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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34
votes
6answers
28k views

What type of investor is willing to be short gamma?

As far as I understand, most investors are willing to buy options (puts and calls) in order to limit their exposure to the market in case it moves against them. This is due to the fact that they are ...
25
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4answers
1k views

Who has introduced the term 'vega' and why?

The sensitivity of the option value $V$ to volatility $\sigma$ (a.k.a. vega) is different from the other greeks. It is a derivative with respect to a parameter and not a variable. To quote from Paul ...
22
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3answers
3k views

When do Finite Element method provide considerable advantage over Finite Differences for option pricing?

I'm looking for concrete examples where a Finite Element method (FEM) provides a considerable advantages (e.g. in convergence rate, accuracy, stability, etc.) over the Finite Difference method (FDM) ...
21
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7answers
17k views

What is the “delta” option quoting convention about?

At my work I often see option prices or vols quoted against deltas rather than against strikes. For example for March 2013 Zinc options I might see 5 quotes available for deltas as follows: ...
16
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5answers
7k views

How to get greeks using Monte-Carlo for arbitrary option?

Let's assume I have an arbitrary option that I can price using Monte-Carlo simulation. What is the general approach (i.e. without relying on specific option type) to calculating the greeks in this ...
16
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3answers
5k views

How can one compute the Greeks on VIX Futures

I am guessing the short answer to this question is "use the chain rule and linearity of the derivative," but I am looking for more specific advice on how to compute the derivatives of a VIX futures ...
14
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1answer
923 views

How much can be said about the Greeks without picking a model?

Let $C(S, K, \sigma, r, T)$ be the price of a call option. How much can be said about the Greeks without picking a model? Or at least without full Black-Scholes? Below, I write down everything I know ...
13
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2answers
815 views

The greeks: where do they come from?

I’m studying the BSM model and having a look at the greeks. I was reading Derivatives, by Paul Wilmott, and he gives the closed form solutions without making the reader see where these solutions come ...
12
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1answer
2k views

How do different models impact option Greeks?

If I trade an option using delta, vega, Prob OTM, etc. these are derived from a model. How do leading models impact valuations in terms of the Greeks? I suppose to form a baseline it would have to be ...
11
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3answers
1k views

Which greeks do you need to hedge if you want to implement an implied-volatility security?

Assume you want to create a security which replicates the implied volatility of the market, that is when $\sigma$ goes up, the value of the security $X$. The method you could use is to buy call ...
10
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2answers
19k views

How to numerically obtain delta?

The delta in option pricing, also called the hedge ratio, is expressed as the sensitivity of the option price to the underlying price change. The analytical solution for the most common option ...
10
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6answers
6k views

Vanna - any practical uses for risk or pnl attribution purposes?

What is the practical use for Vanna in trading? How can it be used for a PnL attribution?
8
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1answer
18k views

What does it mean to be long gamma?

When you are "long gamma", your position will become "longer" as the price of the underlying asset increases and "shorter" as the underlying price decreases. source: http://www....
8
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3answers
3k views

Variance swap replication and variance vega

Noob here. I've been trying to gain a better understanding of variance swaps and what better way than to replicate it with a portfolio of better understood instruments. I have read the GS 1999 ...
8
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2answers
2k views

How to estimate the greeks with a Monte Carlo simulation?

I am simulating the path of three indices to price a 1 year basket option. All the indices are domestic, so there is no currency component. At each time step I am using the local volatility ...
7
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4answers
7k views

What is the intuitive reason why the Gamma and the Theta tend to have the opposite sign?

Quoting Hull's book: When gamma is positive, theta tends to be negative. The portfolio declines in value if there is no change in S, but increases in value if there is a large positive or ...
6
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2answers
787 views

Mathematical underpinnings of the square root of time rule

Often when I am reading about options pricing (and/or options greeks) the square root of time continually comes up. What the mathematical justification for why this keeps on turning up?
6
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1answer
7k views

Link between Vega and Gamma

"The vega is the integral of the gamma profits ( ie expected gamma rebalancing P/L) over the duration of the option at one volatility minus the same integral at a different volatility...Mathematically,...
6
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1answer
377 views

How does Algorithmic Differentiation work and where can it be applied?

