A general closed form option pricing formula

A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram–Charlier series expansion, known as the Gauss–Hermite expansion. This expansion converges for fat-tailed distributions commonly encountered in the study of financial returns. The expansion coefficients can be calibrated from observed option prices and can also be computed, for example, in models with the probability density function or the characteristic function known in closed form. We investigate the properties of the new option pricing model by calibrating it to both real-world and simulated option prices and find that the resulting implied volatility curves provide an accurate approximation for a wide range of strike prices. Based on an extensive empirical study, we conclude that the new approximation method outperforms other methods both in-sample and out-of-sample.

     

Quantifying the recapitalization fund premium using option pricing techniques

The purpose of the paper consists in developing a formula for quantifying the premium a bank is expected to pay for a fund that provides recapitalization in order to allow orderly failure if the bank is in financial distress. The main finding is that such a premium can be computed as the difference between the prices of two European put options.