This paper investigates Black–Scholes call and put option thetas, and derives upper and lower bounds for thetas as a function of underlying asset value. It is well known that the maximum time premium of an option occurs when the underlying asset value equals the exercise price. However, we show that the maximum option theta does not occur at that point, but instead occurs when the asset value i...

Monte Carlo simulation is one alternative for analyzing options markets when the assumptions of simpler analytical models are violated. We introduce techniques for the sensitivity analysis of option pricing which can be efficiently carried out in the simulation. In particular, using these techniques, a single run of the simulation would often provide not only an estimate of the option value but...

We study the problem of finding probability densities that match given European call option prices. To allow prior information about such a density to be taken into account, we generalise the algorithm presented in Neri and Schneider (Appl. Math. Finance 2013) to find the maximum entropy density of an asset price to the relative entropy case. This is applied to study the impact of the choice of...

This study estimates the value of the early exercise premium in American put option prices using Swedish equity options data. The value of the premium is found as the deviation of the American put price from European put-call parity, and in addition a theoretical estimate of the premium is computed. The empirically found premium is also used in a modified version of the control variate approach...

We propose a quasi-Monte Carlo (qMC) algorithm to simulate variates from the normal inverse Gaussian (NIG) distribution. The algorithm is based on a Monte Carlo technique found in Rydberg (Rydberg 1997), and is based on sampling three independent uniform variables. We apply the algorithm to three problems appearing in finance. First, we consider the valuation of plain vanilla call options and A...