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Questions tagged [delta]

The tag has no usage guidance.

3
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1answer
128 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 ...
1
vote
1answer
75 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 ...
1
vote
1answer
43 views

Port a model dependent swaption sensitivity to a new model

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 ...
0
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0answers
48 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 ...
2
votes
1answer
88 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 ...
3
votes
2answers
107 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 ...
2
votes
0answers
83 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-...
1
vote
1answer
85 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 ...
1
vote
1answer
53 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 ...
0
votes
1answer
131 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) = ...
0
votes
2answers
104 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 ...
0
votes
1answer
97 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?...
6
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1answer
331 views

Different versions of sticky strike, moneyness and delta

I head a lot of versions of those three concepts: sticky strike, sticky moneyness and ...
2
votes
1answer
230 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 ...
0
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0answers
42 views

Going from Stochastic Discount Factor / Risk Neutral Density -> Hedge Ratio

Assuming a probability distribution function is known in its entirety, what methods are available to construct a hedge ratio? For guidance, I went to the canonical Empirical Pricing Kernels and found ...
0
votes
1answer
74 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 ...
2
votes
1answer
175 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 ...
5
votes
1answer
79 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?
1
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0answers
118 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 ...
1
vote
1answer
204 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.
2
votes
2answers
90 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?
1
vote
1answer
242 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 ...
1
vote
2answers
248 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 ...
1
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0answers
86 views

Should I interpolate before or after to find option price using Vanna-Volga method?

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 ...
2
votes
0answers
112 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 ?
-3
votes
1answer
173 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 ...
1
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0answers
192 views

Does delta adjusted exposure make sense for an equity variance swap?

The software vendor that I am using for the calculation of the market risk exposure claim that they cannot compute the delta adjusted of the equity variance swap positions since there is no specific ...
-1
votes
1answer
764 views

What is the delta of a zero coupon bond? [closed]

I understand that zero coupon bond changes as interest rates change. But I am unsure of how to get the delta. Say I buy a 5Y zero coupon bond with notional amount 5M USD. How do I calculate the delta? ...
2
votes
0answers
66 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 ...
3
votes
0answers
44 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 (...
3
votes
1answer
222 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 ...
2
votes
2answers
387 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 ...
1
vote
2answers
4k views

Strike / delta relationship for FX options

I am tryinto find out how to go from delta to strike. If wee look at the bloomberg I am looking at 1M ATM volatility. I have included the Bloomberg data as a picture where we have following ...
0
votes
1answer
253 views

Delta FX of a quanto put

I've heard that quanto options are not sensitive to the FX...but when i draw the graph of the FX delta of the put i find a positive value for all K. For very deep ITM quanto put the FX delta is ...
1
vote
1answer
84 views

Estimate American-style option delta from similar options

I have a data set which looks something like this, referring to American-style put and call options: ...
4
votes
1answer
393 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}(...
-2
votes
1answer
296 views

Option delta difference between OTM call and OTM put

Looking e.g. at Natural gas futures options, I see for June contracts (expiration 25th May) the follwing data: Call 4.3 (26.8% difference to Underlying) 36.2% IV and a delta of 0.04 Put 2.5 (26.3% ...
0
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0answers
338 views

How to calculate Delta of an option in the Local Volatility model?

Let $dS/S = \sigma(S,t) dW$. Let the local volatility be known, i.e, we know the formula $\sigma(S,t)$. How do I derive $\Delta$ of a regular call in this model? Let BS be the Black Scholes price, ...
2
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0answers
846 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
67 views

Delta of a Single Future Commodities ETC

I have seen marketing materials advertising ETCs on single commodities futures to track the commodities performance (or better the corresponding front month future contract) as Delta 1 products. ...
4
votes
1answer
407 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
1answer
394 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 ...
0
votes
1answer
182 views

Strange Delta for FX Down And Out Call, Strike below Barrier

Based on this text about FX options on pages 139, 141 and 145 I'm trying to compute the delta of a down and out call with the strike below the barrier. Here is a quick and dirty Python code (I assume ...
0
votes
1answer
3k views

Skew and shadow delta

The presence of skew causes a correlation between volatility and spot. This correlation produces a negative shadow delta for all forward starting products (forward starting options have a theoretical ...
3
votes
2answers
800 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 ...
2
votes
3answers
85 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 ...
1
vote
1answer
712 views

Bachelier option delta = probability of exercise?

Under the Black-Scholes model, the delta of a call option is sometimes interpreted as the probability for the option to end in the money. If I assume that the underlying follows a normal distribution ...
-2
votes
2answers
4k views

why is the delta of a short call option negative? [closed]

Why is the delta of a short call option negative? In Black-Scholes-Merton equation the delta of a call option is always a probability function therefore it does not imply such a consequence. How do I ...
3
votes
3answers
7k 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). ...
3
votes
0answers
613 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 ...