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Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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FX Option and Greeks Value in Dollars

I'm trying to replicate the Example given in pag. 229-230 of Dynamic Hedging by N. Taleb and I am not sure on how to convert the Greeks in Dollars and how the author is computing the Greeks. Start ...
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Comparing implied volatility in 2 different correlated assets

The general idea here is that I am trying to compare the volatility surface of two different financial assets whose prices and returns time series exhibit a strong relationship/correlation : The ...
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fx option atm and delta conventions for G10

I want to know about, G10 + USDKRW, USDHKD Fx option quote conventions ATM convention(for short/long maturities) Delta convention (unadjusted vs p.a. / spot delta vs forward delta)
MeowMaster2's user avatar
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Which option strikes are better to sell for mean reversion strategies [closed]

Suppose I have an underlying with following values: Spot Price: 100 Average: 98 Now let's say this stock goes to 108 and according to systematic evaluation it is overbought. I want to take a short ...
Dsp guy sam's user avatar
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How is it true that options can be equivalently seen as being written on the spot or its future?

I was recently told that options with expiration $T$ written on an underlying asset $(S_t)_{t\in\mathbb{R}}$ could also be seen as options on its future $(F_t)_{t\in\mathbb{R}}$. This makes totally ...
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The value of theta of an ATM option is proportional to the volatility, but for OTM/ITM options theta is not proportional to vol, why?

I have seen a graph of theta v/s volatility where the theta of ATM changes linearly with the volatility whereas for ITM/OTM options the theta didn't show a direct proportional relation with volatility,...
Gues's user avatar
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3 votes
1 answer
151 views

Cost of Hedging and Ito Calculus

In Dynamic Hedging by N. Taleb, at pag. 198, is presented a stop loss strategy that potentially could replicate an option. In particular, suppose one sells a call on an underlying and hedge it with a ...
Enrico's user avatar
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Delta of ATM barrier option

Can you please share the intuition behind the delta of a ATM down & in PUT being less than a ATM plain vanilla put (usually around 0.3 instead of 0.5)?
mark resen's user avatar
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1 answer
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P/L of a position described in terms of Up-Gamma and Down-Gamma

I can't visualize the profit/loss of a position described in terms of its Up-Gamma and Down-Gamma. The question arise from pag. 193 of Dynamic Hedging by Taleb. How would you describe a position that ...
Enrico's user avatar
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Indian options market historical data

I am wondering where a reasonable (and reasonably priced) endpoint for getting high resolution options price data. (high resolution = 1 sec or better), for the usual suspects (NIFTY fifty, or some ...
Igor Rivin's user avatar
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Vol Shift by Term over Time

Below is a plot of AAPL vol vs. Strike for October and November, last market close vs 3 weeks prior. The plot shows that both curves shifted up by an approximately constant amount with the October ...
PentiumPro200's user avatar
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How to derive renko volume from candle OHLCV data

i have been recently trying to generate Renko bricks from my OHLCV data, I'm currently using stocktrends module and have successfully generated the bricks, but I'm having trouble with generating the ...
chethanRaj's user avatar
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Vega for ITM and OTM options against the ATM one

In Dynamic Hedging by Taleb, at pag. 182, is presented the concept of "Vega ratio". If I understand correctly, the author in Table 10.3 confronts the Vega of an OTM option with the one of an ...
Enrico's user avatar
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Potential arbitrage opportunity or fallacy?

Suppose we have two European options with the same expiration: a call priced at $c$ with strike price $K_1$ and a put priced at $p$ with $K_2 (>K_1)$. Further, suppose the zero-points of the two ...
Ambitious-Walk3171's user avatar
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Understanding basic options arbitrage in Hull

I’m reading Hull’s book, Options, Futures and Other Derivatives. In Chapter 11 he discusses put-call parity and the arbitrage opportunities that can result from its violation. I’m having a basic issue,...
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Implied Vol under CEV model

Consider the following steps: Suppose the underlying equity follows a CEV model $dS_t = rS_t dt + \sigma S^{0.5} dW_t$. Use the above CEV model to simulate Monte Carlo paths and price a large set (...
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Complicated barrier options

We have the following contract consisting of barrier options: If $S_t$ is above the barrier level $B$ during the contract duration, we receive $N\cdot \max (S_T-4.45,0), 4.45>B$ from the bank, ...
timofiej8384's user avatar
1 vote
1 answer
137 views

