Questions tagged [delta]

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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 ...
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27 views

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 ...
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41 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 ...
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74 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 ...
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50 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 ...
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1answer
55 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.
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78 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 ...
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38 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 ...
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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 ...
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81 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 ...
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1answer
49 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 ...
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86 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 ...
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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 ...
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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 ...
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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-...
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1answer
317 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 ...
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1answer
119 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 ...
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1answer
289 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) = ...
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175 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 ...
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1answer
127 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?...
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539 views

Different versions of sticky strike, moneyness and delta

I head a lot of versions of those three concepts: sticky strike, sticky moneyness and ...
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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 ...
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1answer
92 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 ...
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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 ...
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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?
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160 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 ...
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1answer
290 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.
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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?
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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 ...
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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 ...
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92 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 ...
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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 ?
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185 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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232 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 ...
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1answer
987 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? ...
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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 ...
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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 (...
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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 ...
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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 ...
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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 ...
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1answer
317 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 ...
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123 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: ...
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1answer
476 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}(...
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330 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% ...
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376 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, ...
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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 ...
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86 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. ...
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485 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 ...
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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 ...
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197 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 ...