# Tag Info

12

Gamma is the second partial derivative of the change in the price of the option wrt to the change in the underlying. Said another way, it is the change in delta. If you write down the Black-Scholes pricing formula, you's see the gamma term: $$...\frac{1}{2}\frac{\partial^2C}{\partial C^2}(\Delta S)^2...$$ Notice that the $\Delta S$ (change in stock price) ...

11

I might be misunderstanding your question. My thoughts: being short gamma is being long volatility your comment re gamma increasing regardless of direction only holds for ATM options. For ITM options, being short gamma is being long the underlying. For OTM options, being short gamma is being short the underlying. Some graphs: Below, except as ...

9

Delta is the partial derivative of the value of the option with respect to the value of the underlying asset. An option with a delta of 0.5 (here listed as +50 points) goes up \$0.50 if the underlying asset goes up \$1.00. Or goes down \$0.50 if the underlying asset goes down \$1.00. Keep in mind that delta is an instantaneous derivative, so the value will ...

8

You need to compute your greeks as finite differences, but the full procedure may be pretty tricky. I will use vega $\aleph$ as the example here. Let's begin by designating your Monte Carlo estimator as a function $V(\sigma,s,M)$ where $\sigma$ is the volatility as usual, $s$ is the seed to your random number generator, and $M$ is the sample count. To ...

8

Being short gamma simply means that you are short options regardless of whether they are puts or calls. The most common type of investor that is willing to be short gamma is someone who sells options, also known as a premium collector. These investors commonly use strategies such as short puts, covered calls, iron condors, vertical credit spreads, and a ...

8

This is in fact a tricky matter. As you say one way is to calculate delta by an analytic formula, i.e. calculate the first derivative of the option pricing formula you are using with respect to the underlying's spot price. The second way is to do it numerically, i.e. change the spot price by a small value $dS$, calculate the value of the option and then ...

7

Pretty much irrelevant for vanilla markets but really cannot be ignored when pricing exotics such as barriers. Basically, if you do not hedge vega you are likely to sell lots of cheap exotics. Webb discusses the practical relevance of vanna and vomma in "The Sensitivity of Vega" (Derivatives Strategy, November (1999), pp. 16 - 19).

6

I dusted off my oldest option theory books and searched the indexes for "vega". The oldest reference I found was in Option Volatility and Pricing Strategies (1st ed.) by Sheldon Natenberg, copyright 1988. When discussing the sensitivity of prices to volatility (p. 132), he says, [T]here is no single commonly accepted term for this number. It is ...

6

I handle volatility curves where moneyness is quoted in delta by an iterative guess: Use an initial guess for delta of 0.5 (call)/-0.5 (put) Look up the volatility on the curve using the guess for delta Calculate delta for the option using the vol found in 2. Repeat using Newton-Raphson, until the difference in delta is small enough.

6

Short gamma is a bet on volatility (expressed as hedging costs) not getting too large. The key concept here is that you get paid to be short gamma. Consider that any option is sold for a bit more more than its intrinsic value (the extra bit is often called volatility value.). If nothing moves, then the option ultimately expires precisely at intrinsic ...

5

For non-interest rate derivatives with not-so-long maturities worrying about rho is uncommon. Think about it: interest-rates do not change that often relative to options expiring next week, next month or at most next year. LEAPS are obviously another turf. You could think about gamma, but the intimate relation of gamma and vega (at least in BS model) makes ...

5

You are absolutely right to point out that most proactive participants in options markets prefer to be long gamma, and it is typically reactive market makers who take the opposite side of their trades. While the typical options trader (I find it difficult to call anyone trading options an "investor") does not hedge his position, market makers will attempt ...

5

FDMs represent PDEs over a simple grid shape; the different implementations are just different recurrence relations to approximate the solutions to the PDE between boundary values (e.g., for options pricing, $T=[t_\mathrm{now},t_\mathrm{maturity}]$ and $S=[\mathrm{deep\_itm},\mathrm{deep\_otm}])$. FEM is a general name for a lot of different ...

