# Animations on statistical finance

## Payout distributions when an ATM call is written

### Gauss and Student distributions of the underlying

The animation shows histograms of payout distributions
when an European at the money call is written and hedged with a single period
hedging.
The distribution of the asset follows geometric Gaussian and
Student processes,
with degrees of freedom 4.

The hedging parameter varies between 0.1-0.9
and
the moneyness index is 1,
where the moneyness is defined as S0/K, where S0
is the initial asset price and K is the strike price.
The initial asset price is taken to be 100.

The yearly volatility is 0.2,
the time to expiration is 0.25 in fractions of year,
the risk free interest rate is 0.
The histograms are based on 5000 simulated trajectories and have 40 bins.