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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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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47 views

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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1answer
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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285 views

How accurate are Black-Scholes estimates of Vega, Volga, Vanna

Wikipedia provides analytical formulas for calculating Greeks. I can get Delta, Gamma, Theta all from Bloomberg. I need Vega, Volga, Vanna for my research. Should I use these analytical formulas for ...
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168 views

Vega with SVI Gatheral bumps

How would one go about computing a vega profile of an exotic derivative where the volatility surface is modeled using Gatheral's SVI parameterization? In particular, I am thinking about bumping each ...
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57 views

Positive Heston model theta

Under the Heston model, is there a concrete example where the theta $\frac{\partial C}{\partial t}>0$ where $C$ is the price of a European call?
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280 views

What is the vega profile of an up-and-out call option? And why is this important in structuring?

I had this question during an interview but I can't seem to find the answer on the internet.
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2k views

How to derive the Greek theta from Black-Scholes solution formula?

Which are the steps to compute the theta greek from the BS solution: $$c(t, x) = xN(d_+(T-t,x)) - K e ^{-r(T-t)}N(d_-(T-t,x))$$ with: $$ d_\pm (T-t, x) = \dfrac{1}{\sigma \sqrt{T-t}} \left[ \ln \...
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62 views

The interpretation of discounted Greeks

I understand that Delta measures the rate of change of the theoretical option value with respect to the change of the underlying asset price. This also represents the number of shares a call option ...
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328 views

Is the replication porfolio for a European Call, self financing for changes in time?

I was reading slide 29 here: http://people.hss.caltech.edu/~jlr/courses/BEM103/Readings/JWCh11.pdf (mirror) Sub-heading: "An interpretation of the Black-Scholes formula" It is saying that the below ...
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205 views

Adjoint Algorithmic Differentiation: swap pricing

I have tried to implement an AAD routine to price call options using the Black-Scholes formula, but my greeks are not quite agreeing with the expected ones, so I have decided to start with something a ...
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28 views

in long term options on equities, what is the greek used for security lending rate, and what formula do you use?

in long term options on equities, what is the greek used for for security lending rate, and what formula do you use? would it often move contrary to moves in risk free (ois) and so in practice is it ...
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336 views

Calculating Greeks for basket option

I am stuck with obtaining nice relative error of my analytical derivative of a function. I am comparing values of my function at points $x$ and $x+ \delta$ and the difference does not coincide with ...
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81 views

Delta of an option in two cases

Let C be the prime of a call in fi=unction of the price in term F, Strike K, volatilité $\sigma$ and maturity t: $C(F,K,\sigma,t,r) $ We assume that we know $\delta$ $\delta=\frac{\partial}{\...
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249 views

Computation of option vega under CEV

It is easy to define the option vega $\nu=\frac{\partial C}{\partial \sigma}$ under Black Scholes model since volatility is a single quantity. However, under CEV or local volaility model, it is ...
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3k views

Calculating Greeks using BinomialTree in Matlab [closed]

section 1. Calculating sensitivity of the price of derivatives American or European option using binomial tree model section 2. Calculating first order greeks the code compiles till this point ...
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1answer
95 views

How to manage risk on a call calendar when underlying is falling

Let us say I bough a call calendar spread. Now, at expiry of the short option, the underlying has decreased significantly, and I am approaching my max loss(i.e both the options are close to 0). In ...
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137 views

Straddle neutral strategy

What does it mean to implement a delta-neutral strategy for straddle ? A straddle consists in buying a call and a put simultaneously, at the same date, on same underlying, with same maturity and ...
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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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134 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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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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54 views

What's the formula to compute the divided difference approximation for the third order greeks?

I can't seem to find the quotient required to approximate the third order greeks Speed, Zomma, Color and Ultima
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1k views

Proof Black Scholes Theta

I saw the following proof of theta in a paper I read, and I thought it looked pretty neat. Unfortunately I don't understand the step that they do. This is what they do: Now, I don't get how they go ...
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91 views

option price change

I am trying to match change in European Call option price to greeks using the calculator here e.g. for S=95, K=100, r=0, V=25, t=5 and dividend=0, I get ...
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106 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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345 views

Implication of the Greeks under jump diffusion model

Consider jump diffusion model proposed by Merton and Kou. As far as i know, most paper only dealt the valuation of option under the jump diffusion model. As i expected, because of the ...
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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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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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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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42 views

Where can I find the formulas to compute the Greeks for European Call and Put Options Assuming no annual dividend yield?

