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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questions with no upvoted or accepted answers
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Risk management tools for long term Gamma/Vega sellers subject to margin calls
TL;DR: if you're a retail investor and you systematically sell long-term vertical spreads while staying Delta-neutral, your main risk comes from Vega and the Gamma of opening gaps that can throw you ...
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option chain data visualization, sunburst
I think option chains are not represented in the best way. With more and more options products coming out and trading on the various exchanges, I see vendors struggling to keep up with a good way to ...
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What is the most convenient data structure for backtesting a model of futures options prices?
I have an empirical model for the dynamics of futures prices in a particular market that I have implemented using a long series of the front five contracts. (I account for the roll in my model.) I ...
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Basket option density in BS model
Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
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Implied vol bounded if and only if instantaneous vol bounded
I'd like to show that in diffusion models IV is bounded iff instantaneous vol is bounded if there is to be no arbitrage. So, assume a model under the pricing measure of the form
$$
dS_u = \sigma_u S_u ...
user34971
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Libraries for calculating options strategy-based margin
Hopefully, this is an acceptable question in this forum, even if it isn't analytically focused.
As part of an effort to analyse the effect of different option trade structures on a portfolio, I need ...
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Measuring implied move priced into an event
It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
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Has a closed-form formula for the collateral choice option been found?
The collateral choice option problem has been formulated in e.g. Fujii and Takahashi (2011), Piterbarg (2012) or Antonov and Piterbarg (2013), as the computation of an expectation of the following ...
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Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative
Let $X_t$ be an american style financial derivative with random exercise time $T$
where $t$ and $T$ belongs to some finite set $A$.
Buying this derivative requires the buyer to pay $p_t$ up to time $T$...
user2688
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How companies choose earnings release dates, & effect on Implied Volatility
A company's earnings release date significantly affects weekly or monthly option prices/implied volatility. For companies that typically release earnings on the cusp of monthly options expiration, ...
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How are VIX futures being priced when the VIX itself is not being calculated because of circuit breakers
I see that CBOE has halted trading all SPX options, which means the VIX cannot be calculated. Yet VIX futures are still trading and we are very close to the last trade date for the March contract.
I ...
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Working with wide bid ask spreads in option pricing model
I'm trying to fit an Heston model to market data. But market is data has some terms (<3M) with quite wide bid-ask spreads (12%-25%). Should I just use mid volatility? Is there maybe a model to pre-...
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pricing option with two stocks
Let $\left(S_t^{(1)}\right)_{t\ge0}$ and
$\left(S_t^{(2)}\right)_{t\ge0}$ be the price processes of two stocks
with dynamics
$$ \begin{align}
& dS_t^{(1)}=\sigma_{11}S_t^{(1)}dW_t^{(1)}
\...
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Risk neutral measure in exponential levy model
Is there a method of finding a risk-neutral measure for assets driven by the levy process? I understand there is the esscher transform but I think it tends to transform the processes into ...
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What's the typical markup on quoted exotics, and what drives this premium?
I'm curious about the typical markup on quoted exotic options as well as what drives this premium.
You call up an options desk for a quote, and they'll give you a spread that reflects their market on ...
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Delta hedging the day before expiry
In practice, how do people usually delta hedge options the day before expiry? Would you still use the black Scholes delta and then close out the position in the underlying immediately after expiry? ...
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IR Cap Forward Premium
A well known broker quotes cap/floors as spot premium for ATM straddles but forward premium for the skew, given that the difference between spot premium and forward premium is that the option is not ...
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Finding optimal calendar spreads and diagonals
I am looking for some pointers on risk/return profiles of calendar spreads and diagonals with different strikes and expiration dates, preferably based on historical backtests with SPY options.
Please ...
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Pricing of strange Asian lookback option with European-style payoff $\max\{ \max_{u\in[0,T]}S_u-\frac1T\sqrt{\int_0^TS_t^2\mathrm{d}t},0\}$
I am trying to price the Asian lookback option at time $t$ with time-$T$ (European) payoff $\max\{M_T-A_T,0\}$, where $$M_t=\max_{u\in[0,t]}S_u,\quad A_t=\frac1t\sqrt{\int_0^tS_u^2\mathrm{d}u},$$
and $...
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FX American call option optimal exercise and holding region
Problem
I am considering an American call option which gives a domestic investor the right to buy a unit of foreign currency at a strike of $K$ units of domestic currency. I have an exchange rate $S_t$...
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What put options would the Universa Tail Fund have bought?
According to this Bloomberg article, Universa was up 3,600% in March 2020, by hedging with extremely out-of-the-money puts: https://www.bloomberg.com/news/articles/2020-04-08/taleb-advised-universa-...
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How is the implied risk neutral density affected when changing numeraire?
For example i would like to price
\begin{equation*}
E^{Q} \left[ e^{-\int_{0}^{T}r_{s}^{cur}ds} f \left( S_{T_f}^{cur_1} \right) | \mathcal{F}_{0} \right] = B_{cur}(0,T)E^{Q^{cur}_{T}}[ f(S_{T_f}^{...
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R: How do i finish the tails in the risk neutral density, obtained from option prices
Im currently working on constructing the risk neutral probability distribution of a stock, based on the option prices. In doing so, i calculate the implied volatilities from the option prices, and ...
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GARCH(1,1)-M MLE optimization with fmincon in R
I've searched thru dozens of papers and did not find in any of them satisfying and enough theoretical answers to my concerns. So I've combined everything what I found below. Please indicate if my ...
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Is there an arbitrage free option model that treats volatility as a deterministic function of strike?
I am trying to get a good understanding of the different models out there, and thus be able to study hedging errors, and strengths and weaknesses. My understanding of the Local Volatility model in ...
