Pricing and hedging exotic options in insurance and finance / Ng Ze-An

Ng , Ze-An (2024) Pricing and hedging exotic options in insurance and finance / Ng Ze-An. Masters thesis, Universiti Malaya.

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Abstract

This thesis concerns the theoretical pricing and hedging of options, financial instruments that give a payoff at a set date based on the price of one, or several other financial assets, known as the underlying assets. The underlying assets are usually taken to be stocks, but can also be bonds, securities, portfolios, or other financial instruments. In this thesis we study two types of options - life contingent options and barrier Asian options. Because the options examined in this thesis are relatively uncommon, with a novel mechanism of action, they are known as exotic options. The analysis takes place in a stylised mathematical model of a financial market known as the Black-Scholes model. We show for the life contingent option that there exists a minimal super-hedging portfolio and determine the associated initial investment. We also give a characterisation of when replication of the option is possible. Next, we investigate the pricing problem for barrier Asian options with short maturity times. Due to the nature of Asian options, closed form formulae for the fair price of the option are relatively difficult to obtain. Using novel results from the theory of stochastic calculus, we obtain closed form asymptotic formulae for the price of short maturity barrier Asian options. Finally, we demonstrate our results with some explicit examples.

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