Questions tagged [delta]

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1answer
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Given a cointegrated portfolio of stocks, how to build a synthetic option position by using the options on the stocks

The setting Let stocks $A$, $B$, and $C$ are cointegrated. Moreover, we know the weights of the cointegrated portfolio (scaled so that the absolute value of the maximum weight is $0.5$): $w_A = 0.15$ ...
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1answer
56 views

Delta and Gamma profile

There is an active spread option traded in ICS as described here - https://www.theice.com/products/28881205/Crude-Future-Brent-1-Month-Calendar-Spread-Options I am ...
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1answer
66 views

Hedge error - Willmot and Ahmad

I'm currently reading the paper: Willmot and Ahmad: Which free lunch would you like today, Sir? Delta Heding, volatility arbitrage. In case 1: They delta hedge with the actual volatility, by going ...
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0answers
29 views

Local Volatility Monte Carlo option price - different starting index level

I constructed the local volatility surface of S&P 500 from implied vols and was able to price the options accurately using Monte-Carlo. Let's say I priced a 80% of S0 put option with S0 = 4000. ...
0
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1answer
77 views

VIX ATM Options Delta

VIX ATM options seem to have delta that is very far from .5 (.18/.82 for 60dte now) with .5 being in 30 territory. Why is this very different from stock options? Why is atm put much less sensitive to ...
1
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5answers
117 views

Why isn't the delta of a slightly in the money American option 1?

Doesn't the intrinsic value rise 1:1 with stock price when an American option is in the money? Also, you can exercise the option at any time to capture the intrinsic value (even though this would be ...
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0answers
33 views

comparing volatilities of 2 different commodities when no delta is provided

If I wanted to compare the relative volatilities of options on 2 different commodities, but the deltas are not provided, is it sufficient to compare by the % each commodities strike is in or out of ...
4
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1answer
179 views

Gamma of interest rate derivatives

consider an interest rate derivative whose value $V$ depends on $n$ interest rates $r_1, \dots, r_n$. Hence $V$ is a function in $n$ variables $V(r_1, \dots, r_n)$. My question concerns the gamma $\...
0
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1answer
58 views

Estimating delta of VX futures to S&P 500

I'm trying to think about the right way to estimate the delta of a VX contract to the S&P 500. VX futures are on the VIX index, which is a basket of S&P 500 options. By extension, VX and ES (E-...
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2answers
266 views

Option seller: Why is delta hedging required if I am long/short the underlying with same number of lots as the OTM options I sold?

Situation: Sold OTM call while long the underlying. Stock did not tank, it went up too much breaching the breakeven point (strike price+premium). If I sell 1 lot of call options and I am being long ...
0
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1answer
92 views

Delta and vega sensitivities for Cap

I have a task to do but it is very difficult.. I have to calculate the: Delta Sensitivity analytically, that is the first derivative of caplet price wrt the forward rate, using the black model to ...
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0answers
208 views

FX Delta of a cross currency basis swap

I would like to understand in which case there is a presence of FX delta risk factor when trading a Cross-currency basis swap. By FX Delta, I mean the sensitivy of my swap PV with respect to FX Spot ...
1
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1answer
133 views

Why would a 15Y swap index=EUR3M and discount=OIS, show only a EUR3M-delta at 15Y

When computing the index-delta for a swap in a multi-curve framework, only the last cash tenor seem to show sensitivity. Could anyone explain with formulas why it is the case ? For example a 15Y swap ...
0
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1answer
105 views

in bloomberg, how do they calc dv01 per leg of a IRS

note: i am asking about dv01 per leg. i see the fixed leg has virtually all the dv01, floating has hardly any, which tells me they are treating each leg as a bond in some way. it looks like they calc ...
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2answers
48 views

10-day VaR for a portfolio

So, Bank ANZ owns a portfolio of options on the USD/GBP exchange rate. The delta equivalent position of the portfolio is GBP 56.00. The current exchange rate is 1.5, with a daily volatility of 0.7 ...
1
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1answer
116 views

Why my delta position is increasing with increase in spot?

