Questions tagged [gamma]

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Gamma smoothing of vanilla options

I want to ask a question about the answer provided here: https://quant.stackexchange.com/a/35211/61083. I'm wondering if there is mathematical proof as to why it is working. Meaning if I reprice a ...
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How to forecast volatility using gamma exposure index?

Brainstorming this afternoon. GEX is the gamma exposure index (https://squeezemetrics.com/monitor/static/guide.pdf). It's the sum of gamma exposure for call and put. Using IV, strike and BDS you can ...
5 votes
1 answer
192 views

Why does a long gamma trader sit on the bid and offer?

I have read in Bennett - Trading Volatility the following quote. As shown above, a long gamma (long volatility) position has to buy shares if they fall, and sell them if they rise. Buying low and ...
3 votes
1 answer
268 views

Can we trade theta?

The context is this theoretical result from Black-Scholes-Merton differential equation that the effects of theta and gamma cancel each other. Equation (5.23) from the book titled "Option Trading&...
3 votes
1 answer
249 views

Gamma squeeze - mathematical explanation

I am trying to understand from a mathematical and financial point of view the mechanism behind the so-called gamma squeeze. Is there a good source to read about this/ My questions are: what are the ...
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3 votes
1 answer
553 views

What is gamma to do with realized volatility?

I keep hearing that gamma is a bet on realized volatility. That is, if we are long gamma then we need higher realized volatility to come in the future in order to make a profit. from other source: If ...
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Cross Gamma PnL Formula

sort of dumb question. I understand well the relationship between Gamma/Theta pnl for options on single underliers. I'm (attempting) to move onward and upward to options on baskets. Conceptually, I ...
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277 views

Gamma, Theta, Vega, Vanna and Volga PnL under Bachelier

Is there a PDE that decomposes the daily PnL as delta, gamma, vega vanna and volga but under Bachelier model (assuming normal vol) ?
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1 answer
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Realizing the same PnL as Gamma Vs Vega

Consider a delta hedged option postion. Futhermore assume that I can perfectly forecast realized volatility over the life of the option. Vol I buy the option at = Implied Vol (IV) Realized volatility ...
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2 answers
237 views

Gamma PnL when hedging with implied volatility - where is the mark to market PnL?

It is well known that hedging with implied volatility involves a PnL: $0.5*(σ^{2}_r−σ^{2}_i)S^{2}*Γ_{i}dt$ In the Wilmott paper (http://web.math.ku.dk/~rolf/Wilmott_WhichFreeLunch.pdf), they imply ...
3 votes
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Calculate Gamma and Vega of a portfolio of convertible bonds

I am being asked to calculate the gamma and vega of an existing portfolio of convertible bonds. does anyone has a documentation of direction that i could use to get going pls? This is a premiere for ...
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4 votes
2 answers
110 views

For single barrier options, why is a plot of gamma so scattered compared to other greeks?

Is this to be expected or is there something wrong with the model? I am getting scattered gamma plots for all types of barriers like U&O, D&I, etc However a basic vanilla options has a smooth ...
1 vote
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Purpose of Vega Hedging

I am trying to understand the principle of vega hedging. When should a market maker vega hedge his position ? Let's suppose that a market maker delta and gamma hedge himself, and carries his position (...
1 vote
1 answer
153 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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2 answers
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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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2 votes
0 answers
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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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6 votes
1 answer
450 views

Vol, Gamma, Vega -- essentially all the same?

When talking to traders I hear this sentence a lot I am a buyer/seller of X where X = {vol, gamma, vega} Is X basically all the same -- they are just saying -- I think implied volatility is cheap or ...
3 votes
1 answer
549 views

Why is gamma exposed through the square of spot prices?

