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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Interpolation 2dimension in Python

I am in trouble with the Chebyshev Interpolation with a function that depends by two parameters. In the case of just one parameter it works, my goal is to approximate the first and second derivative ...
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110 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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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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244 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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49 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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47 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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1answer
98 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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44 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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76 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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67 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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145 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
71 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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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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77 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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754 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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1answer
72 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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77 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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41 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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154 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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122 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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87 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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129 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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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
154 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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181 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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46 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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259 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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182 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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680 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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71 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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439 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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203 views

How to calculate theta/rho for interest rate derivatives?

For interest rate derivatives priced with the Black model, we calculate some sort of forward rate that can be inserted into the Black formula. Calculating the greeks of the Black formula is easy ...
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Path dependency for Delta hedge value

This is actually a follow-up questions for the two threads below - value of a delta hedged option: Delta hedge value formula Continuous delta hedge formula My question is that how the drift (mu) ...
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207 views

Greeks for Futures [closed]

Is there some general result on the sensitivity of futures price to its maturity? For example, I have two futures on the same underlying, but maturing at different dates. Can I say which one is more ...
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1answer
87 views

When calculating delta, should you recalculate vol?

Delta is the rate of change of price to the spot. If the spot changes, so does the vol, so if you wanted to e.g. calculate delta as a finite difference $$\frac{f(spot+h)-f(spot-h)}{2h}$$ would you ...
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127 views

How should I interpret this Put Option delta graph?

In the following graph there's an example of Delta for a Call Option and a Put Option. I understand what this greek means and I understand why it's positive for calls and negative for puts. What I don'...
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Greeks for options without bid price

It is very common to be long option without any bid price. What would be the best way to estimate Greeks for such an option? At the ask price? 1/2 of ask?
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1answer
126 views

Expected Forward Volatility vs. Different Strikes

While theoretical options prices are derived from models, such as Black-Scholes, IV and IV skew reminds us that options prices are ultimately based on supply and demand. My question is the following: ...
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1answer
287 views

Negative theta for a short put

I am getting a negative theta for a short put deal Is it possible and if yes then under what conditions. Kindly explain I am just learning these concepts so my question may sound vague to some of you ...
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1answer
201 views

Gamma and Gamma Hedge [closed]

I have a very basic question: Is this gamma value has something to do with the gamma hedge? In delta hedge, it's done by buying/selling delta amount of underlying. But in textbook, for a put option, ...
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202 views

Autocallable option Delta

There have been numerous exotic trading desk blow ups lately, related to various reasons. However, in particular, one bank had some issues where they were pricing autocallable notes with Local ...
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258 views

Greeks: Estimate gamma by Monte Carlo finite difference

When I was using Monte Carlo to calculate the gamma of a vanilla call option by finite difference method, I stuck in this weird situation as below. Consider this, $$ Gamma = \frac{CallPrice(S^{up}_{T})...
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63 views

Deriving American option greeks

I am using integral representation of option value instead of trees, so I imagine to derive greeks we have to integrate across time for the boundary to get the EEP (Early Exercise Premium) component ...
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1answer
39 views

How do short stock positions lower the value of calls and raise the value of puts?

I'm reading Option Volatility and Pricing by Sheldon Natenberg who in the chapter on Risk Management is trying to explain the effect of interest rates on options. He says The value of a stock option ...
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1answer
358 views

Why is providing liquidity on Uniswap a “negative gamma” trading strategy?

I know the basics about options greeks, but I heard traders extrapolating the concept to portfolios composed not just of options. Providing liquidity on Uniswap, an automated market maker (AMM) built ...
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218 views

Does anyone have any suggestions on using Monte Carlo simulations to calculate Greeks of basket option?

I'd ideally like to use algorithmic differentiation or finite difference methods to approximate the Greeks of a basket option. It would be a European style basket on $N$ stocks with the payoff being $\...
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52 views

Greeks and splits

Should we adjust greeks on stock splits? Let's just ask about splits instead of reverse splits. I'm also interested how answers change if we change models/assumptions. I have some contradicting ...
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120 views

Asian option sensitivity

I am looking for some materials for profiling all options sensitivities for Asian options with both geometric averaging and arithmetic averaging . The underlying price $S_t$ follows a standard GBM. Is ...
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407 views

Confusion about replicating a call option

Assume standard Black-Scholes model, $$dS(t)=S(t)(rdt+\sigma dW(t))$$ where $\sigma$ is a constant and $W(t)$ is a Brownian motion under the risk neutral measure. A call option is replicable, so if we ...

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