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 two of its 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 prope...

There are two common methods for pricing European call options on a stock with known dividends. The market practice is to use the Black-Scholes formula with the stock price reduced by the present value of the dividends. An alternative approach is to increase the strike price with the dividends compounded to expiry at the risk-free rate. These methods correspond to different stock price models a...

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...

We examine the small expiry behaviour of the price of call options in models of exponential Lévy type. In most cases of interest, it turns out that E ( (Sτ −K) ) − (S0 −K) ∼ { τ ∫ R (S0e x −K)+ ν(dx), S0 < K, τ ∫ R (K − S0e) ν(dx), S0 > K, as τ → 0+, i.e. as time to expiry goes to zero. (We have written ν for the Lévy measure of the driving Lévy noise.) In “complete generality”, however, we can...

We consider the hedging of options when the price of the underlying asset is always exposed to the possibility of jumps of random size. Working in a single factor Markovian setting, we derive a new spanning relation between a given option and a continuum of shorter-term options written on the same asset. In this portfolio of shorter-term options, the portfolio weights do not vary with the under...

Abstract In recent years a number of authors pointed out significant stability and convergence problems while using Cox-Ross-Rubinstein binomial method to price and hedge barrier options. Different modifications were suggested to improve the convergence and stability of the binomial method. However, as this article shows, lattice approach in general has limited stability factor when applied to ...

This paper questions one of the fundamental assumptions made in options pricing: that the daily returns of a stock are independent and identically distributed (IID). We apply an estimation procedure to years of daily return data for all stocks in the French CAC-40 index. We find six stocks whose log returns are best modeled by a first-orderMarkov chain, not an IID sequence. We further propose t...

Previous studies of the information content of the implied volatilities from the prices of call options have used a cross-sectional regression approach. This paper compares the information content of the implied volatilities from call options on the S&P 100 index to GARCH (Generalized Autoregressive Conditional Heteroscedasticity) and Exponential GARCH models of conditional volatility. By addin...