As per this article, "the mathematically intuitive way to expose gamma is through the square of the underlying price": https://llllvvuu.dev/blog/unbundling-gamma Can someone explain this? ...
2 votes
0 answers
110 views

Net delta and gamma profile of a put spread

I have a question regarding the description in Simon Gleadall's book -- option gamma trading which you can find a copy HERE. The following paragraph he discussed about gamma and delta profile of a ...
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1 answer
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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 ...
1 vote
0 answers
56 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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1 vote
1 answer
189 views

Gamma-neutral delta-neutral call ratio spread

I have been looking into options strategies that minimize risk via delta neutrality. One such strategy seems to be the gamma-neutral delta-neutral call ratio spread, in which the gamma is neutralized ...
1 vote
2 answers
188 views

Derivation of the Gamma approximation formula from the Delta approximation formula

The formula of $Gamma = (Vplus + Vminus - 2V0)/(V0 * dS^2)$, where $V$ is the contract value, $S$ is the stock price. We also know that $Gamma = (Dplus-Dminus)/(Splus-Sminus)$, where $D$ is the ...
1 vote
0 answers
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Gamma PNL for Convertible Bond

so just trying to compute gamma PNL for some CB positions using Bloomberg data for delta/gamma. for a CB, BBG has delta 0.74 and Gamma 0.00524. if I want to compute the delta PNL and Gamma PNL for a ...
0 votes
1 answer
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Delta and Gamma profile

There is an active spread option traded in ICS as described here - https://www.theice.com/products/28881205/Crude-Future-Brent-1-Month-Calendar-Spread-Options I am ...
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1 vote
0 answers
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Why should a seller of autocall (down out ones) cover gamma risk?

I wonder why sellers of Autocalls should cover the gamma ? The autocall I'm talking about is of this type : While the spot never goes below 70 % of the initial value, nothing happens. If it happens, ...
4 votes
2 answers
502 views

Gamma of interest rate derivatives

consider an interest rate derivative whose value $V$ depends on $n$ interest rates $r_1, \dots, r_n$. Hence $V$ is a function in $n$ variables $V(r_1, \dots, r_n)$. My question concerns the gamma $\...
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2 votes
1 answer
387 views

Relationship between time decay and gamma

In a paper titled Investing in Volatility published in 1998 by Emanuel Derman, Michael Kamal, Iraj Kani, John McClure, Cyrus Pirasteh, and Joseph Z. Zou, I found the following assertion (on page 9) ...
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1 vote
1 answer
375 views

Meaning of Rebalancing the Gamma in Options?

What does rebalancing the gamma mean? In the Book: Dynamic Hedging at the beginning says: Rebalancing the gamma corresponds to buying and selling the underlying security in order to replicate the ...
1 vote
0 answers
343 views

How to use gamma theta and theta gamma ratios for managing short positions?

I'm starting to sell ATM options in order to buy the tails, and I would like to know how to use gamma/theta or theta/gamma ratio or their sum to manage and exit the short position before the gamma ...
0 votes
1 answer
347 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, ...
1 vote
1 answer
706 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 ...
0 votes
1 answer
211 views

Realizing profit with Gamma Trading doubt

Lets suppose we have a delta-neutral portfolio and that we want to trade the gamma. If we are long gamma, we can profit from every rebalancing to keep the portfolio delta-neutral. Lets suppose the ...
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3 votes
1 answer
366 views

Gamma PnL from Itô's Lemma derivation

The change in a call portfolio ($f$), derived from Itô's Lemma, is: \begin{align*} \left( \frac{\partial f}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2 f}{\partial S^2}\right)\mathrm{d}t &=...
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0 votes
1 answer
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Long positions (call or put) have positive gamma, and short positions (call or put) have negative gamma

I was reading a lot about the idea that long positions (call or put) have positive gamma, and short positions (call or put) have negative gamma. But I couldn't understand why. In "Bunds and Bund ...
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0 votes
1 answer
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Historical PNL using Taylor Expansion for Gamma Ladders

I have DV01 and Gamma Ladder for IR Swaptions and the historical market data of the underlying swap curve. Can someone please help me understand how to calculate historical PNL using taylor expansion ...
1 vote
0 answers
174 views

Vega hedging swaption with caplets - precisely, what will go wrong?