The title says it all, but let me expand on it. Algorithmic differentiation seems to be a method that allows a program / compiler to determine what the derivative is of a function. I imagine it's a ...
6
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1answer
1k views

Can I add the greeks of individual postions to obtain greeks for the portfolio

I understand that the delta of an option portfolio is just the sum of the deltas of the individual option positions. What about the other Greeks like gamma and vega? Do the vega and gamma of a ...
5
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3answers
3k views

Why gamma for ATM option decreases as volatility increases

Why is the gamma for an at the money option less when volatility increases. Intuitively ,I thought that increasing volatility means more uncertainty,hence the option price will be more sensitive to ...
5
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2answers
562 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 ...
5
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2answers
436 views

Does higher vega imply higher IV and vice versa

If an option A has higher vega than option B, does that also mean that A has a higher IV than B? I understand that by definition, a higher vega means that A's price is more sensitive to its IV than B. ...
5
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3answers
11k views

What is the relationship between Time-To-Expiry and Delta?

Is there any regular relationship between Delta and the Time-To-Expiry of an option? I have observed that options that expiry sooner are more sensitive to underlying movements (with equal strikes). ...
5
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1answer
5k views

derive vega for black schole call from this formula?

Is it possible to get the right formula for vega of a call option under the black scholes model from this formula? $$\frac{\partial{C}}{\partial{\sigma}}=\frac{S_0}{\sqrt{2\pi}}{e^\frac{-d_+^2}{2}}(\...
5
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2answers
1k views

is there an analytical proof that vega-neutral also provides (gamma & theta) neutral?

I've read an answer here that say if your security has vega, then it has gamma and theta. is there an analytical proof that vega-neutral also provides (gamma & theta) neutral?
5
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2answers
621 views

How to quickly sketch a second order greek profile for a vanilla position?

Assume that you are given an arbitrary payoff profile for European vanilla position (e.g. butterfly). How to make a back of the envelope sketch of a second order greek profile for it (i.e. plot ...
5
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2answers
1k views

Why is the Vega positive?

We know that in the Black-Scholes model, the Vega of a European call option is always positive. This can be proved easily, so my question is not really about the result per se. My problem is that I ...
5
votes
2answers
5k views

Equity option portfolio greeks with underlying

I'm curious about how to construct the five basic greeks for an equity option portfolio when there are shares of the underlying in the portfolio. For example, a portfolio of 100 call options and 100 ...
5
votes
1answer
151 views

evaluation of option pricing models based on Greeks empirical hedging effectiveness

I’ve studied many different pricing models (B&S, Vasicek, CIR, Merton jump, Heston, ecc), each of them gives as output a different price and different values for the Greeks. So, for example, if ...
5
votes
1answer
797 views

How to interpret this CDS spread sensitivity pattern?

From page 27, Table 6: Why are sensitivities of CDS slightly negative before the maturity of the CDS? I do not get the intuition: if I am long a 5-year CDS, the spreads <5y increase, and the 5y ...
5
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2answers
2k views

Is there any gamma in basis (i.e., floating for floating) interest rates swaps?

It is well known that vanilla fixed for floating swaps usually have a bit of gamma, but does a floating for floating (basis) swap have any? For the sake of simplicity, let's assume that both legs of ...
5
votes
0answers
785 views

Greeks of a Basket Option

I want to estimate delta, vega and gamma for a basket option. This option is a European Call option. The underlying is $S=\omega_1 S_1 +\omega_2 S_2$ Where: $S1$ = stock price of asset 1 $S2$ = ...
4
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2answers
3k views

American Options relation between greeks

Considering an American option in a Black-Scholes model, is there a relation between Vega and Gamma as it holds in the European case? I am aware an exact relation would be difficult to find. But in ...
4
votes
2answers
680 views

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 ...
4
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2answers
322 views

How do I calculate the probability of a short option position expiring worthless?

