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3
votes
1answer
79 views

Estimating $\mu$ - only increasing $T$ improves estimate?

Assuming an asset price $S$ follows a geometric Brownian motion (GBM), the log returns $R$ are distributed as $$ R_i := \log\left(\frac{S_i}{S_{i-1}}\right) \sim \mathcal{N}\left(\left(\mu - ...
2
votes
2answers
600 views

Local volatility SVI parametrization

In this paper Gatheral presents the following parametrization of the implied total variance $w(k,T) = \sigma_{BS}(k,T)^2T$ for each slice $k \mapsto w(k,T)$: $$ w(k) = a + b\{\rho (k-m) + ...
5
votes
2answers
366 views

How to calibrate a volatility surface using SVI

I've read the following paper by Gatheral and Jacquier and have several question regarding the calibration of a volatility surface in a arbitrage free way and some theoretical aspects. Let me first ...