Mate choice models derive from traditional microeconomic decision theory and assume that individuals maximize their Darwinian fitness by making economically rational decisions. Rational choices exhibit regularity, whereby the relative strength of preferences between options remains stable when additional options are presented. We tested female frogs with three simulated males who differed in re...

Consider an investment system with a nonnegative expected return in a one period economy. We show that, for an option with a given strike price, there exists a pricing interval [pC , pW ] such that replacing the original investment with the option will benefit judging by the Kelly criterion only when the price of the option lies outside of the interval. More specifically, buying call options wi...

We examine a Markov tree (MT) model for option pricing in which the dynamics of the underlying asset are modeled by a non-IID process. We show that the discrete probability mass function of log returns generated by the tree is closely approximated by a continuous mixture of two normal distributions. Using this normal mixture distribution and risk-neutral pricing, we derive a closed-form express...

Volatility is a statistical measure that describes the amount of fluctuation in prices for a given investment; generally, the higher the volatility for an investment, the riskier it is perceived to be. Traders study volatility history so that they can make informed decisions on how to invest capital. The purpose of this article is to analyze implied volatility values, which are derived from the...

Incorporating prior knowledge of a particular task into the architecture of a learning algorithm can greatly improve generalization performance. We study here a case where we know that the function to be learned is non-decreasing in its two arguments and convex in one of them. For this purpose we propose a class of functions similar to multi-layer neural networks but (1) that has those properti...

This paper presents a numerical method for pricing American call options where the underlying asset price follows a jump-diffusion process. The method is based on the Fourier-Hermite series expansions of Chiarella, El-Hassan and Kucera (1999), which we extend to allow for Poisson jumps, in the case where the jump sizes are log-normally distributed. The series approximation is applied to both Eu...

The pricing of options is a very important problem encountered in nancial markets today. The famous Black-Scholes model provides explicit closed form solutions for the values of certain (European style) call and put options. But for many other options, either there are no closed form solutions, or if such closed form solutions exist, the formulas exhibiting them are complicated and diicult to e...

Robust, or model-independent properties of the variance swap are wellknown, and date back to Dupire [19] and Neuberger [37], who showed that, given the price of co-terminal call options, the price of a variance swap was exactly specified under the assumption that the price process is continuous. In Cox and Wang [11] we showed that a lower bound on the price of a variance call could be establish...

We derive a small-time expansion for out-of-the-money call options under an exponential Lévy model, using the small-time expansion for the distribution function given in Figueroa-López&Houdré[FLH09], combined with a change of numéraire via the Esscher transform. In particular, we find that the effect of a non-zero volatility σ of the Gaussian component of the driving Lévy process is to increase...

One of the most widely studied problems in financial mathematics is the pricing of derivative securities, also known as contingent claims. These are securities whose price depend on the value of another underlying security. Financial options are the most common examples of derivative securities. For example, a European call option on a particular underlying security gives the holder the right t...