I am trying to form a kind of unified perspective of how (vega) hedging an exotic with vanillas, or hedging a 'basket option' with vanillas will go wrong. So in particular, I want to be able to ...
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7 votes
2 answers
4k views

Is there anywhere I can read the paper, "The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves"

Hello there was a paper published by: M. Arslan, G. Eid, J. El Khoury and J. Roth titled "The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves" (2009). I believe they ...
0 votes
1 answer
2k views

How does delta-gamma VaR work in practice and when can it be preferable to Monte-Carlo VaR?

So I will start off by just stating my understanding of the two methods through some examples and lead that into my question. Hopefully it is correct but if not then perhaps the answer to my question ...
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7 votes
1 answer
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Gamma-Vega Neutral Portfolio Not Possible with Only 3 Options

Let's say we have sold a call option, x, on a share and we have 2 other call options, y & z, with different strikes and maturities to try and achieve a portfolio that is both Gamma and Vega ...
2 votes
0 answers
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Are there trades that long gamma (convexity) and short volatility at the same time?

Likewise, are there trades that short gamma and long volatility at the same time? Under fixed income context, are there trades that short convexity and long volatility at the same time?
1 vote
1 answer
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Making portfolio Delta and Gamma neutral using 2 derivatives

We have an option portfolio with delta =2 and gamma 3 and we want to making this portfolio delta and gamma neutral using two derivatives D1 and D2: ...
5 votes
2 answers
405 views

Gamma for ATM options with low spots

I'm trying to compute gamma for a vanilla call with spot and strike equal to 0.001. BLACK & SCHOLES formula gave me a value of 554.761 for gamma which is a very high. I have then two questions: ...
5 votes
2 answers
1k views

Numeric example to understand the effect of option gamma

Gamma of an option is the second partial derivative of the theoretical value of an option wrt the underlying. It should be the rate of change of Delta wrt to a small change on the underlying. However ...
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2 votes
1 answer
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How to prove Gamma is the same for a European call and European put with the same inputs?

I saw from a text "From put-call parity, call and put with the same inputs have the same gamma", but I don't see how put-call parity is related to Gamma. Can someone explain? Thanks!
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4 votes
1 answer
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Gamma PnL Formula and Break-Even volatility

When we derive the P&L of a delta hedged option we obtain: $$ \text{P&L}=\dfrac{1}{2}\Gamma(\delta S)^{2}-\theta\delta t $$ and setting equal to zero and rearranging we obtain: $$ \dfrac{1}{...
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1 vote
1 answer
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What does "Gamma profit/loss" mean?

I understand the Greeks as derivatives, but I'm very confused with terms like "Gamma profit/loss""Theta profit/loss". What do these terminologies mean? I've searched online but can't find a proper ...
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2 votes
1 answer
1k views

Variance of cash gamma (or dollar gamma)

Let us assume we are in the Black-Scholes model. Is there a closed formula for the variance of the cash-gamma? I define cash gamma as $CG = S_t^2 * \Gamma(t,S_t)$, assuming interest rates are 0 to ...
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10 votes
2 answers
1k views

Expectation of Gamma times S$^2$ in Black-Scholes model

Can somebody prove that: $$E[S_t^2 \times \Gamma(t,S_t)] = S_0^2 \times \Gamma(0,S_0)$$ where $S_t$ follows a lognormal process as in the Black-Scholes model, and Gamma is the second derivative $\...
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6 votes
2 answers
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Conceptual explanation of the relationship between gamma and vega plotted against delta for a European call option

I recently plotted Gamma and Vega against Delta for a European call option and found that the graphs look very similar. This makes sense to me mathematically since the two formulas are pretty much the ...
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