I want to be able to determine the probability of a short option position (call or put) expiring worthless. Don't know where to start but I see probabilities derived from the greeks on some web sites?...
4
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6answers
2k views

Intuitively speaking, why do at the money options have no volga/convexity?

I was wondering if someone could give me an intuitive explanation as to why the vega of at the money options doesn't increase with volatility. I've seen some mathematical explanations showing the ...
4
votes
3answers
758 views

Can I get Black-Scholes option price from greeks?

I am unpleased with current Interactive Brokers risk graph for option strategies, so I'm planning on writing an application myself to plot it. My initial idea is to get the option greek values from ...
4
votes
2answers
3k views

Why gamma and theta have opposite signs?

I saw some textbooks use B-S equation to explain why gamma and theta have opposite signs in most of the cases. For example, John Hull's classic book. The explanation is, first write B-S equation in ...
4
votes
2answers
2k views

Multi asset option portfolio risk management (greeks and FX exposure)

I am running an options book containing listed options across multiple products. I trade mostly equity and index related options - with a preference for European expiration products. I trade products ...
4
votes
2answers
307 views

Greeks and Option Premium

If a linear sum of options is constructed such that the premium payout is zero, then does it mean that resultant greeks of the cumulated options positions will be nearly zero. For simplicity, lets ...
4
votes
1answer
652 views

Standard Deviations out the money where options will respond to underlying asset price changes

Is there an understood way of determining how far out the money an option can be, before it starts/stops responding to the underlying asset price changes? I usually look at the greeks, gamma, delta, ...
4
votes
1answer
123 views

Option pricing: Relationship between Theta and early exercise

I am confused about the following: For a European put option, the parameter $\Theta$ is given by $$ \Theta= \frac{d V}{dt} = -\frac{SN'(d_1) \sigma}{2 \sqrt{T-t}} + rK e^{-r(T-t)}N(-d_2).$$ My ...
4
votes
1answer
694 views

MTM Hedging Performance of Vanna-Volga

I was wondering how well Vanna-Volga (VV) Implied Vols "perform". So I experimented with the following option parameters $$S_0=100,\ K=92,\ r=0.03,\ q=0.01,\ T=2$$ and VV parameters $$K_1,K_2,K_3=...
4
votes
1answer
255 views

Why do options market makers make their spread as wide as the corresponding vega?

I've heard that option market makers make their bid ask spread as wide as the vega of the contract they are quoting. If the quoted spread is narrower than the vega of the option it is said that the ...
4
votes
1answer
3k views

Gamma Imbalance Explanation

Can someone please give me an explanation as to what put-call gamma imbalance specifically refers to (imbalance of what?), and why they may exacerbate volatility from a market perspective, and why the ...
3
votes
2answers
243 views

How to adjust delta hedging if stock price decreases?

Question: You are long a call option no MITCO stock. You have delta hedged your position. You hear on the radio that the CEO of MITCO has just been arrested for running a massive Ponzi scheme. The ...
3
votes
3answers
544 views

Derivation of BS PDE problem using Delta hedging

I've always been confused with Delta hedging. It is well-known that for a (smooth enough) function of $(S,t)$ we have, due to Ito's lemma, that: \begin{eqnarray*} dC = \left(\frac{\partial C}{\partial ...
3
votes
2answers
1k views

Gamma/delta dynamics in the Black Scholes model and it's relation to PnL (Basic of option theory)

If we are in a Black Scholes setup and a I have a Call option and hedged it by shorting delta amount of its underlying. What does the second derivative of the call with respect to Price of the ...
3
votes
3answers
215 views

Explain that gamma is positive for standard call and put options without using heavy mathematics

Gamma is positive for any standard put and call options seems like a standard fact. A proof can be found in this post. However, the answer provided in that post involves heavy mathematics. Is ...

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