Questions tagged [delta]

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12
votes
1answer
2k views

How do different models impact option Greeks?

If I trade an option using delta, vega, Prob OTM, etc. these are derived from a model. How do leading models impact valuations in terms of the Greeks? I suppose to form a baseline it would have to be ...
10
votes
5answers
16k 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 ...
8
votes
3answers
11k views

How do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)?

In markets, many instruments are quoted in volatility, but how we can tell what kind of volatility is this? Is it normal volatility, or lognormal volatility. because it affect our hedging positions. ...
7
votes
4answers
717 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 ...
7
votes
1answer
537 views

Different versions of sticky strike, moneyness and delta

I head a lot of versions of those three concepts: sticky strike, sticky moneyness and ...
6
votes
3answers
3k views

Greeks: Why does my Monte Carlo give correct delta but incorrect gamma?

For a vanilla European call, my Monte Carlo method gives the right option price and delta but the wrong gamma. In particular, the value of gamma varies wildly each time I run the method. I estimate ...
5
votes
0answers
309 views

EUR/PLN and EUR/USD delta-term-vol surface quoting convension

does anyone know for sure what is the FX market convension to quote delta-term pairs for EUR/PLN, for EUR/USD. I know that for EUR/PLN it should be delta p.a forward, for EUR/USD it should be delta ...
4
votes
3answers
8k views

What is the relationship between Time-To-Expiry and Delta?

Is there any regular relationship between Delta and the Time-To-Expiry of an option? I have observed that options that expiry sooner are more sensitive to underlying movements (with equal strikes). ...
4
votes
1answer
4k views

Effect of volatility on the delta of a call option

In the book 'Dynamic Hedging', Nassim Taleb writes: ...
4
votes
1answer
496 views

Black model: Delta - strike relationship regardless of expiry?

While wandering through some QuantLib experimental classes for FX trading, I've found this Black Delta Calculator. By reading its .cpp, it seems that no use of ...
4
votes
1answer
6k views

Find call and put volatilities using ATM, Risk reversal and Butterflies volatilities

I have to plot the implied volatility surface for EUR/USD. So, my goal is to produce something like that, from put delta 10 to call delta 10: Searching for informations, I found that I could find ...
4
votes
2answers
9k views

How can I calculate the strike price or implied volatility from a given delta?

I have calculated the implied volatility for all strikes of a certain product (options on futures) and approximated the ATM volatility. My question is how can I figure out the implied volatility for a ...
4
votes
1answer
114 views

What is the probability distribution of the changes in $\Delta$?

What are the odds that a 10 delta option will become a 30 delta option in "N" number of days? Is that calculation possible? For instance, I want to know the probability with which my 56 day, 10 ...
4
votes
1answer
92 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?
3
votes
1answer
248 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 ...
3
votes
2answers
211 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 ...
3
votes
1answer
370 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 ...
3
votes
1answer
473 views

European call delta derivation

Let's write $S(T) = S_T$ and $S(0) = S_0$. We want to compute $\frac{d}{dS_0}\mathbb{E}[f(S_T)]$. From a previous discussion this is equal to $$\mathbb{E}_{S_0}\left[f(S_T)\frac{g'_{S_0}(S_T)}{g_{S_0}(...
3
votes
2answers
218 views

Is the European call option delta an increasing function of the spot?

In the Black-Scholes' setting, the delta hedge ratio of a European call option is given by $N(d_1)$, which is an increasing function of the underlying equity spot $S_0$. Does this property hold ...
3
votes
1answer
483 views

Why is the dividend risk of an option equal to its delta?

In this document, https://www.eurexgroup.com/blob/2435406/f1b0086a8c6d05954c58a8dc24308c81/data/20160304_Colin-Bennent-Trading-Volatility-.pdf, it states that "This is because the dividend risk of ...
3
votes
2answers
866 views

Delta hedging frequency, Gamma PnL

I want to know the expectation and the variance of the Gamma PnL for different hedging frequencies. Let's say the return of the underlying follow a normal process: $dr= \sigma*dW$, the market trades ...
3
votes
1answer
497 views

Deltas and CC Basis Swaps

How do I calculate the dollar impact of basis change for a portfolio of cross currency basis swaps which hedged loans/bonds? I am thinking it might have something to do with delta and tenors but I ...
3
votes
1answer
910 views

Delta of an option derived from the binomial model

I have the following function $V=V(S,t)$, $V^- = V(vS,t+\delta t)$, $V^+ = V(uS, t +\delta t)$. The book proceeds to explain that if we use Taylor series expansion on the above we will confirm that $\...
3
votes
0answers
65 views

European call option delta and maximum principle

From comments, the maximum principle for parabolic PDE can be used to show that the European call option delta cannot be greater than 1. I am looking forward to such derivations.
3
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0answers
87 views

