Let F be the gamma distribution function with parameters a > 0 and $\alpha > 0$ and let Gs be the negative binomial distribution function with parameters α and a/s, s > 0.

Arithmetic Asian options are difficult to price and hedge as they do not have closed-form analytic solutions. The main theoretical reason for this difficulty is that the payoff depends on the finite ...

If a lifetime T has the generalized gamma distribution, then the logarithm of the lifetime X = log (T) has the generalized log-gamma distribution, with the following probability density function g(x).

See the "Response Probability Distributions" section for the definition of the gamma probability density function. A value of 1 for the index parameter corresponds to the exponential distribution .

So we can parameterize the gamma function and with a calculus program like ‘Matlab’ or ‘ Excel’ we can evaluate the probability density function as indicated in figure 1 or figure 2 (note that k shall ...