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.
2,624 questions
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Market impact models for vanilla options
What are the common ways of modelling slippage (bid/ask spreads + market impact) of vanilla options?
E.g. in linear instruments it is common to model the costs as a term proportional to bid/ask spread ...
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Single Callable Bond - from Option Price to Z-Spread
The pricing software I use requires the specification of a z-spread for the valuation of a single callable bond. According to many sources, however, the Z-spread is determined based on the bond price, ...
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Convergence of Numerical Methods on Lookback Options in R
I have been practicing using R code for my Quant course and I came across an issue when testing the convergence of numerical methods for lookback options to the analytical solutions provided by Hull ...
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Capped Option Value
I am trying to understand intuitively how to price the following:
Suppose I have a call option today that is worth fair value $V_0$.
At any time, you can sell the option at $V_o$, in part or in whole.
...
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How to price 0DTE options?
I am trying to write a function that uses Quantlib to price 0DTE options. The use-case isn't real-world trading or pricing, it's a tool for myself to roughly model option-price dynamics relative to ...
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Compo options on forwards - computing vega correctly
Trying to price compo options on commodity forwards and wondering how vega should be represented.
The vol used to price is the "composite vol", which is:
$$\sigma_Y = \sqrt{\sigma_{udl}^2 + \...
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Option Hedging: simulation of cumulative hedged paths and discounting
I'm trying to replicate the Figure 5.1 at pag 96 of Volatility Smile by Derman & Miller where they show that the (cumulative discounted) P&Ls of a hedged portfolio, where the call is evaluated ...
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Mid curve options on 1M SOFR futures
Are mid curve options traded on 1M SOFR futures as they are for 3M?
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Where to get market prices for Vanilla Call Options
I have implemented a SABR(Stochastic Alpha, Beta, Rho) model. I am in the process of calibrating Alpha, Beta, Rho values as per market prices
Can someone suggest where can I get the actual market data ...
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Option contract and directional trade
I am referring below article from Bloomberg.
https://www.bloomberg.com/news/articles/2025-08-01/goldman-told-clients-to-go-long-copper-a-day-before-price-plunge
One particular thing that caught my ...
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Use Options Vertical Spreads to Find Probability of Distribution
I saw this interesting argument that you can use the value of a put spread to find the approximate market implied probability of underlying finishing below the mid point of the two strikes, assuming ...
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Implied Volatility Approximated with Average of Local Volatilies: where are the paths?
In the book The Volatility Smile by Derman & Miller, at pag. 262, is given this approximation of the implied volatility in terms of local ones:
$$
\Sigma(S,K) \approx \frac{1}{K-S}\int_S^K\sigma(S'...
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Volatility of Hedging Error and Statistical Uncertainty of Estimates
In The Volatility Smile book by Derman & Miller at pag. 113, I don't understand the statistical uncertainty in the measurements of volatility and how to interpret the notation.
The authors state ...
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Volatility smile construction for fx options confusion
I am working through the paper "FX volatility smile construction" by Wystup and Reiswich (2010). I am trying to replicate the results they obtained with the model they define in the paper.
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Realised American Put Premiums from Historical Data?
It's possible to calculate European Put Premiums from historical data (see plot below) as:
$$P_{eu}(K|Q_{vol}) = E[(K/S_T-S_T/S_0)^+|Q_{vol}]$$
It's not possible to estimate Americal Premium same way. ...
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structured bond exercise
I'm struggling to find the value of this structured bond, especially understanding how to construct this payoff with options.
My idea was to sum Zero coupon + Coupon Bond + Short put. But doesn't make ...
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Fit Option Premium Surface directly
Goal - smooth surface to interpolate option premiums, over sparse and noisy market data. OTM puts and calls only, ITM ignored.
It's possible to approximate it indirectly, by choosing underlying ...
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Implementation of standard stretched Brownian motion in Python
I am trying to implement a standard stretched Brownian motion 1,2in Python. This requires finding a fixed point of the equation
$\mathcal{A}:CDF \to CDF$,
$\mathcal{A}F = F_\mu \circ(\phi*(Q_\nu \circ(...
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What is geometric or physical meaning of American Option?
The premium of the European Option C(K) is the center mass of the density beyond the K (center mass - if you shift x axis, so 0 will be in K).
Is there a similar way to express visually or physically -...
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How to quantify Vega PNL from volatility moving along a steep moneyness surface when bucket Vega shows zero?
Based on this answer:
Question:
When the implied volatility surface remains identical over two consecutive days, my current Vega P&L calculation yields zero. However, market movements cause ...
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path dependency when delta-hedging options
I've heard often that unhedged option PnLs have path dependency, but when you delta-hedge options, that removes the path dependency. I've seen the formulation that for a delta-hedged PnL, under ...
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Pricing far OTM CALL via Put-call parity is different from Expected Value
With real probabilities, to price call option $C(K)$ we need to know $[K,\infty)$ part of the distribution.
Which is hard for OTM calls with $K > 1.5$ as the probability estimation errors grow ...
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question about short strangle rollup
As the title says, about a week ago
sto 6/20 TSLA.CALL 390
sto 6/20 TSLA.PUT 300
I know that 30dte options are less sensitive to gamma and it's easy to achieve delta neutrality
Lately, TSLA has been ...
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What is the purpose of risk neutral valuation vs replicating portfolio approach
I'm currently writing a bachelor's thesis on GPU accelerated option pricing algorithms. As a CS major I'm not knowledgeable on the higher level math, but I have tried learning the basics of option ...
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How to see which ETOs on CME have futures-style vs equity-style margining
CME describes two styles of determining variation margin on exchange-traded options: equity-style and futures-style, and indicates that the margining style affects the value of a contract.
https://www....
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