# 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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### Implied state price density (Question 1 - derivation of the formula)

I came upon the term "implied state price density" in a couple of papers. As far as I understand the concept one basically tries to extract the "pricing density" from the market data. For the sake ...
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### Lower bound of ITM Calls when computing Implied Volatility

Assuming the Black Scholes model and pricing formula of a European call option. Then, if the call is ITM, i.e. if $ln(\frac{S}{K})>0$, the $d_1$-term will go towards infinity as $\sigma$ goes to ...
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### call vs put open interest

I have been observing the data for US stock options. In general, it seem like there are more open interest for call rather than for put, is there a reason people like to write more call? at the ...
830 views

### Pricing when arbitrage is possible through Negative Probabilities or something else

Also now asked about here: Is it fair in an introductory stochastic calculus/derivatives pricing class to ask for the price when absence of arbitrage is violated? Assume that we have a general one-...
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### Other numerraire choices when applying Feynman Kac

all of the books and notes I have seen on the Feynman Kac formula mostly applied to Risk neutral measure, i.e. different interest rate models, stochastic volatility, etc. I think risk neutral measure ...
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### How does an option's time value depend on moneyness?

How does an option's time value (also known as extrinsic or instrumental value) depend on how far it is in the money or out of the money? In other words, how does the time value change as the ...
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### Greeks for binary option?

How to derive an analytic formula of greeks for binary option? We know a vanilla option can be constructed by an asset-or-nothing call and a cash-or-nothing call, does that help us? Wikipedia states ...
3k views

### pricing using dupire local volatility model

I am reading about Dupire local volatility model and have a rough idea of the derivation. But I can't reconcile the local volatility surface to pricing using geometric brownian motion process. If I'm ...
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### European Call price for an asset with mean reverting (Vasicek model) dynamics

Let's look at a stock with a mean reverting price dynamics: $$dS_t = a(S-S_0)dt + \sigma dW_t$$ If we let $\sigma=0.25$ and $a=-0.5$ then the variance of this process is: $$Var(S_t) = 0.199\sim0.2$$ ...
511 views

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### Why FX Vanilla Options are quoted in volatility

I've been curious why vanilla options are quoted (and traded) in terms of volatility. Considering that every financial institution has its own options pricing model, volatility as an input would cause ...
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### Link between Vega and Gamma

"The vega is the integral of the gamma profits ( ie expected gamma rebalancing P/L) over the duration of the option at one volatility minus the same integral at a different volatility......
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### Pre-trade evaluation and risk assessment of option trading strategies (in market practice)

When a trader gets conclusion of the volatility is being underestimated (via volatility cone or some other technology), actually there are multiple ways for his trading. (Let's assume the underlying ...
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### Why are options called what they are called?

This may be a very obvious question, but can someone tell me where and when the names call and put originated? And similarly, where do the terms American and European option come from? Aside from the ...
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### Constructing an approximation of the S&P 500 volatility smile with publicly available data

Besides of the VIX there is another vol datum publicly available for the S&P 500: the SKEW. Do you know a procedure with which one can extrapolate other implied vols of the S&P 500 smile with ...
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### Which is riskier: a call option or the underlying?

From Joshi's Quant Interview Questions and Answers: What is riskier: a call option or the underlying? (Consider a one day time horizon and compute which has bigger Delta as a fraction of value). I ...
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### Call vs. Put Option

I have two interrelated questions that have been bothering me for some time. I have read all the stuff online and it still doesn't make sense to me: Let us assume: 0% interest rate (both hedge ...
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### Can the concept of negative probabilities be used to price a call option?

Edit: I'm a dumbass. The thing below is supposed to be just the motivation of asking. I want to ask for below and in general, hehe. Assume that we have a general one-period market model consisting of ...
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### Where can I find API access to historical options data? Paid or free?

I'm looking for a company or website that provides API access to historical options data. I would prefer a provider that has a python module to access the API. Any leads would be appreciated.
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### Why is the vega of an at the money option so insensitive to movements in volatility? I.e, why do ATM options have such little Vomma?

I've been trying to understand why at the money options have very little vomma. I was reading and came across a graph that showed vega as volatility changes and I couldn't grasp how the relationships ...
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### What is the importance of alpha, beta, rho in the SABR volatility model?

I just read that SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the ...
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### How do you check your option calculations?

I'm implementing a bunch of different algorithms to price options/find Greeks: finite difference, Monte Carlo, binomial... I'm not really sure how to check my calculations. I tried using QuantLib to ...