Questions tagged [asymptotics]
The asymptotics tag has no usage guidance.
4 questions
1
vote
0
answers
69
views
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.
$$P(k, \sigma(k))...
- 19
1
vote
0
answers
57
views
Forward price of dividend paying asset and IV skew asymptotics as $T\to\infty$
Assuming for simplicity deterministic interest rate and dividend yield, then the forward price of an asset is
$$
F = Se^{(r-q)T}
$$
where $T$ is maturity date.
In studying IV skew asymptotics, the ...
- 2,681
3
votes
0
answers
90
views
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 + \...
- 2,536
5
votes
4
answers
395
views
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 ...
- 688