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Binary option pricing under geometric brownian motion

If an asset did indeed follow ln(St) ~ N(ln(S0)+ut,s2t), then a binary option on it would go to 0.5 as s->∞. However, such an asset would have E[St]=S0eut+s^2*t/2, so as s->∞, E[St]->∞, ...
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3 votes

When to use a Local Vol model vs Stochastic Vol Model?

First, what is the SLV? It combines LV (not really a model, just uses vanilla surface to get a grid) with SV (in a nutshell, BSM with a separate stochastic process for vol, hence multiple dynamic ...
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6 votes
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ATM Implied Volatility and Expected Variance

I am not so sure about the ATM approximation from the other answer (i.e. I don't think it's a great approximation). I think it comes from the following for $T \ll 1$: \begin{align} E \left[ \frac{1}{T}...
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1 vote

implied volatility and strike price

Notations: $T,K$ are the maturity and the strike of a vanilla call of price $C(T, K)$. $(S_t)_{t\in [0,T]}$ the price process of the underlying. $\mathbb{Q}$ is the risk neutral measure. $x(T,K) = ...
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Model-Free Implied Volatility: Data of Expired Options and Bond Price

With BBG, you can use OPT_CHAIN (on FLDS - hence Excel) using SINGLE_DATE_OVERRIDE with a date in the past in YYYYMMDD format to get tickers back until 2012. 2000 is generally possible, but not ...
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1 vote

Help needed in replicating FX Implied Vol Surface

You still did not post your exact formula, which means it's impossible to determine what is wrong. Therefore, I'll post a working example. I used Julia and manually defined the ppf. This is ...
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Calibrate the SABR model to the implied volatility surface

> However, I'm wondering if it is possible to just calibrate the SABR parameters to the entire volatility surface No, this is not how it supposed to work. SABR model describes dynamics of a single ...
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2 votes

What is the meaning of an implied volatility of an Asian option?

Practitioners use Monte Carlo methods, the moment matching method (Levy approximation) and when they want to be super-precise, the Curran method.
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-2 votes

implied vol smile relative to atm vols

Your essentially talking about a pitchfork type approach
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