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...

Investment behaviour, techniques and choices have evolved in the options markets since the launch of options trading in 1973. Today, we are entering the field of Big Data and the explosion of information, which has become the main feature of science, impacts investors' decisions and their...

A barrier option is a financial derivative which includes an activation (or deactivation) clause within a standard vanilla option. For instance, a copper mining company could secure to sell in at least K dollars each ton of copper during the next year, by buying M European put options. However,...

The market for ultra short-term (zero days-to-expiry or 0DTE) options has grown exponentially over the last few years. In 2023, daily volume in 0DTEs reached over 45% of overall daily options volume. After briefly describing this exploding new market, we present a novel pricing formula designed...

This thesis investigates the predictive power of the Skewness and Kurtosis Adjusted Black Scholes model of Corrado and Su (1996) (CS) model in pricing three Australian option contracts (ANZ, BHP and CBA) maturing in March, June, September and December, during the 2007/2008 financial crisis...

The “practitioner Black-Scholes delta” for hedging options is a delta calculated from the Black-Scholes-Merton model (or one of its extensions) with the volatility parameter set equal to the implied volatility. As has been pointed out by a number of researchers, this delta does not minimize...

We develop approximate formulae expressed in terms of elementary functions for the density, the price and the Greeks of path dependent options of Asian style, in a general local volatility model. An algorithm for computing higher order approximations is provided. The proof is based on a heat...

We apply the Malliavin calculus to the stochastic string framework and obtain a Clark-Ocone-like formula. This result allows us to rewrite the hedging portfolio explicitly in terms of the Malliavin derivative of the discounted payoff. We illustrate this new result with two applications. Firstly,...

In this paper, we derive closed-form, interpolation-based expressions for European call options written on defaultable assets. Our results are based on the work of Henderson at al. (2007), who derive formulas that incorporate standard static no-arbitrage restrictions, and Orosi (2014) who...

In this paper, I have used simple arbitrage argument to derive a dozen of model-free option price properties. In addition to deriving the Greeks under the model-free framework, the results show that first, in contrast to the traditional view, a European call (put) option for a...