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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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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Term Structure Model : 10 Period Black Derman Toy Model
Hello, please assist me with the answer to this question. I've been stuck for quite some while.
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How to price vol for options on forwards when forward settlement does not match option expiry
This is a question about how to compute vol for non-listed options for OTC pricing
Say you have the following quoted options on commodity futures (option expiry/fwd contract settlement):
2 months / 2 ...
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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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What to use as the risk-free rate when working with historical data? [duplicate]
When analyzing option data, the concept of a risk-free rate is at the basis of risk-neutral valuation/discounting and when working with historical option data, I assume this is not much different. ...
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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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Vega hedge an average priced option using bullet or shorted option
I was looking at a portfolio which contains mainly Average monthly options( APO ), and trying to hedge it. delta hedge is fairly straightforward when we assume the underlying is liquid, but what about ...
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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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Trying to understand bloomberg's OVML quanto adjustments for commodities options
In the image we can see a screenshot of OVML pricing an option on soybean futures.
My main issue is that I expect the quanto forward to align with:
F_qto = F * exp(-rho * asset_vol * fx_vol * T), but ...
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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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How can one price European digital options across strikes using only a single realised‐volatility estimate?
I’m in a setting where no implied‐volatility surface exists (e.g. illiquid or bespoke contracts). All I have is a single realised‐volatility (RV) number for a fixed tenor, which correctly reproduces ...
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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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Why is the forward measure needed for options on futures when the risk-neutral measure suffices?
I have been running around in circles with this attempting to make sense of this.
Universal pricing theorem
Given a numéraire asset $(N(t))_{t \geq 0}$ such that for all tradeable assets $(S(t))_{t \...
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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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Why Deep ITM European Put Options have positive vega?
Could you explain, not from the perspective of B-S formula, but from intuition, why Deep ITM European Put Options have positive vega?
To take an example, if I have a European put options on a stock, ...
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