Every formula I come across involves a $q$ (the annual dividend yield). Where Can I find the formulas to compute the greeks assuming no dividends?
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175 views

How is the performance measure computed here?

The image is from John C Hull Textbook titled Options, Futures and Other Derivatives ( page 407 - Ninth Edition). The table above was obtained after computing the delta of stock price, shares ...
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113 views

How to calculate the multi-asset class portfolio vega?

I am viewing a risk report of a hedge fund and the portfolio vega seems to be a plain summation of the vegas of the different asset classes the fund invests in (i.e. Equity, Credit etc) As far as I ...
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923 views

fx vanilla option's forward delta in single currency

According to Black formula , a vanila fx call option's pricing is $$C(F,\tau) = D[N(d_+)F - N(d_-)K]$$ , where $\tau$ is the time to expiry, $D =e^{-r\tau}$ the discount factor, $F=S/D$ the outright ...
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309 views

If you have a delta-hedged position and you're short gamma, why are spot price movements bad?

I simply can't wrap my head around the concept of Gamma. I've read multiple sites and explanations and for some reason can't wrap my head around the logic, so I feel that it'll really help for me to ...
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567 views

Finding the delta and gamma with historical data

I have a complicated product with knock-out barriers combined with other exotic options. I am curious if there is a fast and loose way to figure out the delta, gamma, rho, theta and possibly vega, ...
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3k views

From Delta to moneyness or strike

If I have volatility smile quoted with respect to the delta of an option on the forward, how can I convert this delta into the moneyness or strike of the option? Is there any bult-in function of ...
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754 views

Hedging and measuring repo rate risk

How is repo rate risk hedged? And is repo rate dv01 the usual greek for this? i am talking about repo risk in a derivative on a bond
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1k views

Calculation of option Greek (sensitiviety) theta via finite difference

I am able to get good approximations for delta, gamma, and rho via finite difference method, but not theta. I believe my issue is the value of h. Theta is basically the difference between the price ...
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1answer
290 views

Extracting IB market data: bid and ask for greeks and IV

I wrote a piece of code to get option chains with volatility and greeks from IB market data. After testing yesteday, it seems to work, but I am surprised of seeing bid and ask for impliedVolatility ...
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153 views

Interpretation of vega out of BS formula

I am comparing Monte Carlo estimates of VaR (using importance sampling) under both the normal and student distributions. I am also considering risk factors other than log-prices; in particular, ...
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141 views

In this scenario could gamma be higher for OTM options?

Let's say there is a $1 stock, with say 1 day to expiration. The 1.5 strike call, is probably a 0 delta at this point; however, a 1 point increase would mean the stock would be at trading at 2 dollars;...
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193 views

Why theta multipled by days to expiry exceeds the total time premium of the option

Sometimes, I find an option where the total time value of the option may be 5 cents(rest is intrinsic value) and there are about 15 days to expiry and theta is .08 (8 cents). How is this possible. If ...
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273 views

Option greeks: sensitivity to 1% move

In a Black&Scholes framework how can I compute the following sensitivities: to 1% move in the underlying price to 1% move in implied volatility I would like the greeks to tell me how many ...
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2answers
314 views

Suppose you bought a July ITM call and sold an August ATM put, am I net long or short?

Here is the full question, even though ive broken it down to the mini question above. Suppose you have bought a July ITM call and sold an August ATM put. What would be your delta in this position? ...
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99 views

how market makers set the time factor to calculate option greeks on the expiration day?

how market makers set the time factor to calculate option greeks on the expiration day? does they set time equal 1/24or 2/24 when only 1hour or 2hour left? what frequency market makers update new time ...
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537 views

Can one use the Greeks (delta,gamma,theta) to show that the Black-Scholes call formula satisfies the Black-Scholes PDE?

If so, is there a derivation anywhere that shows this? I was told that this could be done in a class but I don't see how it's possible.
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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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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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46 views

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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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 ...