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Alternative Method for Determining Option-Implied pdf
As I am refining a pricing model to incorporate skew, and not just ATM volatilities, I need to create random realizations of the underlying consistent with the skew-implied pdf. When searching, one ...
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Structured Energy Option Pricing
Let's say I have an option with the following terms. This is for an energy product (ie natural gas)
The contract will last for 6 months
The payoff is the difference between the first of month index ...
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Higher Order Greeks
In studying options pricing a while back, I had learned of the higher order sensitivities of of Speed and Color.
Speed was the rate at which the gamma changes with the underlying.
Color is a ...
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Rationale behind volatility dispersion (or correlation) trading
When looking at the explanation of CBOE S&P 500 Implied Correlation Indices available here, it is written that such indices:
[...] "may be used to provide trading signals for a strategy known as ...
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How to estimate option implied skewness and kurtosis in R
Suppose that i have data that for each day i have more than one option, either put or call. I.E. I have more than 20 put options and 20 call options for each specific day.
What is the way to estimate ...
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ODE Solution in Carr's Randomized American Put
In Carr's 1998 paper Randomization and the American Put, he sets up the following ODE for the value of an American put with expiration given by the first jump time of a Poisson process with rate $\...
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Match different option high frequency databases
I downloaded the “E-mini S&P 500 (Dollar) Options for 1/10/11” Top-of-Book (BBO) data. If you are interested you may download the data from the following link (approx. 80MB zipped and 1GB unzipped)...
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Are there academic papers on the 'term structure' of adverse selection for futures and options?
By term structure I mean a non-stationarity in the pattern of intraday adverse selection as a given instruments approaches its expiry. Note that I am interested in the adverse selection on the ...
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Modeling market sentiment and pricing options by volume, open interest
Are there any empirically-proven methods/formulas for weighting IV surfaces, pricing a discount/premium in an option, and/or adjusting any of the 1st- or 2nd-order Greeks for the magnitude (volume or ...
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Forecasting amount of slippage in executing option spreads
Is there a good quantitative model to estimate how much slippage is required to execute a particular option spread trade?
For example, let's say you want to execute an Iron Condor. Given X, Y, Z ...
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How to price an option with two volatilities?
Imagine you have two volatilities, the second which is "activated" when the stock crosses a barrier called $p_b$. The present price is $p_1$. ($p_b>p_1$).
This can be used to price options after a ...
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What is the longest number of consecutive days that options implied volatility has stayed "extremely high" for any particular underlying?
Curious as to whether or not there is any sort of all time record. Any index, future, or stock will do. Volatility must be well above the average 1 year volatility for all periods.
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Correlation sensitivity of Rainbow options
I read from various sources (eg. Exotic Options and Hybrids, M. Bouzoubaa) that the correlation sensitivity of Rainbow options (say a call price on a basket made of 50% of the best stock, 20% of the ...
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Popular treasury futures bond options volatility surface model/s
I am looking for volatility surface parametrisation model used for treasury futures bond options. I know that most popular for options on equities its SVI, on FX its Vanna-Volga, on rates its SABR. ...
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When calculating VIX, how to deal with the problem of asymmetry of put and call data?
I'm trying to calculate the VIX index according to the methodology of CBOE. I am looking at commodity options. I found that at some time, like at this minute, there are 13 call options out of the ...
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How an Option market-makers make money?
This might be a very broad question, but I would like if someone can please explain to me how a market makers make money in Options market ? Thank you
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Single barrier options in stochastic volatility models
In this note/sketch, I derive among others a closed-form formula for an up and in put (UIP) in stochastic volatility models of the form
$$
dS(t) = \sigma(t) S(t) \left[ \rho dW(t) + \sqrt{1-\rho^2} dZ ...
user34971
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Delta of FX Options, Different Currency in Trading Book - Trading Interview Question
Having done stochastic analysis in university, together with tons of other math courses, do never prepare you for an actual interview in trading. Stumbled on what I believe might be an easy question, ...
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Cash less exercise and redemption feature in SPAC warrants
Public and private warrants of a SPAC post merger (Initial Business Combination or IBC) are often very similar. Notable differences are 1) cashless exercise of the private warrants and 2) redemption ...
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Deriving Bachelier Greeks
I am working on the Bachelier Model with r not equal to 0 as described in the first and most upvoted answer in following link:
Bachelier model call option pricing formula
This is fairly easy to code ...
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CMS cap has more vega exposure than CMS floor for same strike
When I priced a 10y expiry single look CMS30 ATMF CAP, I noticed that the vega exposure is higher than that of the same 10y expiry single look CMS30 ATMF FLOOR. Why is that?
I have a suspicion that it ...
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Why does it hold true that $\theta_{t} d\overline{X}_{t}$ is a local $Q$ martingale if $\overline{X}$ is a local $Q$ martingale
I am learning from Bernt Oksendal's Stochastic Differential Equations and on page 276 Lemma 12.1.6, it is stated that:
The existence of an equivalent martingale measure $Q$ on the discounted price ...
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Pricing/Hedging a yield curve spread option (YCS)
I have 2 perspectives as to what model to use for a YCS option:
It is an at the expiry option, so hit the marginals, correlate them with a copula, and be done with it.
To hedge the vega, I will need ...
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Far OTM calculation issue on Bjerksund-Stensland
Has anyone come across and fixed calculation issues on boundaries using Bjerksund-Stensland 2002 (Hull, Haug or Rouah implementations) ?
Thanks in advance
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For any twice differential continuous function C(T, K), does there exist a sigma(t, S) that can reproduce C(T, K)?
In the Dupire's paper, he assumes that there exits a function $\sigma(t,S)$ that can reproduce $C(T, K)$. My question is that: is the assumption true for any twice differential continuous function $C(...
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