Intraday Value at Risk approximations

We use full valuation of derivatives portfolios using scenarios from historical data. For simple contracts, this is relatively fast. For contracts requiring monte carlo simulation, this becomes ...
2
votes
2answers
401 views

why Delta increases as interest rate increases

I just would like to know why $\Delta$ increases as $r$ increases. I would like an intuitive answer, without model (I can compute my greeks myself). Thanks
2
votes
3answers
89 views

Why “ Even if the underlying asset price remains unchanged, the option delta for an in-the-money option increases as expiration nears”

I saw this line on some website but can not understand it. Can anyone explain it? "Even if the underlying asset price remains unchanged, the option delta for an in-the-money option increases as ...
2
votes
2answers
5k views

Calculate strike from Black Scholes delta

I have a list of deltas and their corresponding volatilities in an FX market but I want to go from delta to strike price. In this Question similar problem is being discussed How can I calculate the ...
2
votes
3answers
437 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 ...
2
votes
1answer
100 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 ...
2
votes
2answers
94 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?
2
votes
2answers
115 views

If you try to capture short term delta by anticipating moves in the underlying, why would vega pnl be so bad?

Since calls and puts have opposite sign delta, but both are positive vega, it feels like a strategy that buys/sell or sells/buys calls and puts on underlying moves to capture delta should generally ...
2
votes
1answer
188 views

Approximation of an option price

The value of an option in the money is 11.50 Euros. The parameters of the market are: -The price of the underlying stock: 81.4 Euros. -The volatility ofthe underlying is : 34.65 % The ...
2
votes
2answers
501 views

Is commodity futures's delta equal to 1?

According to John Hull's book, equity futures delta does not equal to one. For commodities futures, since there is no centralized exchange for physical commodities, do commodities futures' delta equal ...
2
votes
1answer
444 views

How to compute delta and delta-hedge in practice?

I keep hearing things like \begin{align*} ``\text{Traders make their book delta-neutral at the end of each trading day''} \end{align*} I am wondering what this means, and why this is supposed to give ...
2
votes
1answer
3k views

What is the difference between par delta and zero delta?

I was looking at different methods of calculating delta for Interest Rate Swaps(IRS) and came across the words par delta and zero delta. I am not sure of the difference between the both and when to ...
2
votes
1answer
783 views

Value at Risk from Delta of a single asset portfolio

I am trying to figure out the following, for me unfamiliar type of question: Given is a single asset portfolio: the Delta of the portfolio is 15, the value of the asset is 10 and the daily volatility ...
2
votes
2answers
374 views

Deduce expected exposure profile from option/structure delta?

I am thinking about whether there exists a relationship between the delta of an option (or any structured derivative) and it's expected positive/negative exposure? An intuitive question would be the ...
2
votes
1answer
9k views

Gamma and delta P&L example question

I'm trying to get a basic understanding of this example delta ladder ...
2
votes
1answer
316 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 ...
2
votes
1answer
236 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 ...
2
votes
2answers
3k views

VaR calculation methods of options

I am a little bit confused about VaR in Options and I need a clarification for. I collected the following formulas, can you suggest what is the best formula and explain me why, please?
2
votes
1answer
131 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-...
2
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0answers
141 views

Option delta under Black mode vs SABR

Under what scenarios would the Deltas for Options on Bond Futures differ the most between Black vs SABR models ?
2
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0answers
77 views

'Market price' based Delta vs 'Model Price' based Delta for Bond Future Options?

My understanding of Delta is the change in the Option's price relative to the change in the underlying asset's price. In the case of Treasury Future Options (ie those on CME), one intuitive way to ...
2
votes
0answers
46 views

Calculate latest underlying price (or option), given new option (or underlying) market price?

Given a reference underlying price, reference option price, delta and gamma, if I receive a new underlying/option price what equation should I use to calculate the respective option/underlying price (...
2
votes
0answers
936 views

how to calculate forward delta (not spot delta) of a swap?

how could I calculate the forward delta of of a cross currency swap? Suppose I have a swap contract to exchange 1 mio USD with 66.15 mio INR, 3 months later, current Spot is 65.04, how can i ...
2
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0answers
744 views

Conversion of a premium-adjusted delta to a strike

I am trying to compute the calibration of an FX market volatility surface, and especially I want to retrieve the strikes from the deltas quoted. I don't have any trouble reverse-engineering the ...
1
vote
2answers
164 views

Why not delta of Call option is stochastic or random variable?

Delta of an option is defined as ratio of change in price of call option to change in price of underlying securities. If, $c_t$ is call option price at time $t$ and $S_t$ is the price of underlying ...
1
vote
1answer
269 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 ...