This paper constructs a new theory of social networks based on the options individuals buy on each other. The model assumes that when an individual connects with another it is equivalent to buying options on the other's reputation. The option model confers advantages not present in existing...

The reputation of an individual is the aggregate opinion of them. Reputation is usually explained by attributes of the one reputed, not the motivation of those doing the reputing. In this paper, we develop a model of reputation where the opinions are assets that leverage the reputation of...

Risk neutral densities (RND) can be used to forecast the price of the underlying basis for the option, or it may be used to price other derivates based on the same sequence. The method adopted in this paper to calculate the RND is to firts estimate daily the diffusion process of the underlying...

We estimate the process underlying the pricing of American options by using higher-order lattices combined with a multigrid method. This paper also tests whether the risk-neutral densities given from American options provide a good forecasting tool. We use a nonparametric test of the densities...

We explain the valuation and correlation hedging of Foreign Exchange Basket Options in a multi-dimensional Black-Scholes model that allows including the smile. The technique presented is a fast analytic approximation to an accurate solution of the valuation problem.

In Monte Carlo simulation, Latin hypercube sampling (LHS) [McKay et al. (1979)] is a well-known variance reduction technique for vectors of independent random variables. The method presented here, Latin hypercube sampling with dependence (LHSD), extends LHS to vectors of dependent random...

No front-office software can survive without providing derivatives of option prices with respect to underlying market or model parameters, the so called Greeks. If a closed form solution for an option exists, Greeks can be computed analytically and they are numerically stable. However, for...

Many economic and econometric applications require the integration of functions lacking a closed form antiderivative, which is therefore a task that can only be solved by numerical methods. We propose a new family of probability densities that can be used as substitutes and have the property of...

In Kusuda [45], we developed equilibrium analysis in security market economy with jump-Wiener information where no finite number of securities can complete markets. Assuming approximately complete markets (Björk et al. [11] [12]) in which a continuum of bonds are traded and any contingent claim...

This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. It consists in determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining...