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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87 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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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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35 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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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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65 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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86 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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71 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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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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91 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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137 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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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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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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131 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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50 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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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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Why is this investment strategy negative gamma?

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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103 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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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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88 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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How to calculate Greeks for leveraged Barrier options?

I am wondering how to calculate option Greeks for Down-and-out barrier Call options with leverage. The option characteristics are as follows. The buyer of the option pays a fraction of the spot price <...
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358 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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81 views

How to understand broken wing butterfly option strategies?

I feel very confused about the greeks analysis for the broken wing butterfly strategy. Let's say for the stock ABC, we enter into a such strategy: we long a put option with strike $k_1$ and another ...
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What are the formulas to compute the greeks of a gap option?

I'm having a problem to calculate the gap option greeks since there are 2 different exercise prices K1 and K2. Do you know the answer or where can I read about these particular greeks?
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148 views

How does a pricing model 'understand' the cost of hedging?

Suppose I am pricing a multi asset at the expiry payoff. Theoretically I define their joint distributions in the risk neutral measure, and price using expectation. However, how do I know that the ...
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Question about greeks and put options

I am trying to establish the relationship between put options and greeks through a general form problem. Suppose that there is a company that at market opening trades its shares at a price $p_1$.Now ...
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Can Call and Put Vega be different (for the same strike)

I'm calculating the volatility of an options market (description of market below) by fitting 2 functions: 1. fitting the on book call prices 2. fitting the on book put prices And I'm getting a ...
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Normal vs. Lognormal Greeks for Negative Rates Options

My understanding is that for some of the G10 currencies with negative rates (CHF, EUR), Swaption and Cap / Floor prices are quoted in terms of BOTH, normal and log-normal Vols. That in itself is not ...
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132 views

What is the source of gamma risk?

I have two quasi definitions or interpretations of gamma risk in the context of the BSM model (please correct me if these don't make sense): 1) it is the option's sensitivity to jumps in the ...
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207 views

Vega of binary option

I'm calculating the greeks for a hypothetical binary option, and I'm getting a symmetrical parabola for the vega's of both put and call options that are OTM, ATM, and ITM. Both of them dip into ...
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120 views

Calculate Third Order Greeks Options

Hope you're doing great! I'm struggling to develop the code for the Third Order Greeks. In all places I have searched, the development is missing. For example: But I don't know how to develop it, ...
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Back Scholes theta of the call at any time t

I 'm trying to get the theta of a Call in the classical Black Scholes model. We have (classical result with usual notations) : $$C_t = S_tN(d_1) - Ke^{r(T-t)}N(d_2)$$ When deriving according to time,...
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565 views

Problem with the concept of Dollar Gamma

I was reading up on variance swaps and encounter the notion of Dollar Gamma, which is defined as the change in dollar value of the Dollar Delta (Δ * S) for a 1% change in spot (S). The formula for ...
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137 views

How to manage theta, gamma, vega, and delta risk in options market making simulation

I'm just starting to learn how to trade options and as part of an algorithmic options market making simulation I have risk limits for the greeks (gamma, vega, delta, and theta). There are 9 strikes ...
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Implied volatility and greeks of options

When we are calculating deltas or vegas for different strikes should we use the underlying asset's volatility or should we use the implied volatility for the specific strikes at a fixed maturity? ...
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132 views

What is the delta of an at-the-money European call option with respect to volatility?

Question: What is the delta of an at-the-money European call option with respect to volatility? Note that $$\frac{\partial\Delta}{\partial\sigma} = N'(d_1) \frac{\partial d_1}{\partial\sigma} = N'(...
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Understanding Options strategies pros and cons

I have been trying to understand options and how to choose Strike prices and Expiration dates as well as the greeks, but I'm not sure I get it. I've ignored volatility or vega for now. From what I've ...
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Is gamma always positive for American call/put options under Black-Scholes framework?

Most reference I could find only consider European options, but I would like to know whether this also holds for American options in general (with continuous dividend yield and/or discrete dividends)?
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VIX OTM put options decrease value after sharp decrease of underlying

I was wondering about disentangling an effect I saw on the market yesterday. I saw nearly all OTM VIX put options with maturity date 15/04/2020 decrease in value while at the same time the VIX took a ...
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117 views

Monte carlo delta calculation for Worst/Best Of Option

I try to calculate the Delta for WO by finite difference. For example, $K = 1.$ $$ S_t = S_0 e^{(r - d_1 - \frac{\sigma_1^2}{2})t + \sigma_1 W_t^1} $$ $$ F_t = F_0 e^{(r - d_2 - \frac{\sigma_2^2}{...
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Greeks, European puts

I'm trying to solve this question but i have a lot of problems with it. European puts with maturity 6 months are written on an asset with current price $S_0=150.$ The annual interest rate is $r=16\%$ ...
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108 views

Proof that adding some quantity of stocks in a portfolio of option does not change the portfolio Gamma

I would like to proof mathematically and intuitively that adding some quantity of underlying to a portfolio of option does not change the overall gamma. Can you help me?
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152 views

Option PnL Attribution

I am trying to compute the pnl of an option where for the both days option greeks delta, gamma, vega, theta and stock price and IV is given. I know the option pnl will be the sum of delta pnl+ gamma ...
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107 views

Delta of an option which is approaching expiration when stock price decreases

The following is an interview question. It is 10 months since you sold a one-year European call option to a customer. You have been delta-hedging your exposure to the written call since it was sold....
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238 views

Black Scholes theta as function of time to maturity

I would like to understand why the Black and Scholes greek letter theta for european call option behave in the following way: as time to maturity is far away (right part of the x-axis in the the ...
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0 Delta on Forward starting Equity basket option

I wanted to confirm the inherent reasoning behind 0 delta on a weighted equity basket option. For instance, if we have a basket option with a forward starting initial fixing date, we can expect the ...
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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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theta for SPX options vs. E-mini future options

Interactive Brokers currently shows the following data for SPX options at strike 3000 and expiry 2020-09-17: calls: bid/ask 234.10/236.30, theta -0.362 puts: bid/ask 146.70/148.40, theta -0.225 Then ...
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computing theta of black normal model?

I've been trying to create a black normal model and have used http://janroman.dhis.org/finance/Swaptions/normal%20swaptions.pdf as a guide. I am trying to validate the theta formula in this paper - ...

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