Pricing barrier options under scalar diffusions using the eigenfunction expansion approach

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In this thesis, we will present some methods used to price barrier options. We first price barrier options under the Black-Scholes model. Then we will discuss some of the shortcomings of the Black-Scholes model. Next we derive prices for barrier options under different classes of scalar diffusions. In particular, we will use eigenfunction expansions to price barrier options under the CEV model of price dynamics.
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