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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How to calculate the most realistic historical option prices with additional publicly available parameters
This is a follow up question of this one.
My aim is to create the most realistic historical option prices possible with publicly available data. I want to do this for backtesting purposes.
The ...
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Calculating dealer gamma imbalance/exposure for an options strip
Have seen this being done for years (primarily by J.P. Morgan and a couple other bank research desks) and am attempting to re-create for my own personal research. I’ve read the forums on here but no ...
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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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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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using quantlib function in my c++ program
I want to include the QuantLib function for option greeks calculations in my own C++ code.
My question is: can I just include those functions? I don't want to use the rest of their stuff.
I obviously ...
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Path-dependent options valuation
Assume that we have an arbitrage-free and complete market. The well known formula for the arbitrage-free price of an attainable derivative $X$ at time $0 \leq t \leq T$ is given by:
\begin{align*}
V(t)...
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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 ...
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What are popular metrics for Option Skew?
What are popular metrics to track skew? Would it be the difference between OTM option and ATM option IV? Would it be a percentage difference in IV?
Also, if both are valid, would a % change be ...
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What is the intuitive reason why the Gamma and the Theta tend to have the opposite sign?
Quoting Hull's book:
When gamma is positive, theta tends to be negative. The portfolio
declines in value if there is no change in S, but increases in value
if there is a large positive or ...
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How to calculate Implied Volatility for out-of-the-money options?
I'm trying to calculate the implied volatility for out-of-the-money options, and to a lesser extent, in-the-money options. Most of the literature estimations I could find for implied volatility were ...
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How to price an option allowing to change a call into a put?
A recruiter asked me this question:
Suppose you have the following contract:
a call option with maturity $T$ = 2 years
the possibility to change this call into a put at $t$ = 1 year
What is the ...
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What is the market standard for IR option pricing when moving to SOFR
From books it looks like market standards to price IR options, like swaptions, are SABR, LMM or mix of the two (SABR-LMM).
But LMM models the forward LIBOR rate. What will happen to it once LIBOR ...
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Replicating portfolio and risk-neutral pricing for interest rate options
For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing ...
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How do you calculate the implied liquidity of an option?
How does one calculate the implied liquidity of a specific option contract given a set of vanilla puts and calls with various strikes and maturities on a single underlying?
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Swaptions Gamma Interview Questions
A while ago, I interviewed for a trader role and was given the below assignment (I didn't get the job). I wanted to revisit the questions to learn from my mistakes and be better prepared next time. ...
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How we can derive the PIDE of double exponential jump-diffusion model (Kou model)?
I'm working in double exponential jump-diffusion model known as the Kou model with following form, under the physical probability measure $P$.
$$ \frac{dS(t)}{S(t-)}=\mu dt+\sigma dW(t)+d(\sum_{...
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What's the point of discounting in risk-neutral pricing?
Let $\phi$ be a self-financing strategy that replicates a time $T$ option payoff $X$ on stock $S$. By definition of a trading strategy, $\phi$ is previsible. Finally, let $V_t$ be the time $t$ value ...
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Model Price vs Market Price in terms of Fair Price (Options)
Before I start: Ok, this is something I investigated for a fair amount of time and my question is semi-academic. To simplify, I will introduce the short bit (TLDR) of my question and then lay out ...
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The Holy Grail of Volatility Modelling: The SPX & VIX - Why?
I am currently researching a pre-print article by Julien Guyon & Jordan Lekeufack (2022): Volatility Is (Mostly) Path-Dependent.
Their model is quite impressive in both its simplicity, as well as ...
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Vanilla Option Prices from Local Vol Surface (using neither MC nor PDE)
There are numerous papers that describe the derivation of the Local-Vol equation using available market prices of options. For example:
Dupire's formula (see e.g. OpenGamma (2013)) gives us LV in ...
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Can one use options on Treasury futures to hedge a portfolio?
Can one use options on Treasury bond futures to hedge a typical fixed income portfolio? If so, how can one estimate the duration for an option on a Treasury futures contract, and taking this a step ...
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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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Why do ATM call options have a delta of slightly bigger than 0.5 and not 0.5 exactly?
From the formula of the delta of a call option, i.e. $N(d1)$, where $d_1 = \frac{\mathrm{ln}\frac{S(t)}{K} + (r + 0.5\sigma^2)(T-t)}{\sigma\sqrt{T-t}}$, the delta of an ATM spot call option is ...
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Heston Model Integration Oscillations
Is there a way to reduce oscillations for the numerical integration when evaluating the Heston model. I am pricing a series of 5000 options scattered over the Heston model parameter space and I find ...
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What really drives option implied volatility?
A common and oft repeated belief regarding options volatility is that implied volatility increases due to people bidding up a contract, usually related to anticipation of the outcome of an expected ...
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Breeden-Litzenberger formula for risk-neutral densities
Based on this topic:
How to derive the implied probability distribution from B-S volatilities?
I am trying to implement the Breeden-Litzenberger formula to compute the market implied risk-neutral ...
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Papers and algorithms on bidding schemes for best order execution?
I'm building an automated option trading bot that executes common options multi-leg strategies (straddles, spreads) and I want to learn the best way to execute my orders.
As you know, the bid-ask ...
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Basket option pricing: step by step tutorial for beginners
I would like to learn how to price options written on basket of several underlyings.
I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in ...
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What changes to put-call parity are necessary when evaluating american options on non-dividend paying assets?
If an underlying doesn't pay dividends (for our purpose defined as any distribution to the underlying's holder) directly or indirectly (e.g. options on futures) how does put-call parity change from ...
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What is the industry standard pricing model for CME-traded Eurodollar future (American) options?
The CME-traded Eurodollar futures option is an American option.
What is the industry standard pricing model for this product?
Does the industry practice to treat CME-traded Eurodollar futures ...
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How to approximate the time to mean reversion for implied volatility
Given an option and its implied volatility, and also the mean value of the implied volatility over the last 30 days, if we find that the current IV is significantly (> 1 std dev.) away from the mean, ...
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Derivation of the formulas for the values of European asset-or-nothing and cash-or-nothing options
The asset-or-nothing European option pays at t = T the value of the stock when
at time T that value exceeds or is equal to the exercise price E, and nothing if
the value of the stock is below E. So, ...
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Black Scholes vs Binomial Model
I'm trying to confirm my understanding of the 2 models. It is my understanding that the black-scholes is a special case of a binomial model with infinite steps.
Does this mean that if I were to start ...
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Call option arbitrage opportunity
I am having trouble wrapping my head around some text provided to us by our lecturer (unfortunately he is currently unavailable). If we let $c$ be the price of a European call option, $S_0$ the ...
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Simple model for option premium (for covered call simulation)?
Given a historical distribution of weekly prices and price changes for a stock, how can I estimate the the option premium for a nearly at-the-money (ATM) option, say with an expiration date 3 months ...
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Does it make sense to use upward and downward volatility in option pricing?
Historically stocks have a higher likelihood to increase in price than to fall in price. As such would it make sense to split a stocks volatility measurement into upward and downward components?
For ...
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Valuing a warrant on a warrant
How would you go about valuing a European warrant that entitles you to a) 1 share of a company and 2) 1 warrant on that same company?
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Prove or disprove "If at least 10% of an option's value is time value, it has a delta less than 90"
"If at least 10% of an option's value is time value (ie. time value >= 0.1*call price), it has a delta less than 90".
In practice and after doing many tests with an option pricing calculator, this ...
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Can American options with no dividends and zero risk-free rate be treated as European?
Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the ...
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What is more appropriate: the EMA of the option price or the EMA of the underlying?
I'm progressing, all too slowly, on a site that aims to show real-time numbers for options that are listed on the CBOE. Most of the instantaneous numbers are all set. Now I'm going to pay attention to ...
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How are the BKM risk-neutral moments derived?
I've been doing a lot of research on implied volatility skewness, and one of the most commonly cited papers I've come across is "Stock Return Characteristics, Skew Laws, and the Differential Pricing ...
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What do we really mean by put-call ratio and how should it be expressed?
I need to calculate the put-call ratio for an American option. But I'm a complete naïf: I don't know how. I think I'd use the put open interest and the call open interest. I can imagine two ways to ...
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VIX = Vega of S&P500 options?
ok, so let assume I can predict the daily change in the VIX itself (in points) every day. what would be the best way to play this with OPTIONS? well, obviously VIX options, but if I can look at the ...
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When pricing options, what precision should I work with?
I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and ...
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How sensitive are vertical spreads to changes in implied volatility?
How sensitive are vertical spreads to changes in volatility / implied volatility in the money, at the money, and out of the money?
I'm thinking for 1 point spreads this would be very small / neutral ...
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Heuristics for calculating theoretical probabilities of being ITM at time T for listed options
I'm looking for a heuristic way to calculate the probabilities of being in the money at expiry for non-defined risk options combinations (listed options).
I use delta as a proxy for this probability ...
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Vega of exotic options
I'am wondering if there is a standard definition to the Vega of an exotic product when the underlying model is not Black-Scholes.
Let me give some examples :
What is the Vega if the price is ...
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Creating Options Database
I am trying to create a database which will hold information for various stock options and will need to be updated daily. The idea is to use this database to keep track of changes in the open interest ...
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What are VIX back-month futures based on?
The VIX calculation is a weighted average of prices for front-month out-the-money options on the S&P index.
So for VIX futures, this makes sense for the front month vix futures (being based on a ...
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How can one determine approximately what percentage of options trades are buyer-initiated vs. seller-initiated?
How can one determine approximately what percentage of options trades are buyer-initiated vs. seller-initiated? What measures of order flow are available specifically for options, preferably for ...