# Tag Info

10

You may want to first broadly categorize volatility models before comparing between them within each class, it does not make sense to compare standard deviation models with an implied vol model. I would broadly classify as follows: Historical realized volatility: Those include standard deviation (sum of squared deviations), realized range volatility ...

6

The Black-Scholes option pricing model provides a closed-form pricing formula $BS(\sigma)$ for a European-exercise option with price $P$. There is no closed-form inverse for it, but because it has a closed-form vega (volatility derivative) $\nu(\sigma)$, and the derivative is nonnegative, we can use the Newton-Raphson formula with confidence. Essentially, ...

6

It is a very simple procedure and yes, Newton-Raphson is used because it converges sufficiently quickly: You need to obviously supply an option pricing model such as BS. Plug in an initial guess for implied volatility -> calculate the the option price as a function of your initial iVol guess -> apply NR -> minimize the error term until it is sufficiently ...

4

First of all, may I point out two big misperceptions that you may have: Implied Volatility (IV) is the input to any vanilla option pricing model (not just Black Scholes (BS) that impacts the pricing the most. You can verify this by flipping through the different risk exposures (greeks and higher order sensitivities) and study mean volatilities in such risk ...

4

In that white paper itself they quote where it came from: “More than you ever wanted to know about volatility swaps” by Kresimir Demeterfi, Emanuel Derman, Michael Kamal and Joseph Zou, Goldman Sachs Quantitative Strategies Research Notes, March 1999. This is a classic article which you should definitely read if you are trading volatility. While there might ...

4

You can see concavity in mean-reverting underlying assets where the option tenor is comparable to the characteristic reversion time of the asset. For a geometric brownian motion, all underlying prices are possible, so any mean reversion or other limitation on large changes that might occur in reality would ultimately appear as a skinny tail and negative ...

3

So we have the identity $$g(S,\sigma, t, C,C_t,C_S,...)=g(S, t,\sigma, V,V_t,V_S,...)$$ where $S$, $\sigma$, and $t$ are independent variables and $V=V(S,\sigma,t)$, $C=C(S,\sigma,t)$ are some unknown functions. But we can also treat the above identity formally and assume that the functions $C,C_t,C_S,...,V,V_t,V_S,...$ are themselves independent ...

3

I think you would find the following paper very useful. It compares different pricing models applied to VIX options. You can use it as starting point to apply to VSTOXX options and see where it gets you. The Performance of VIX Option Pricing Models: EmpiricalEvidence Beyond Simulation The following models were tested: Whaley (1993) Grunbichler and ...

3

This is definitely a valid (and possibly viable) strategy. I think that your constraint of zero costs is a red herring and serves no useful purpose beside forcing you to take lopsided bets in the direction of the cheaper option. I would try instead to build a portfolio that has zero vega (hedged against overall moves in market-wide implied volatility) and ...

3

If you look at tick data, you will probably get an even better analysis. However, vix correlation tends to be negative with spx but remember that this is generally more true for when spx tanks. When spx goes up, the correlation isn't as strong. Why? People panic after a drop, therefore leading to people buying options. They don't care about black scholes ...

3

Squaring normally distributed variables results chi-square distributions, which (as you imply) is why the chi-square distribution is used in hypothesis tests for the variance. If you estimate a Garch model and obtain the conditional variance at every point in time, you could use a chi-squared hypothesis test to ask a question like is the variance in a ...

2

There are essentially two approaches you can take: Approximate changes in IV by establishing a relationship between IV and option prices through a function of IV solely dependent on option price. While it is computationally very convenient it introduces huge estimation errors in certain cases. As pointed out in my comment above one such case is a slide in ...

2

If you can get anywhere close to the same open-interest and volume using European options as the corresponding American ones, you'll have a much easier time just using them. American options with high probability of early exercise don't contain information about that back end of the vol surface, and it's kind of hard to decide just what to do with their ...

2

The line Dim S, X, T, r, d, Price As Double is better written as Dim S As Double, X As Double, T As Double, r As Double, d As Double, Price As Double because 'as' only applies to the variable directly before it. The bisection algorithm seems to work as advertised. You could check with an online calculator such as this one. I've rewritten the ...

