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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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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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Looking for a Book

I hope everyone is well. While I was looking for derivations of Greeks I came across part of a book. Could you help me to find its name please ? Here is the link: http://centerforpbbefr.rutgers.edu/...
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Conceptual explanation of the relationship between gamma and vega plotted against delta for a European call option

I recently plotted Gamma and Vega against Delta for a European call option and found that the graphs look very similar. This makes sense to me mathematically since the two formulas are pretty much the ...
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Greeks and options hedging

Why is it that theta is sometimes taken as the proxy for gamma of the underlying asset in options hedging?
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Could option gamma be larger than option nominal value? [duplicate]

Assume FX Option giving a right to buy/sell some notional value in currency. Could it's gamma be larger than its notional value? Gamma achieves its maximum value at maturity. How can I rigorously ...
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323 views

why gamma decreases when option is deep in the money? [closed]

Gamma decreases when a call option goes either deeper in, or deeper out of the money. That is due the demand for the call option. I can imagine the demand for the option would decrease as it goes ...
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How to compute gamma for at-the-money regular calls and puts when they approach expiration to avoid explosion of portfolio's gamma?

When and at-the-money regular call or put approaches expiration, gamma tends to infinity. However, for practical purposes, there is only a finite change in delta. The problem is that if any of the ...
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1answer
75 views

For equity options, does the implied vol change if the price of the underlying does?

For example, consider S&P options. My reasoning is rooted in the fact that VIX returns and S&P returns have a negative relationship, since VIX is a measure of S&P options' implied vol. ...
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107 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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220 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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143 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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207 views

Why do we need to calibrate vega?

I was going through some paid video on options. The tutor in the video asked the following question: Person $A$ has the following portfolio at the start of April Portfolio of options with vega $20,...
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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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70 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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381 views

Option greeks as dollar P&L

If I write the value of an option as O(S, K, T, V), where S is the underlying price, K is the strike, T is the time to expiry and V the implied volatility, how can I compute the dollar amount that I ...
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Impact analysis of parameters in the 2 Factor Hull White Model

Through the 2-Factor-Hull White Model you can model the yield curve if you have the parameters $a, b, \sigma, \eta$ given. Is there any way to measure the impact of these parameters on the yield ...
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558 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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1answer
828 views

Option Greeks' Formulas for Black & Scholes vs Black 76

I know Black76 uses forward prices instead of spot and that D1 calculation doesn't use the interest rate. Are there any other differences between the two? I'm calculating: theoretical value, delta, ...
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319 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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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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73 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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247 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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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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117 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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177 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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292 views

Black Scholes Theta Finite difference

I am trying to obtain the Theta from Closed Formula by using Finite Difference methods and I observe some discrepancies. For instance, here with the following parameters: Spot:50, Strike:50, Rate: 0....
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170 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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1answer
394 views

MTM Hedging Performance of Vanna-Volga

I was wondering how well Vanna-Volga (VV) Implied Vols "perform". So I experimented with the following option parameters $$S_0=100,\ K=92,\ r=0.03,\ q=0.01,\ T=2$$ and VV parameters $$K_1,K_2,K_3=...
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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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2answers
602 views

Gamma/delta dynamics in the Black Scholes model and it's relation to PnL (Basic of option theory)

If we are in a Black Scholes setup and a I have a Call option and hedged it by shorting delta amount of its underlying. What does the second derivative of the call with respect to Price of the ...
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58 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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522 views

Which barrier option has negative gamma?

As said in my book, there exists a kind of barrier option which has negative gamma. I tried the knock in and knock out option, their gamma are positive. Could anyone provide an example where a barrier ...
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193 views

Floating Strike Lookback Delta Risk

I'm running through some delta hedging simulations of floating strike lookback call options (that is, I'm short the options) during a volatile (downside) period for the underlying and some very odd ...
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176 views

Can we 'predict' the delta of a stock? The delta of a stock is $\pm 1$ right? [closed]

“A stock is like a living organism. A sparrow, say. And we are able to create an emergent-based abstraction of that sparrow, which closely approximates the sparrow itself, accounting for migration ...
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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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American Options relation between greeks

Considering an American option in a Black-Scholes model, is there a relation between Vega and Gamma as it holds in the European case? I am aware an exact relation would be difficult to find. But in ...
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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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5k views

What is the intuitive reason why the Gamma and the Theta tend to have the opposite sign?

Quoting Hull's book: When gamma is positive, theta tends to be negative. The portfolio declines in value if there is no change in S, but increases in value if there is a large positive or ...
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Attempt of an analytical proof that a call price decreases as its strike increases

I'm stuck trying to analytically prove that a partial derivative of a specific, lower defined function $C$ is negative. The context of this problem is actually a Black-Scholes market situation, where ...
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1k views

Delta Hedging with fixed Implied Volatility to get rid of vega?

I'm wondering if i should use a floating IV or a fixed IV to delta hedge my options every day. I've read this post but would like different information : Delta Hedging with fixed Implied Volatility ...
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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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175 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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398 views

How to validate option greeks/implied volatility data calculated in-house using Black model on a mass scale in an automated fashion?

I have created a platform that computes implied volatility, option theo prices and greeks using Black 1976 model. I use this platform to calculate above mentioned numbers for a variety of options ...
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108 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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1k views

Delta on Bond Future Options

When talking about Options on Bond Future on CME (American options), we have 2 definitions of Delta and Gamma. One is 'Price Delta/Gamma' and one is 'Interest Rate Delta/Gamma'. My understanding is ...
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Derivation of BS PDE problem using Delta hedging

I've always been confused with Delta hedging. It is well-known that for a (smooth enough) function of $(S,t)$ we have, due to Ito's lemma, that: \begin{eqnarray*} dC = \left(\frac{\partial C}{\partial ...
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Estimate Options Delta By Hand [duplicate]

Underlying = 100 K = 90 1 year Put at K is trading 5. What's the approximate delta of the put?
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343 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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2k 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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1answer
242 views

Gamma of a Lookback Option

From this book, http://docs.finance.free.fr/Options/Exotic_Options_Trading.pdf, it states that The gamma profile of a Max lookback option becomes intuitive when viewing it as a ladder option. ...