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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Modelling forward and correlation dynamics for options on the best-of multiple commodity spreads

I am looking at best-of options on futures (commodities), let's take for example the following payoff specification: $ max(a_{1}-c_{1}, \ a_{2}-c_{1}, \ a_{3}-c_{1}, \ b_{1}-c_{1}, \ b_{2}-c_{1}, \ ...
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Best approach to select strike prices for an Iron Condor?

Options beginner here. I'm aware of three popular ways to select strike prices for Iron Condor. Select strikes such that they are equidistant from the CMP. Select strikes such that the they form a ...
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Does the usual theory (e.g. Black-Scholes) make sense for FX options?

When you open any book about option pricing theory, you have this kind of setting: A risky asset whose value at time $t$ is $S_t$. A risk-free asset whose value at time $t$ is $S^0_t$. A portfolio ...
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Options Market making, what to do with ITM options

I am a option market maker. Say at some point in the time, I end up having only but ITM options in my portfolio and I want to reduce my risk exposure ( delta, Vega, gamma), what can I do to make ...
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Weekly S&P500 options price data

I cannot find free data on S&P500 options price, call and put, at different strikes of weekly options, on a daily basis, with maximum and minimum prices. I would like to have this data to study it....
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The option is "purer" in its risk---what is meant by this?

In the book "The Concepts and Practice of Mathematical Finance" author M. Joshi writes on page 12 the following: "From the point of view of risk, we can regard an option as an attempt ...
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Option's Delta Investopedia Question

New to this. In this Investopedia article on Delta the following looks like a typo - How Do Options Traders Use Delta? Delta is used by options traders in several ways. First, it tells them their ...
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What do "heating degree day" prices actually measure?

The futures for Dallas Heating Degree days for July 2022 are trading around 6.83 But Dallas is hot in July and does not typically get any heating degree days So, what does the 6.83 for July 2022 ...
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Pricing Options on Inefficient/Illiquid Assets

I'm currently trying to gather more information on option pricing in very inefficient markets for the underlying. By inefficient, I mean markets with consequential bid-ask spreads (5% or more) and ...
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When is the gamma of an iron butterfly spread positive? (Assuming stock price at t=0 is equal to the highest strike price)

I know the Gamma of a butterfly using calls is $$\Gamma_{butterfly} = \Gamma_{C_{K_3}}-2\Gamma_{C_{K_3}}+\Gamma_{C_{K_3}}$$ Where K3-K2 are the same as K2-K1 and S=K1, But under what condition is the ...
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Payoff of a Butterfly spread under risk neutral measure is always positive for any t<T

In a situation where $$K_3-K_2=K_2-K_1=h>0$$ and $$K_1\le S_t\le K_3$$ where $$S_T=S_t.e^{[(r-\sigma^2/2)(T-t)+\sigma(W_T-W_t)]}$$ (i.e. Stock process follows GBM under the risk neutral measure). I ...
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Do you roll back the maturities and schedules when backtesting VaR for portfolios of bonds, options or future contracts?

I want to backtest VaR models which are applied to portfolios of products which have maturities (options and futures) and even schedules (bonds). I have a question which never came up when backtesting ...
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Finding optimal option to maximise gains under given price hypothesis

Let's have Stock S at \$100 on January and my hypothesis is S will be trading at \$150 in July. Is there any Python/R package that I can feed with option prices from my broker and it would return the ...
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Pricing any Payoff structure using Binomial Tree(Pricing DDTPS)

I just wanted to confirm if its theoretically possible to value any derivative with a payoff that can be replicated by a portfolio of options,underlying and bonds. I wanted to value DDTPS which is a ...
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What is gamma to do with realized volatility?

I keep hearing that gamma is a bet on realized volatility. That is, if we are long gamma then we need higher realized volatility to come in the future in order to make a profit. from other source: If ...
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How to compute the price range for an American call and put option?

A non dividend paying stock has the following details for its European option: Time to expiry – 1 year, Risk free interest (Continuous)- 5%, Exercise price = 42, Current Stock Price = 40, Call option=...
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What is the optimal time for exercising American call and put option?

A 9 month American option (underlying) is known to pay dividend of USD 1 and USD 0.75 at the end of the ...
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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 ...
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How to price an Equity Structured products [closed]

I'm new to equity structured products, I understand the overall construction but I want to have an example of an equity structured product with the steps of creation from seller point view of this ...
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implied vol smile relative to atm vols

Am I correct in saying that most stochastic vol models are meant to behave in a way that as atm vol goes up the smile comes down and risk reversals become "less stretched?" - by that i mean ...
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Negative-gamma delta hedging (for a call option writer): how will the stock price affect the portfolio profit?

Suppose a (European) call option writer is hedging their risk by taking a long position in stocks (holding $\delta_C$ shares). The value of the portfolio is $V(S)=\delta_CS-C$. Then is the gamma of ...
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Does it matter that Bachelier IV differs from BS IV for a given option price?

In one sense, it’s just an accounting convention, so it doesn't matter. In another sense, the implied volatility can be interpreted as the minimum realised volatility which implies that your option ...
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Cross Gamma PnL Formula

sort of dumb question. I understand well the relationship between Gamma/Theta pnl for options on single underliers. I'm (attempting) to move onward and upward to options on baskets. Conceptually, I ...
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Deriving strike from Delta

According to the following thread: How can I calculate the strike price or implied volatility from a given delta? To back out some strike given some Delta, you simply use realized vol (plus a few ...
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Short put prices different strikes

I was looking at Robinhood and can't find a rational reason for a put price for the $\\\$117$ strike to be higher than both the $\\\$116$ and the $\\\$119$ strike.
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Computing Delta-Hedged Option Returns

I was reading some papers on delta-hedged option returns and came across an intriguing paper that I found quite interesting. However, I was a bit confused on the authors' methodology of computing ...
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Best Way To Compute the Volatility Risk Premium

I'm trying to come up with a measure for the volatility risk premium (VRP) for a strategy I want to implement, but I'm not entirely sure how to proceed. My situation is as follows. The underlying is ...
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Approximating SPX index skew using PutDex & CallDex

I hope someone can help me with this. As I don’t have access to historical options data I am wondering if it is possible to deduce SPX options skew from various volatility indices - in particular ...
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When does the underlying become the derivative?

Since options contracts are created by open interest in the contract, it is conceivable that the notional of the total options contracts can exceed the value of the underlying. If that happens, does ...
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Quantlib in Python

I have been playing around with QuantLib in Python and have been struggling with couple of simple tasks I would like to share and hopefully get help from the community debugging: The fact that it's c++...
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Volatility Options

I'm working on a scenario needs to price an option on volatility. After googling, there is no clear relevants in this field. VIX options pricing is one way, while seems it takes the VIX (a volatility) ...
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Put call parity with american options

I am trying to back out the put call parity price of an American call option for a 10 min period with tick data (using CME ES Futures Options in this example, see plot below), using the standard PCP ...
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BKM risk neutral moments in python

I am trying to compute the BKM implied moments (Bakshi, Kapadia and Madan 2003) in python by following this paper: Neumann, Skiadopoulos: Predictable Dynamics in Higher Order Risk-Neutral Moments: ...
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Showing that pnl from gamma and theta cancel

I've seen a few questions state without proof that $0.5 \Gamma S^2 \sigma^2 = \Theta$. That is, the gamma and theta pnls cancel out. For example: Relationship between time decay and gamma My question ...
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Term for a class of multi-asset options that determine the joint distribution of a set of assets?

For a single asset we can infer (in theory) the exact distribution of future outcomes via option prices: Either via option butterflies or the Breeden-Litzenberger formula. Is there a name for (one of) ...
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How would one construct a volatility surface given only the spot price?

The traditional way to build a volatility surface is to pull options data and then do some form of interpolation. What happens if there is no existing options market and only a spot market for asset X?...
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Is float32 enough for option pricing?

Most quantitate libraries use float64 precision for monte-carlo or other method. Some academic papers do experiments on float16 and find it has some restrictions on float16. I just wondering if ...
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Option name: mandatory exercise, unknown date

What is the name for an option with mandatory exercise but where the holder can choose the exercise date? Is this even an option since there is mandatory exercise? Mainly interested in a situation ...
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The Wikipedia formulas for Vanna differ by a factor of 100x, why is that?

For a given: Stock price ${\displaystyle S\,}$ Strike price ${\displaystyle K\,}$ Risk-free rate ${\displaystyle r\,}$ Annual dividend yield ${\displaystyle q\,}$ Time to maturity ${\displaystyle \...
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Is this the right way to accelerate my Monte-Carlo Simulation

I am trying to develop a pricer for Call VS Call and I'm using MonteCarlo method to do so because my stocks are correlated between each others. Basically my inputs are ...
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Put call parity with real time tick data

I am working with some real time options tick data (mainly futures options and index options), and in many cases the quotes are single sided (as seen on bloomberg terminal). I will denote a quote as ...
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Option implied risk neutral distribution vs BKM risk neutral moments

I am doing some research on the option implied risk neutral distribution and methods calculate it, and so far have come across two ways to do so. The first way is through the Breeden-Litzenberger ...
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Implied vs historical volatility in option pricing

I discussed recently with a trader who told me that put options are priced using historical vol, and call are priced using the implied one. My guess would be that as the put option market is much more ...
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What is Phi in Cox-Ross-Rubinstein Binomial Model?

I have a question regarding the Cox-Ross-Rubenstein (CRR) model (Cox et al.,1979). While I do understand how the model is constructed, I am now trying to put it into code and am not sure how to ...
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Quantlib: day-by-day evaluation of option value

I'm using Quantlib in Python to price an FX option. I'm comparing the result to Bloomberg, to make sure the code is working correct. I want to calculate the P&L of a certain option trading ...
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Quantlib: Greeks of FX option in Python

I'm using Quantlib in Python to price an FX option. I'm comparing the result to Bloomberg, to make sure the code is working correct. I also want to calculate all the Greeks, and eventually use those ...
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Systematic trading strategies - Selling 1M Straddle

I am trying to compute the daily P&L of the following systematic trading strategy: sell each day a 1M straddle on EUR-USD from 04th January, 1999 to today. My dataset contains the strike, the spot,...
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What is the name and payoff of this exotic option (where the holder can lock in a price)?

An exotic option is described as follows: Let $S_t$ be the underlying at $t$. The holder has the option to lock in the current price during the lifetime of the option, which he does for $S_{t}=50$. ...
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Option P&L over time

I would like to compute the evolution of the P&L of an FX plain vanilla option. Unfortunately, I am not sure about the correctness of my reasoning. Let's imagine that I sell a 1W call option on a ...
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How can you compare Vega between strikes?

Given a specified maturity is there a way to compare Vegas between different strikes? Surely the Vega of an ATM option will be very different from the same Vega of an OTM option
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