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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12 views

Hand coded algorithm for tangent algorithmic differentiation

I'm looking for a way to hand code the algorithm for the forward/tangent mode of algorithmic differentiation to calculate option Greeks with Monte Carlo simulations. The computational power is very ...
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93 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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639 views

Classic dynamic delta-gamma hedging in Python

I am trying to run a delta-gamma hedge for a Black-Scholes model in Python.The Euler disceretizatioin of the paths is the simplest possible. I wrote the code below but the PnL looks undesirable and ...
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78 views

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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132 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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Greeks Profile for Barrier Options

This may be a very basic question, but can someone help me with the Greek's profiles for Barrier Options. I am looking for Pictorial representations of Simple Barrier Option greeks(KI,KO). Thanks ...
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154 views

Cega - Correlation Delta from multi-asset derivative

I want to calculate the Cega, i.e. correlation delta, for a multi-asset derivative numerically (the difference of the price from a tiny move in correlation). However, I found it is difficult to follow ...
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37 views

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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1answer
103 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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62 views

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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78 views

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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112 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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67 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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87 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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167 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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68 views

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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105 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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202 views

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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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 ...
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94 views

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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78 views

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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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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108 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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261 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 ...
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90 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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353 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?...
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3answers
593 views

How does Rho behaves with moneyness of option?

I was trying to find the relationship between nature of Rho and moneyness of the option. After finding certain values I found that Rho Value keep increases as the option gets further in the money. ...
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133 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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574 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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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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273 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 ...
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Volatility spread of Strangle

It's written in a book by Giles Hewitt : " The bid-offer spread quoted on a Strangle in volatility terms will usually be wider than the ATM spread to the same maturity because strikes away from the ...
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Delta Hedging Example

I was reading Dynamic Hedging by N. Taleb and in the chapter dedicated to the delta, there is this example of a trader position in options (one-month European call, flat yield curve, forward is ...
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some questions about pricing an asset or nothing put option with a strike price equal to St

I am working on a homework exercise where the aim is to price an asset or nothing put with K = St, offcourse the normal formula could be used St * N(-d1), but I was wondering if pricing the asset by ...
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Smile Strangle and Market Strangle

What is the difference between Smile Strangle margin and Market Strangle Margin in fx derivative market? Is it just variation in convention or is there any mathematical relationship between the two?
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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 ...
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What is the name (Greek) for sensitivity of an option's Theta to the Time to maturity?

All other second order sensitivities of option prices to underlying price, volatility and time, seem to have a commonly accepted names: Gamma, Vanna, Charm, Vomma/Volga, Veta as documented here (...
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How to shock the IV surface w.r.t VIX and keep AOA

I have to compute the sensitivity of a set of option prices on a single sotck (range of tenor is over the whole surface) to an increase of 100% in the VIX.. and I am trying to get to the most ...
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249 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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113 views

Compute Vega and Delta in R

I am trying to compute greeks for a large sample of CEO compensation contracts in R. However, my vega computations all result in a value of zero. In doing so, I follow Core and Guay [2002]: Here is ...
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Can someone provide a good definitive explanation for rho in relation to option risks?

I have a pretty good understanding of option risks except for one thing, rho. Unfortunately, interest rates tend to have a small effect on option prices, and thus most literature tend to just gloss ...
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86 views

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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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 ...
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274 views

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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152 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 ...
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210 views

Do Perpetual American Options have closed form functions to compute the Greeks?

I was wondering if there were analytical formulas to compute delta or gamma for perpetual American options?

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