I am trying to take position in future as per the delta position of short put. My strike is 13794 for short put option, spot 10305.3 and volatility is 20.153 then I am getting 5890 position to buy and ...
8
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2answers
1k views

Different versions of sticky strike, moneyness and delta

I head a lot of versions of those three concepts: sticky strike, sticky moneyness and ...
1
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2answers
858 views

Premium Adjusted Delta in fx market

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 ...
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0answers
76 views

How should I interpret this Put Option delta graph?

In the following graph there's an example of Delta for a Call Option and a Put Option. I understand what this greek means and I understand why it's positive for calls and negative for puts. What I don'...
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0answers
30 views

How can cumulative delta for options over an interval be calculated?

How can a graph like on the bottom of the image be created? What information is needed? ()
6
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3answers
4k 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 ...
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3answers
1k views

Which is riskier: a call option or the underlying?

From Joshi's Quant Interview Questions and Answers: What is riskier: a call option or the underlying? (Consider a one day time horizon and compute which has bigger Delta as a fraction of value). I ...
0
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1answer
134 views

QuantLib convertible bond pricing generates strange delta

I am trying to generate equity delta for convertible bond using QuantLib(version 1.14) functions, but the deltas generated either using a repricing approach or by directly obtaining from the tree(code ...
3
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3answers
9k 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 ...
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2answers
113 views

Delta Forward and Put Call Parity

Vanilla options are traded interbank with delta hedge. The instrument employed to a delta hedge is usually a forward with the same expiry (and opposite delta) as the option. This means that in effect ...
2
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1answer
303 views

Price adjustment of Black-Scholes delta and gamma for a quanto option

A quanto option is a derivative with the underlying and strike price denominated in one currency, but the instrument itself is settled in another currency. This has consequences for the calculation of ...
0
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1answer
413 views

Interest Rate Swap Delta ladder, under OIS Discounting

I've been looking on some information when it comes to vanilla Interest Rate Swaps, and building delta ladders under a multicurve environment. IR Swaps - Curve sensitivity at maturity node, this ...
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0answers
112 views

delta of synthetic forward of american options

For european options, we know the delta of a synthetic forward position (long call short put with the same strikes and maturities) because of the put-call parity. However the P-C parity does not apply ...
2
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2answers
7k views

Strike / delta relationship for FX options

I am trying to find out how to go from delta to strike. If we 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
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1answer
490 views

How does delta-gamma VaR work in practice and when can it be preferable to Monte-Carlo VaR?

So I will start off by just stating my understanding of the two methods through some examples and lead that into my question. Hopefully it is correct but if not then perhaps the answer to my question ...
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1answer
131 views

Macaulay duration of an IRS receiver [closed]

how can I compute the duration of an IRS receiver? and how can I use it to compute the Delta of IRS?
3
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1answer
139 views

Quantlib - exercise probability function?

I am using Quantlib to obtain the option value embedded in a convertible bond. I create an american option as follows: ...
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1answer
229 views

Option Volatility Smile vs Delta

I am new to options trading and have been trying to better understand the relationship between implied volatility, delta, and moneyness. I was wondering how a call option's implied volatility can go ...
0
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1answer
111 views

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 ...
2
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1answer
274 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 ...
1
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1answer
90 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 ...
4
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1answer
162 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 = ...
3
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2answers
434 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 ...
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0answers
83 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, $S$ ...
4
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2answers
2k views

Possibility of delta greater than 1 [closed]

Can delta of an option be greater than 1? Please illustrate it with an example.
5
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1answer
577 views

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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0answers
104 views

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 ...
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1answer
1k 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 ...
3
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2answers
932 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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5answers
21k 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 ...
1
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1answer
177 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 ...
1
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1answer
62 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 ...
1
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1answer
91 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 ...
1
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0answers
310 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 ...