Arbitrage between implied and realised spot-vol beta

Let's say there is a discrepancy is the market with respect to implied spot-vol beta (implied skew) and the actual beta of ATM vols with spot. Let's say Put vol > Call Vol but the atm vols are ...
volquant's user avatar
1 vote
1 answer
120 views

An application of Ito's formula with correlated Brownian increments

I am beginning to study (applied) stochastic calculus. I'm unclear on the following calculation which I am attempting to perform. I am attempting to show that if we have $$\begin{cases} dS_1 = a_1(S_1,...
Featherball's user avatar
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1 answer
159 views

Ideas behind early exercise of American Option

In Dynamic Hedging by Taleb, there is an example at pag 24-25 about early exercise of American options, already present here, but without a clear explanation, at least for me, about the cost/...
Enrico's user avatar
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Understanding assumption in Delta hedging P&L from Bergomi Chapter 1

In Chapter 1 of Bergomi's Stochastic Volatility modelling book there is a derivation of the delta hedging P&L to get a black-scholes like formula. The derivation in the multi asset case goes ...
I_cosine_this's user avatar
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Options on Futures, akuna question

From the below question, I am unsure why the option expiring in November is given by the January future. I thought it was a graphical issue, but it is supposed to look like it’s shifted to the right. ...
ayamathss1's user avatar
3 votes
4 answers
385 views

Option: link between Vega and Gamma

I am reading Dynamic Hedging by N. Taleb and I do not understand this statement in Chapter 9: The vega is the integral of the gamma profits over the duration of the option at one volatility minus the ...
Enrico's user avatar
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Why would you take a Loan when trying to Illustrate a Riskless Hedge?

I'm reading an article trying to derive option pricing with a simple approach, but I got stuck. In the second paragraph of this article (Name – Options Pricing: A Simplified Approach), which takes ...
Telefondemonen_se's user avatar
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time value of option proportional to sqrt(time)

I'm reading Natenberg's Options Pricing and Volatility, and in Chapter 18, he mentions this about an example: We can further refine our approximation if we note that an at-the-money option is made up ...
APerson's user avatar
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3 votes
1 answer
181 views

Relationship between Open Interest and Implied Volatility

Reference Request for any papers/articles that test the relationship between options open interest and its implied volatility. E.g. I would assume that a high market maker short interest on a strike ...
volquant's user avatar
-1 votes
2 answers
76 views

Proof of the value of an option using hedging and no-arbitrage [ Paul Wilmott Chapter 3.12.2]

I encounter a difficulty in understanding the proof of finding the value of an option. Before going into the proof, let's talk above the assumptions and parameters of the model. Assume that we know ...
Ricky Pang's user avatar
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56 views

Pricing a custom option in terms of simpler instruments

I have the following custom European Option $F$ on the underlying $S$ whose pay-off at expiry $T$ follows: $$ F(T) = \min{[B, \max{[K_1-S(T), S(T)-K_2,0]}]} $$ where $B$ is a cash position and $0<...
Sid's user avatar
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2 votes
3 answers
275 views

How to calculate overnight implied volatility?

I am trying to workout how to calculate the implied volatility of the overnight movement from market close to open. That is, the volatility of the from the closing price $S_t$ to the opening price $S_{...
Xerium's user avatar
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2 votes
1 answer
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Preferred Option pricing model [closed]

I am at Uni studying mathematical finance and wanted to know which is most preferred /widely used model by Finance Industry Practitioners from the list below. Fourier Transform for option pricing ...
dijoney J's user avatar
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What are $\mu$ and $a$ in $ \mu = a + \frac{\sigma^2}{2} $

Considering GBM: \begin{equation} S(t_i) = S_0 \exp(a \cdot t_i + \sigma \cdot W(t_i)) = S_0 \exp\left((\mu - \frac{\sigma^2}{2}) \cdot t_i + \sigma \cdot W(t_i)\right) \end{equation} I am interested ...
Marlon Brando's user avatar
1 vote
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44 views

How to solve special ATM case for Hagan approximation?

In Hagan et al's original SABR paper (https://www.next-finance.net/IMG/pdf/pdf_SABR.pdf), how do we reduce (2.17a) to (2.18) for the special ATM case? Could someone help walk me through the algebra? ...
user72283's user avatar
1 vote
1 answer
153 views

P/L table for a delta hedged position

I am trying to replicate the table at pag. 119 of Dynamic Hedging by N. Taleb with no success. In the example called "A misleading delta" an operator has the following position: long \$1 ...
Enrico's user avatar
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1 answer
259 views

Market Making in practice

I read some of the papers in the market making literature such as: Avellaneda - Stoikov market making model but was wondering if these types of models are actually use in pratice? It seems that when ...
confucius_is_confused's user avatar
1 vote
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118 views

How does delta adjustment relate to skew stickiness ratio (SSR)?

