questions about greeks of caps floors and swaptions. Are Caps vega positive? Are floors ...
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5answers
187 views

Why isn't the delta of a slightly in the money American option 1?

Doesn't the intrinsic value rise 1:1 with stock price when an American option is in the money? Also, you can exercise the option at any time to capture the intrinsic value (even though this would be ...
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194 views

Hull's book - Futures option's rho

In Hull's book (9th edition), on page 420, in table 19.6, it says rho of a European call on an asset with yield $q$ is $$KTe^{-rT}N(d_2)$$ Below it says we can compute greeks of European options on ...
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49 views

Volatility surface of daily contracts from ATM volatility of quarterly contracts

I'm trying to estimate the volatility surface of an especially illiquid options market; only ATM quotes are available (so Vanna-Volga approximation is not viable) for options on quarterly futures for ...
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317 views

Confusion about Vega P/L

For someone who has a delta hedged options position, the $\Gamma:= \frac{\partial^2V}{\partial S^2}$ roughly quantifies the amount of money made or lost if $$\frac{1}{\Delta t}\frac{(\Delta S)^2}{S^2} ...
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210 views

What is the origin of the names of the Greeks?

I am not sure if this is the right place to ask or if I should head over to HSM (where they may object, too), anyhow: What is the origin of the names of the Greeks? Who introduced those weird names, ...
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772 views

What are "greeks" in general for non-standard options (swaptions, capfloors, etc)

I know what greeks are for standard options: just take the derivative with respect to some parameter, like spot, time, rate, etc. But how does one calculate greeks for swaptions and capfloors? I was ...
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84 views

Dual delta and epsilon

Hey I know that dual delta and epsilon are derivative of option price with respect to strike nad dividend yield respectively. Are they used for something or rather not? Because I heard that dual delta ...
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594 views

Good references on PNL explain?

Can anyone share good references for how PNL explain should be calculated and presented for the best use of a derivatives trading desk?

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