2

Negative excess kurtosis leads to a concave vol smile. By the way, no-arbitrage arguments are of theoretical nature: implied volatilities can exhibit no-arbitrate violations in the theoretical sense for extended periods given that such arbitrate cannot be traded due to other factors, such as liquidity, spreads, transaction related costs...not saying this ...

2

There is another approach to compute Implied Volatility, namely the Model Free Implied Volatility (MFIV). According to this link: "Unlike the traditional concept of implied volatility, where the implied volatility is estimated numerically from an option pricing model, the model free implied volatility (MFIV) is not dependent on any option pricing ...

2

You could sell a high realized volatility against a low implied all day and bust out in a month. Doing this as a inter-stock spread isn't going to make it much of a better trade. If you want to take advantage of realized vol vs. implied vol you need a model that describes the relationship between the two.

2

Here is a paper by the infamous Mark Rubinstein that should get you started. http://www.haas.berkeley.edu/groups/finance/WP/rpf232.pdf And here the trinomial tree version: http://www.ederman.com/new/docs/gs-implied_trinomial_trees.pdf by no lesser than Derman and Kani. This may also help with the actual computations: ...

1

Calendar spreads have a number of disadvantages for trading Vega: Vega in different months are generally not additive, some traders use root-time-Vega but it does not remove the additional risk. You are trading time spread not just volatility, so be careful Calendar spreads are affected by dividends and rate changes - another source of risk. A ...

1

You can construct delta and gamma neutral option portfolio, but: It won't generally stay neutral forever, so you would still have to constantly rebalance it by trading additional options (thus paying more transaction costs and creating mess in the portofolio). Anything will break the neutrality - underlying move, time passage, implied volatility change ...

1

Most likely you are looking at bid prices which are lower that fair (theoretical) price. It is very common that bid price of an ITM option is below the lower bound as bid-ask spreads are wide. The IV of ITM call at theoretical price should match IV of OTM put at corresponding strike. If this does not happen then check your forward price, rates and dividends. ...

1

The lower bound is not just a BS-specific bound. It is a no-arbitrage bound and so if the price is lower than this, you have an arbitrage opportunity (some good explanation here). It doesn't mean it is present in the market necessarily, because mid price is not necessarily the price you can trade and when you take spread into account this is likely to go ...

1

One is computed from historical stock time-series, that is, from observed past, the other is computed from traded option prices (prices of bets made on the stock with payoff at a future time), that is, from a view on the future paid for with cash. They are both equally important and useful (if one has enough data to compute them). Loosely speaking, ...

1

I think there are 2 approaches being a bit mixed up here. You can analyze the option market by looking at implied volatilities and apply Black-Scholes (BS), thus assuming that log-returns follow a Gaussian distribution. Implied volatilies are the parameters that bring together BS and market prices. Then you will observe a pattern of implied volatilies for ...

1

It's got nothing to do with you being identified as a market maker or not. It is simply that the other participants at that time are passive traders. The choice between hitting a bid or lighting a new level with a new offer are distinct and very different (especially, in some markets, in terms of fees paid or rebates received). So, you're not being ...

1

I'm going to start an answer on this and see if it generates discussion: Firstly you can't get the implied vol to a specific period unless there are options that are liquid and traded around the period you are interested in. you have four periods of vol, but you don't have listed options between the time periods (usually). from now until the close of ...

1

The focus on volatility comes about because all price changes "look like" volatility, no matter their source. Improvements in volatility treatment are therefore conflated with improvements in the model, and typically when people consider altered models, they first look to how well the alterations do in providing prices that explain skew for the classical ...

1

You don't need an algorithm to solve that - just program a simple BS option calculator using standard BS with dividend in Excel and fix all the inputs except the volatility. Then use goal seek/solver to change the volatility to get the given price and as a result you will have the implied volatility of the price.

1

you can use this code from Uwe Wystup FX Options and Structured Products. you can find it online. it uses vega and taylor expansion (just to 1st derivative which is vega) to find vol. you have to have code for european call price, but you have it already Function VanillaVolRetriever(spot As Double, rd As Double,rf As Double, strike As Double, T As Double, ...

1

you get a volatility skew by imposing a neumann-like barrier if market makers think a stock won't surpass a certain threshold, a skew is inevitable if one were to match the pricing under a barrier with the BS formula https://en.wikipedia.org/wiki/User:Barrieroption/sandbox

Only top voted, non community-wiki answers of a minimum length are eligible