In this paper we study the pricing problem of multiple exercise options in continuous time on a finite time horizon. For the corresponding multiple stopping problem, we prove, under quite general assumptions, the existence of the Snell envelope, a reduction principle as nested single stopping problems, and a Doob-Meyer type decomposition for the Snell envelope. The main technical difficulty ari...

Previous option pricing research typically assumes that the risk-free rate or the short rate is constant during the life of the option. In this study, we incorporate the stochastic nature of the short rate in our option valuation model and derive explicit formulas for European call and put options on a stock when the short rate follows the Merton model. Using our option model as a benchmark, ou...

This paper shows that many of the empirical biases of the Black and Scholes option pricing model can be explained by Bayesian learning effects. In the context of an equilibrium model where dividend news evolve on a binomial lattice with unknown but recursively updated probabilities we derive closed-form pricing formulas for European options. Learning is found to generate asymmetric skews in the...

We propose a neural network approach to price EU call options that significantly outperforms some existing pricing models and comes with guarantees that its predictions are economically reasonable. To achieve this, we introduce a class of gated neural networks that automatically learn to divide-and-conquer the problem space for robust and accurate pricing. We then derive instantiations of these...

European Range Accrual Option pricing and deviation Formula has been deduced through observing the foundational asset probabilistic distribution characteristics with help of Ito’s lemma, relaxing boundary assumption to infinity zero respectively, classical Black-Scholes option formula worked out. This paper subsequently articulates numerical value simulated computation algorithm using...

European compound option pricing model is established by using the mixed bifractional Brownian motion. Firstly, principle of risk-neutral pricing, formulas and parity are obtained. Secondly, with Delta hedging strategy, corresponding got. Finally, daily closing price data “Lingang B shares” “Yitai respectively, results show that closer to true value than previous model.