5

As far as PDEs (deterministic) are concerned we have the notion of a "strong solution" (directly solving the differential operator in the strong formulation of the problem) and the "weak solution" that deals with a weak formulation of the problem. For the strong formulation, finite differences are the way to go since they are the natural discretization of ...

4

If you get paid enough theta it absolutely makes sense to be short gamma. And the closer to expiration, the faster the time-value flees. Most of the time, most people would prefer to be gamma long though. It's simply a safer bet because of uncertainty: unexpected events can seriously damage your book if you're short vol.

4

Short gamma is being of the view that realized volatility would be less than the implied volatility for the period in which an option is valid. So if you think realized volatility in the future would be consistently lesser than implied volatility at present, then you'd be short gamma. The premium one would receive by selling an option (call or put) is a ...

4

I have no reference, but it's largely phonetic. Must variables in econ/finance are Greek versions English letter you'd want to use. $\omega$ for weight, $\rho$ for rate, $\epsilon$ for error, and so. Vega is partial derivative of price with respect to V olatility. But there's no Greek letter for V. Vega sounds kind of Greek.

4

VIX is calculated from a basket of SPX options, and VIX futures expire into following expiration, e.g. September VIX futures that will expire next Wednesday will use SPX October options chain to calculate settlement value. If $B$ is the value of the basket then VIX value at expiration is $\sqrt{ B }$. Then VIX futures price is the expectation of the basket ...

4

Short Answer : Futures don't have Greeks Long Answer : Assuming a non strictly mathematical (i.e. false) point of view. Well, having Greeks on VIX Futures is not relevant, VIX value is itself a "Greek" (and Futures don't have Greeks). Sensitivity to Price of the Underlying : Insensitive (ν = 0) Volatility of the Underlying : Delta Δ = 1 (to Volatility ...

4

If your "European vanilla options" are restricted to piece-wise linear pay-offs, then the following may help: Remark: I assume you are looking for a rule of thumb to get the profiles without the use of a computer. All piece-wise linear pay-offs can be decomposed into a sum of digital options and call options with different notional (possibly negative) and ...

3

I somewhat disagree (partially) with the other answers so I offer my own. First, most importantly is that you specify exactly what underlying asset you really talk about. Even for non-interest bearing assets an unhedged rho can sometimes have devastating results on your profitability. Imagine a stock denominated in a highly inflated currency. If you buy ...

3

The most general answer is to shift your input to approximate the first derivative. Given that you need Monte Carlo to price this, it may get expensive. But that's the way it goes as when you have no analytical solutions as there aint't no free lunch ...

3

No, there is not. If you are willing to assume the stock price stays constant between now and then, you could do so using the standard formula.

3

At a high level, just look at the delta. If it's so close to zero that it won't shift the price of the option by a penny, then you could say, "the option no long responds to the price of the underlying" Any price it has more or less a function of theta and vega only. In practice however, depending on the model you use, delta has some volatility input. To ...

3

Quoting prices in delta makes it easier for a trader to delta hedge their portfolio. (The trader knows teh delta they are trying to add or cut, so the price quoted in delta gives them the contract qty that they need to trade quickly, without needing a calculator, let alone a pricing model)

3

The question may be motivated by the way closing implied volatilities are reported for LME traded third wednesday prompt metals contracts. Function LMIV on Bloomberg provides vol quotes for 50 delta options and corresponding premiums/discounts for 10, 25 delta puts and calls. LME metals futures are really forward contracts with constant maturity forwards ...

3

It might not work the way you think. Note first that nobody sells options for free so at least one of your integers ($a,b,c$) is negative, meaning you will have nonzero risk of losing money on your short option leg. More specifically, let's pretend $b \geq |c|$. Then since the value of a forward contract is the same as the call minus the put plus strike ...

2

I'm going to disagree with richardh here, since it seems unusual to quote options with 10% delta. Instead, I think "+25 POINTS" means an option whose strike price is 25 points above zinc's current March 2013 futures price (not zinc's current spot price). In other words, an option that's 25 points out of the money (I'm assuming these are calls). Quoting ...

2

Commonly used on FX option markets, see wikipedia

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