# Tag Info

### How do different models impact option Greeks?

This is an interesting and not so easy question. Here's my 2 cents: First, you should distinguish between mathematical models for the dynamics of an underlying asset (Black-Scholes, Merton, Heston ...
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### Problems with local volatility models (vs stochastic volatility models)

1. What does it mean by the vol surface is the current view of vol? The local volatility model is calibrated to vanillas prices (and equivalently their implied volatilities), which reflect the market'...
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### Local vol, stochastic vol, implied vol

Along with Gatheral's book, I'd recommend reading Lorenzo Bergomi's "Stochastic Volatility Modelling". The first 2 chapters are available for download on his website. That being said, let me try to ...
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### Solve the following SDE: $\mathrm{d}X_t = a(b-X_t) \,\mathrm{d}t + c X_t \, \mathrm{d}W_t$

Let \begin{align*} Y_t = e^{(a+\frac{c^2}{2})t-cW_t}. \end{align*} Then \begin{align*} dY_t = Y_t\left[\big(a+c^2\big)dt -c dW_t \right]. \end{align*} Moreover, \begin{align*} d(X_tY_t) &= Y_t ...
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### SSR definition in Bergomi in relation to sticky strike and sticky delta

Some Notations It's easy to get lost so let's introduce some notations and let $$\sigma : (t, S, K, \tau) \to \sigma(K,\tau; S, t)$$ denote the implied volatility smile prevailing at time $t$ ...
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### Bergomi: Skew arbitrage

Great question. Let me try to provide some insights and thoughts regarding the points and questions you raised. It may not be a full answer but hopefully it will help connecting the contents in the ...
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### For pricing, what types of Exotic Options are suitable using Local Volatility Model or a Stochastic Volatility Model?

Whenever you use any model to price anything, all you need to do is make sure you model the underlying dynamics that the product you're pricing actually depends on. Any product will be dependent on ...
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### Modeling Call Price w.r.t. Strike w Models that Capture Vol Smile

The way that I understand your question is that you are looking to fit the market prices of European plain vanilla options of a single maturity and then back out the corresponding implied probability ...
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### Mixed local-stochastic volatility model in Quantlib

Stochastic-Local Vol (SLV) is an attempt to mix the strengths and weaknesses of both Stochastic Vol and Local Vol models. Below, I'll quickly summarise each model and their strengths and weaknesses, ...
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### Book/ Articles recommendation for Volatility models

I have also currently started to learn about the subject. This is some of the material I have encountered: Many people recommend the book "The Volatility Surface: A Practitioner's Guide" by ...
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### 2 Ito processes - $d(X_{t} + X^{'}_{t})^2 = (Y_t + Y^{'}_{t})^2 dt$ why it is true?

$X_t$ being a stochastic process, one cannot use ordinary calculus to express the differential of a (sufficiently well-behaved) function $f$ of $t$ and $X_t$. Instead one should turn to Itô's lemma, ...
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### Problems with local volatility models (vs stochastic volatility models)

The following paper is helpful for understanding the point you raise: Hagan et al.: Managing Smile Risk, January 2002, Wilmott 1:84-108 The main point is given in the paper: [...] the dynamics ...
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### Different volatility surface ( Local vol, Stochastic vol etc.)

I'll answer both of your questions in one go: Your ideas are correct. If the Black-Scholes model was true, the implied volatility surface would be flat but it is not in real life. Thus, the geometric ...
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### SABR calibration: simple explanation and implementation

There are lots of papers online and here are a few I would suggest math.umn riskworx G. Dimitroff, J. de Kock Nowak, Sibetz I you have matlab there is an step step example to calibrate SABR ...
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### Calculating 6-minute, 20-minute, 45-minute, and 3-hour volatility

Quick summary: Your model should still be well specified, as long as: 1) You do the analysis on a heavily traded asset, e.g. IBM on NYSE, and 2) You use heteroskedasticity-consistent standard errors ...
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### Why is there a stong intraday-correlation between spot and vol?

This effect is coming from the supply and demand in the options markets. Many portfolio managers want (or need) to buy out of the money put options, and many are willing to sell out of the money call ...
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