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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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 $S2$ = ...
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63 views

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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411 views

Derivation of the Pnl of a Delta Hedged Straddle and Risk Reversal

In the link below, in the text it states the following equations: Delta-hedged straddle P&L = Volatility Risk-premium ×| Straddle Vega | and Delta-hedged risk-reversal P&L: ...
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717 views

Greeks for a portfolio? PnL for gamma trading

I am a little bit confusded with respect to the PnL of a delta-neutral portfolio. We have $$d\Pi = \Theta dt + \frac{1}{2} \Gamma \Delta S^2$$ So, if our portfolio consists of 1 call options, and ...
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83 views

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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131 views

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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1answer
521 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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117 views

Theta from Black-Scholes PDE - is it possible to use implied volatility?

There is a need to derive theta $\theta$ of an option out of standard Black-Scholes PDE. In usual notation ($P$ - price of an option, $S$ - underlying spot): $\theta=r_dP−Sr_d\delta−\frac{1}{2}\...
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74 views

Computing Malliavin Derivative for European Call Payoff

Let $X_t$ be a continuous local-martingale modeling the stock price given by $$ X_t = \int_0^t \sigma_t(T,K)dW_t , $$ and $\sigma_t(T,K)$ is an $L^2$-measurable process not adapted to $W_t$'s ...
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171 views

Relative Value Trading of American Style Options on Futures, Calcuating hedging ratios?

I am interested in Relative Value Trading of American style options on futures and have not found a whole lot of literature on it. The best resource I have discovered so far is a few pages in Colin ...
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320 views

Trying to understand the sign of Theta

I guess this a pretty easy question to answer, but I'm not able to get the intuition despite reading the concept a couple of times. So, the Greek Theta is almost always negative, except for when an ...
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199 views

What is the highest frequency greek for options on futures on bonds?

I'm considering exchange traded options of futures on bonds. Options on bond futures are usually American, thus the Black model is out of question. Which is the most imporatant Greek with respect to ...
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306 views

Under what circumstances Veta is positive?

In general, as the option moves towards expiry, its vega is decreasing. Are there circumstances where the veta, i.e. the sensitivity of vega with respect to time, is positive, that is when vega is ...
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36 views

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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1answer
80 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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57 views

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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273 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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164 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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56 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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266 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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317 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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201 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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328 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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246 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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136 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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45 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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87 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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38 views

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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42 views

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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102 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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45 views

FX Options Greeks: Is there a meaning in converting the sensitivities values in different currencies?

Suppose you have a Call on JPY, domestic currency is USD The price will be in USD Let's say delta = 0.93 Does it make sense for any reporting reasons to convert this value into JPY ? What is even the ...
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95 views

Kirk Spread Approximation, Greeks by Finite Difference

I am using finite difference on Kirk's Approximation for Spread Options to estimate greeks of the Spread Option. Now this is creating an problem in the estimation of gamma. For at the money options (...
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142 views

Different scaling conventions for greeks

I have been following this tutorial (http://gouthamanbalaraman.com/blog/value-options-commodity-futures-black-formula-quantlib-python.html). It says in the conclusion and I quote:It is worth pointing ...
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181 views

Higher Vega with ATM options when Spot is higher

Which would have larger vega, an ATM call option at spot 100 or an ATM call option at spot 200. Apparently the answer is the one with ATM at spot 200. I am not sure how you get this answer. Why ...
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130 views

How to consider open interest & volume change in option pricing?

Is there publically available option pricing model or theory that considers open interest/volume % change? I believe that laws of supply and demand effect options like any tradable good. However, I ...
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339 views

Ideas for speeding up greek calculations

My current calculations using the vollib library averages 0.5 seconds. Is there any way to get it faster? Any tips/best practice notes will be helpful. This is for a scripting language such as python....