Pentanomial Lattice Models in Option Pricing

Abstract

Options are derivatives which is an agreement linking two persons or more of vested interest whose worth is based on an agreed-upon underlying nancial asset. An agreement de nes the buyer the right, but not the commitment, to purchase or dispose the speci ed asset at a discussed price during a determined period of time on a speci ed later date. Asian option is an option which depends on the past knowledge whose payment is based on the mean-price during a secure duration of time before it matures. How much to spend on option contract is the main problem at the task in pricing options. This becomes more complex when it comes to the case of projecting the future possible price of the option. This is attainable if the probabilities of princes swelling are known, remaining the same or lessening. Each investor’s wishing to maximize pro t. This proposal looks into pentanomial lattice model used in pricing Asian Option models. A Lattice representation is a discontinuous time presentation of evolution of the underlying asset price. The model also takes into account the Kurtosis and skewness of the underlying asset. It splits a certain time interval into n equal strides. The lattice is constructed using positive branch probabilities and takes into account the matching procedures the limiting distribution of lattice model is called compound Poisson process. The lattice model is used to price options more e ciently and easily. It estimates the spread of the underlying asset cost each time step.