An Introduction to Financial Mathematics

A wealthy acquaintance when recently asked about his profession reluctantly answered that he is a middleman in drug trade and has made a fortune helping drugs reach European markets from Latin America. When pressed further, he confessed that he was actually a ‘quant’ in a huge wall street bank and used mathematics to price complex derivative securities. He lied simply to appear respectable! There you have it. Its not fashionable to be a financial mathematician these days. On the plus side, these quants or financial mathematicians on the wall street are sufficiently rich that they can literally afford to ignore fashions. On a serious note, it is important to acknowledge that financial markets serve a fundamental role in economic growth of nations by helping efficient allocation of investment of individuals to the most productive sectors of the economy. They also provide an avenue for corporates to raise capital for productive ventures. Financial sector has seen enormous growth over the past thirty years in the developed world. This growth has been led by the innovations in products referred to as financial derivatives that require great deal of mathematical sophistication and ingenuity in pricing and in creating an insurance or hedge against associated risks. This chapter briefly discusses some such popular derivatives including those that played a substantial role in the economic crisis of 2008. Our primary focus are the key underlying mathematical ideas that are used to price such derivatives. We present these in a somewhat simple setting.

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