Questions tagged [delta]

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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). ...
2
votes
0answers
698 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
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0answers
56 views

Delta hedging of tax option

So corporate profits are taxed as a percentage of the positive earning, but losses will not generate any taxes. Hence taxation have a clear option structure where the government has a call option on ...
2
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2answers
114 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
2answers
381 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
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2answers
4k 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 ...
1
vote
1answer
113 views

How to understand this example from Hull's book?

I just started reading Hull's book, and I got stuck in an example where a financial institution has sold for $300,000 a European call option on 100,000 shares of a non-dividend-paying stock. Stock ...
1
vote
1answer
207 views

Option delta - Conditional probability definition?

Can someone help me interpret this definition of delta? Delta is a conditional probability of terminal value (St) being greater than the Strike (X) given that St > X for a call option. Is the ...
1
vote
1answer
587 views

Derivative: Delta of a Down and Out Call Option with Barrier=Debt(K)

I am trying to compute the derivative of this function with respect to V0: This is the price of a down and out call option, assuming the barrier equal to the level of debt K. In other terms, I need ...
11
votes
1answer
1k 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 ...
1
vote
2answers
158 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 ...
0
votes
1answer
2k 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 ...
3
votes
1answer
475 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 ...
4
votes
1answer
5k 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 ...
1
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2answers
578 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 ...
1
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0answers
80 views

Delta of an option in two cases

Let C be the prime of a call in fi=unction of the price in term F, Strike K, volatilité $\sigma$ and maturity t: $C(F,K,\sigma,t,r) $ We assume that we know $\delta$ $\delta=\frac{\partial}{\...
2
votes
1answer
185 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
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 ...
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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2answers
214 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 ...
1
vote
1answer
193 views

Delta Hedging for 2 Factor Models

If the value of an option at Maturity is what is the off-setting position you take for X and Y, if you are i)Long Call of the option ii)Short Call of the option iii)Long Put of the option iv)Short ...
7
votes
4answers
690 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 ...
2
votes
2answers
361 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 ...
3
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0answers
85 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 ...
3
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1answer
854 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 $\...
0
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0answers
743 views

Delta Volatility Surface Usage to value the option

I always find myself in the unknown charted territory when it comes to non-Linear Instruments. I come across the scenario, How to value the option using Delta Vol surface? Example I have CME traded ...
7
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. ...
2
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2answers
2k 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?
1
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1answer
3k views

Implied volatility interview question [closed]

If an implied volatility of an out of the money call option goes to infinity,what happens to the delta of the said call option?
6
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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 ...
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
476 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 ...
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 ...
0
votes
1answer
239 views

How do I track implied volatility of specific delta?

I'm a newbie with respects to volatility trading and options. I recently purchased a book on the topic called "Trading Implied Volatility -An introduction" by Simon Gleadall. It's been one of the most ...
0
votes
1answer
701 views

Delta formula for FX vanilla option

What value do you use for annual dividend yield? It does not apply in case of FX.
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 ...
1
vote
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 ...
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 ...
1
vote
1answer
150 views

Delta of a standardized at-the-money 30-day put option

The plot below depicts the delta of a standardized at-the-money 30-day put option on the S&P500 tracker SPY over a 14-year period. This is data from OptionMetrics and standardized prices are ...
2
votes
1answer
772 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 ...
1
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1answer
949 views

Delta in Covered Calls?

Just want to check whether i understand it correctly: Long Calls have positive delta Long Puts have negative Delta Long stock has 0.01 delta 100 Shares have 1 delta Therefore: Covered Call = 1 ...
5
votes
0answers
306 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 ...
1
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1answer
387 views

compute FX forward from broker's data

assume I have following delta-term vol data from broker: ...
1
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2answers
2k views

Delta of a Down and Out Call

I came across some graphs depicting the delta of a down-and-out call. They show that, if the risk free rate of return is 0, the delta is constant at 1. However, if the rate of return is for example 5%,...