Questions tagged [asymptotics]

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Asymptotic behavior of implied volatility at probability mass [closed]

For sake of simplicity, let us suppose that interest rate is zero, stock price is 1, and time to expiry is 1. I am interested in implied volatility that gives the following put price. $$P(k, \sigma(k))...
JEK's user avatar
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Forward price of dividend paying asset and IV skew asymptotics as $T\to\infty$

Assuming for simplicity deterministic interest rate and dividend yield, then the forward price of an asset is $$ F = Se^{(r-q)T} $$ where $T$ is maturity date. In studying IV skew asymptotics, the ...
Frido's user avatar
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What is the relationship between the estimated GARCH(1,1) conditional volatility and the true conditional volatility

Suppose that the data has been generated by a GARCH(1,1) model, i.e. \begin{align} y_t &= h_t \epsilon_t, \; \epsilon_t \sim N(0,1) \\ h_t &= \alpha_0 + \alpha_1 \epsilon_{t-1}^2 + \...
Stéphane's user avatar
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Asymptotics of Call Option as $S\to0$

Let $C(S)$ denote the (initial) value of a call option with underlying spot price $S$. I assume that the underlying has continuous sample paths (not necessarily a geometric Brownian motion though). As ...
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