The correct delta hedging of a derivative $V$ in a model where volatility $\sigma$ is a function of the underlier $S$ requires a stock holding of an amount $$ \frac{dV}{dS}=\frac{\partial V}{\partial ...
Mr Frog's user avatar
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Hope you can recommend me some books about building mechanical options trading systems

I have some basic understanding of CTA and am quite familiar with options pricing theory. I am interested in learning about books that discuss the use of options tools to construct mechanical trading ...
BearSpread's user avatar
2 votes
1 answer
234 views

FX Strangle Market Conventions

Info on Risk Reversals for context In the FX vanilla options market buying risk reversal involves selling a lower strike put and buying a higher strike call. The price of such a structure is a ...
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1 answer
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Confusion about how price of a contingent claim at time 1 could give arbitrage

I have been reading the book Tomas Bjork's Arbitrage Theory in Continuous Time and could not understand how there could be arbitrage if the price of a contingent claim is not $X$. To give some ...
KMR's user avatar
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2 answers
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Describing the volatility skew with a set of options

Say you have a set of options data, and you filter the dataset based on certain criteria such as the bid-ask spread, open volume etc. and you end up with a set of liquid options based on said criteria....
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1 answer
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Synthetic replication of a spread option payoff

I have two assets, $S_1$ and $S_2$, and a European exchange-one-asset-for-another call option, such as those introduced by Margrabe (1978). So my payoff at expiration is the difference between the ...
Lisa Ann's user avatar
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0 votes
1 answer
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Interpolation of IV based on delta

I have a dataset with options, all the same date and time to maturity but different IV and delta. Now, I want to find the IV for certain delta values (e.g 0.5) through interpolation. Do you think that ...
Masmar's user avatar
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1 answer
182 views

What is the P&L

I have a question about the P&L calculation, please. If we sell a call option on a stock with a volatility of 16%. Theta is worth 100€/day. Let's assume that the spot moves by 2% in one day. What ...
Raphael Morel's user avatar
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1 answer
160 views

What to predict in delta-gamma hedging?

I am working in delta-gamma hedging with machine learning. I guess I have to predict gamma (since predicting gamma tells you how delta will behave) but I don't know why is it needed. I think that a ...
Kilkik's user avatar
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1 vote
1 answer
101 views

Change in price of underlying impact on delta gamma and vega

I am working my way through Natenberg's book as well as the accompanying workbook, and there is a question I cannot figure out (p86). Futures price = 149.65 time to August expiration = 8 weeks annual ...
nickhealy's user avatar
1 vote
0 answers
70 views

Summarizing the Volatility Skew as a Single Number

Related questions to this topic/subject: Expressing Volatility Smile as One Number Volatility skew and how to capture it? In both posts, the authors/respondents recommend using the second derivative ...
KaiSqDist's user avatar
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Barrier Reverse Convertible Coupon

I want to ask regarding Barrier Reverse Convertible, I got this from https://bookdown.org/maxime_debellefroid/MyBook/barrier-reverse-convertibles.html "The price of this barrier reverse ...
testingBRC's user avatar
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1 answer
76 views

pricing option with two volatility regimes

How would I price a 1-year ATM European call option, given I know that for the first 6 months, the realized volatility will be 20% and the latter six months, the realized volatilty will be 90%? One ...
Sameer L's user avatar
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46 views

Heston model calibration to option prices and implied volatility

I hope that you are having a great day, I am trying to write a research paper on the Heston model deep calibration. I noticed during my literature review that the most common approach is to calibrate ...
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Market Making in ETF, how the hedging is typically done

I was wondering how Market Makers in ETF hedge themselves. I believe that they don't buy the underlying basket because some of the stocks could be extremely illiquid. So my guess is that they buy CALL/...
option_vol's user avatar
2 votes
0 answers
59 views

What is the impact of the rollover of VIX futures contracts on VIX options?

I am inquiring about the potential impact of futures rollover on VIX options prices. I am currently exploring diagonal and calendar spreads on VIX options, and I need to modelize this. Your insights ...
Samuel Dana's user avatar

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