Asian Options, Jump-Diffusion Processes on a Lattice and Vandermonde Matrices

Citation:
Silvestrov K, Ogutu C, Silvestrov S, Weke P. "Asian Options, Jump-Diffusion Processes on a Lattice and Vandermonde Matrices.". In: Modern Problems in Insurance Mathematics. London: Springer; 2014.

Abstract:

Modern Problems in Insurance Mathematics. Springer, London, Chapter 20, pages 337 – 366, XIX, 387 pages.
Summary:
Risk is the uncertainty of an outcome and it can bring unexpected gains but can also cause unforeseen losses, even catastrophes. They are common and inherent in financial and commodity markets; for example; asset risk, interest rate risk, foreign exchange risk, credit risk, commodity risk. Investors have various attitudes towards risk, that is, risk aversion, risk seeking and risk neutral. Over the past few years financial derivatives have become increasingly important in the world of finance since they are kind of a risk management tool. A financial derivative is a financial instrument whose value depends on other fundamental financial assets, called underlying assets, such as stocks, indexes, currencies, commodities, bonds, mortgages and other derivatives (since we can have a derivative of a derivative). As an underlying asset one can also use a non-financial random phenomenon like for instance, weather conditions e.g. temperatures. Pricing derivatives accurately and quickly is important for risk management. This is important for both those who trade in derivatives and those who are willing to insure them. In this paper some lattice methods for pricing Asian options modeled using a jump diffusion process will be described. These methods can often be adapted to pricing of other derivatives or solving other types of problems in financial mathematics, for instance a jump diffusion process can be used to describe incoming claims to an insurance company, see [20].

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