# Questions tagged [delta]

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### Delta heding & PnL

Sorry if it's a duplicate but i didn't find an answer to my simple question in the other posts. Let say we short a call option on a stock. $K = 100$, $C = 1$, $S = 100$ and $\Delta = 0.5$. No ...
59 views

### Calculating Delta of option portfolio using average of inputs

Trying to think through two options portfolio scenarios, which are highly similar. I'm wondering if you can take a portfolio of options, all written against the same underlying product, and use ...
68 views

### Adjusting your delta hedge when the stock crashes and were originally delta hedged

You are long a call option on a stock and you are delta hedged. The stock crashes in price. How do you adjust your delta, do you buy or sell stock? Could answers please be quantitative (i am getting ...
147 views

### Is the vega of a portfolio of a long 0.5 delta and short two 0.25 delta calls positive or negative?

More specifically what I am trying to find out is whether the following relationship is always true or not. Same underlying for the calls, assume the most simplistic assumptions (interest rate = ...
201 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 ...
44 views

### Hedging option delta

Let's say I am long 1000 50 delta call options. I need to hedge my deltas now. There can be infinite ways to do this. How should I think about proceeding wit this? My first thought was, if the ...
134 views

Please explain the concept of premium Adjusted Delta in FX market. In EURUSD, why delta changes if premium currency is changed from USD to EUR and how this new delta is related to the old one with ...
39 views

### Black-Scholes delta of a barrier (knock-out or knock-in) option

I'm trying to calculate the Black-Scholes delta of a barrier option given the following information: Whether it is knock-out or knock-in Barrier price Strike price, $X$ Current stock price, $S$ ...
391 views

### Possibility of delta greater than 1 [closed]

Can delta of an option be greater than 1? Please illustrate it with an example.
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### Stochastic Volatility and Sticky Delta

"Stochastic volatility models can be thought of as sticky delta model. And Local volatility model as sticky Strike." Please help me understand how the author has reached this conclusion.
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### About Dual Delta of FX option in the paper: FX volatility smile construction by Dimitri Reiswich & Uwe Wystup

In the paper: FX volatility smile construction by Dimitri Reiswich & Uwe Wystup. It mentions the computation of premium-adjusted spot delta as follows (Page 6): As a beginner of FX option, I ...
128 views

### Derivation of Call Delta from Black Scholes Model

How is call delta mathematically derived from Black Scholes Model (without approximation) ? Please help me understand each step mathematically. And how it is approximated to say that delta is the ...
322 views

### Portfolio Delta - long call, long put and short call

First and foremost, I'm trying to understand why you would construct a portfolio made up of long calls, long puts and short calls. I find this really abstract and confusing. I've tried drawing the pay-...
17k views

### Are Futures exactly Delta One?

Delta of Future is exactly one I thought. This post here, says otherwise. However, quoting John Hull again: $$f = \text{Value of Future contract} = S_{t=0} - K \exp(-rT)$$ where $S$ it the spot ...
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### Pnl explain using adjusted SABR delta

When looking at SABR, the starting point for a swaption's delta is the usual: $\Delta = \partial V/\partial F$ However, since we have expressed our volatility $\sigma$ as a function of our ...
44 views

### How is $\phi_t = \Delta_t$ in the martingale approach to pricing under Black-Scholes?

In the martingale approach to derivative pricing, we show that there exists a replicating strategy $(\phi_t, \psi_t)$ which mimics the derivative payoff. My textbook then goes on to state that it is ...
80 views

### Black Sholes option pricing with all but Delta [closed]

I'm trying to setup a little option pricing model in excel. I have all the information for the inputs (interest rate, IVs for different deltas, time to expiry, strike price, underlying price) but what ...
68 views

### FX Spot Delta market standard calculation (Trader View)

I am just writing my thesis about FX instrument and hedging and one question popped up which I can't solve. Maybe it is silly but cant find anything about it how the delta of a fx spot is defined and ...
78 views

### What is the shape of the delta graph of the binary option?

I was wondering what the shape of the graph of the delta or the binary option would be.
631 views

### What is the delta of a portfolio invested in different stocks?

I understand that if I have a portfolio invested in stock A and options on stock A, the delta of my portfolio is going to be the weighted sum of the delta of the stock (=1) and of the option. Now if ...
247 views

### What exactly does shifting a barrier in a barrier option mean and how does it hedge delta?

How exactly is shifting the barrier to hedge delta implemented in case of barrier options. Is it just changing the barrier, if so, how does it hedge delta or is it making the barrier a range like a ...
53 views

### Understanding delta based strike selection in an Iron Condor

I am reading a small book on the proper use of Iron Condors (link). I do not use these strategies as I have had a very hard time being profitable on them. This book mentions some strategies to ...
731 views

### Delta Hedging/ Exchange for Currency Options

I'm looking at 2 cases of hedging EURUSD, using call spread or range forward. Lets say spot is 1.1300 and my buy call is at 1.1300 and sell call is at 1.1500. Hypothetically I'm assuming that this is ...
84 views

### Concentration risk in Rates

What are some good ways to assess the concentration risk for a rates curve or by currency when volumes traded by instrument are not easily available? For ex, if for some currencies, the PV01 at ...
53 views

I have a short rate model in which I have (among others) the following metric (for leverages) for a swaption : $$L = \frac{\frac{\partial}{\partial r}V_0^{\textrm{Swaption}}}{\frac{\partial}{\partial ... 1answer 2k views ### What is the formula for beta weighted delta and gamma? I am trying to calculate the beta weighted delta and gamma for a portfolio of options of different underlying stocks, but I can't seem to find the correct formula. Can someone point me to it or a ... 0answers 126 views ### Greeks Intraday Characteristics and PnL of options I am modeling intraday and short term options on Futures.Think Monday, wednesday, friday contracts on these tickers: ES, NQ, CL, ZN, ZF, NG. I am wondering about documentation for Intraday greek ... 1answer 150 views ### How to derive and interpret the duration of a call option? I read here that CFA students are taught that$$ D_{C} = \frac{\Delta_{C} D_{B} B}{C} $$Where D is the duration, \Delta_{C} is the first derivative of the options price with regards to the ... 2answers 471 views ### 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 ... 1answer 439 views ### Getting option volatility off vol surface I am currently looking into FX options. I am given a delta-tenor vol surface and I want to get the volatility of an option given its strike and time to expiry. I am reading about the method used and ... 1answer 211 views ### Value-at-risk and Equity delta How to validate value-at-risk calculation on an equity portfolio using equity sensitivities? I don't have trouble doing that for rates instruments or options but I don't know which underlying risk ... 4answers 795 views ### European Call Option Delta Upper Bound For a pure equity process (with interest rate, dividend, etc., being zero) not necessarily the geometric Brownian motion, is the delta of a European call option always no higher than 1? I am NOT ... 2answers 775 views ### Interest Rate Risk - The Greeks IR Delta and Gamma. Can someone please explain if my understanding is accurate as relates to a 2yr interest rate swap? You are considered to be long Delta in an interest rate swap if you are ... 1answer 398 views ### Delta-Gamma VaR question on inputs (do I need only one delta or the delta for the past 500 days?) When calculating a VaR using the Delta-Gamma approach, I am supposed to use this formula: ∆(V) = Delta * ∆(X) + 0.5 * Gamma * ∆(X)² where: ∆(V) = change in value of the asset in portfolio ∆(X) = ... 2answers 278 views ### Delta neutral strategy using a combination of put and call options I am learning about quantitative finance and currently learning about delta neutral strategies. The examples given are most of the times of the form: if you buy call options, you can hedge your ... 1answer 144 views ### ATMF FX straddle delta I am trying to price an ATMF FX (say Usdidr) straddle - the fxdelta for call and put leg are quite different with put fxdelta being higher than call delta. (Absolute values) Why would this be the case?... 1answer 702 views ### Different versions of sticky strike, moneyness and delta I head a lot of versions of those three concepts: sticky strike, sticky moneyness and ... 1answer 402 views ### Black-Scholes: Delta/probability of exercise increases with volatility The delta for an ITM call option with increasing volatility initially decreases, reaches a global minimum, and then increases. If we consider delta as a representation of risk-neutral probability of ... 1answer 310 views ### Kirk Approximation and Exercise Probability I have a question about spread options. I'm pricing a put option on two assets, with a strike value of 0: max(K-(F_1-F_2);0)=max(0-(F_1-F_2);0)=max(F_2-F_1;0) I know this kind of options could be ... 1answer 257 views ### Mathematical equation relating \frac{dV}{dS} to \frac{dV}{dK} Please help me figure out what is the mathematical relationship between \frac{dV}{dS} (Delta) and \frac{dV}{dK} (K=strike), taking into account vol skew. I ask this because I want to figure out ... 1answer 102 views ### What vol to use when implying strike from delta? I have a set of implied vols in delta space and want to derive for each delta the corresponding strike. I understand the procedure, but I am not sure what implied vol I should use, whether this has to ... 1answer 101 views ### Using BS Delta to hedge in a LV Model Why do some people use a Black Scholes Delta instead of the delta given by the Local Volatility model? 1answer 3k views ### Use of cash delta vs forward delta and the mirror image rule There has been no mention in this text of why this formula uses forward delta not cash delta. Why should have this been obvious to the reader? How can a put be delta neutral at 30%, what does this ... 0answers 189 views ### QuantLib in Python, are there any existing methods to handle the options delta on expiration day? Tried [ql.Settings.instance().includeReferenceDateEvents = True] and it works for the calculation of NPV using intrinsic value of the option. But Delta is nan for an in-the-money option. I understand ... 1answer 370 views ### On a FX volatility smile, Is a-delta put volatility equal to (1-a)-delta call volatility? On a FX volatility smile in terms of delta, If I want 95-delta put vol, Is this volatility equal to a 5-delta call vol, and viceversa? Thanks. 1answer 200 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 ... 2answers 96 views ### Why do we only need to buy or sell stock to hedge when the underlying is close to the strike? Delta mesure the slope of the digital option.It also provides hedging information. Why do we only need to buy or sell stock to hedge when the underlying is close to the strike? 1answer 288 views ### Call option Delta I have an exercise where I need to show that the prices of call options  C(t,K)=E((S_t-K)^+),t \in [0,T] with Strike K for fixed t:$$\frac{\partial ^+C(t,K)}{\partial K}=-P(S_t>K). We ...
I am trying to calculate the implied option premium $C(K)$ and $\Delta$ using the procedure outlined by Castagna and Mercurio in this paper - http://www.fabiomercurio.it/consistentfxsmile.pdf My ...