| Summary: | This dissertation presents two different approaches to path dependent option pricing with discrete sampling.
Provided the underlying asset of a path dependent derivative contract follows an affine process, we use the forward characteristic method to evaluate its fair price. Our study shows that the valuation method is numerically accessible as long as the contract payoff is a linear combination of log return of its underlying asset price. We compute various examples of such contracts and give contract-tailored formulas that we use in these examples.
In the second part, we consider variance options under stochastic volatility model. We analyze the difference between variance option prices with discrete and continuous sampling as a function of N, the number of observations made in the former. We find the series expansion of the difference with respect to 1/N and find its leading term. By adding this leading term to the value of continuously sampled variance option, we obtain a simple and well-understood approximation of discretely sample variance option price.
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