THESIS
2014
iv leaves, v-xv, 105 pages : illustrations ; 30 cm
Abstract
In this thesis, pricing formulas for various discretely sampled variance
derivatives are derived under the 3/2-model and the time-changed Lévy model.
In the first part, we consider pricing of various types of exotic discrete variance
swaps, like the gamma swaps and corridor swaps, under the 3/2-stochastic
volatility models with jumps as this model has been shown to fit the market data
better than the popular Heston model. By using the partial integro-differential
equation formulation, we manage to derive quasi-closed form pricing formulas for
the fair strike values of various types of discrete variance swaps. Pricing properties
of these exotic discrete variance swaps under different market conditions
are explored. The second part suggests a numerical method of pricing options...[
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In this thesis, pricing formulas for various discretely sampled variance
derivatives are derived under the 3/2-model and the time-changed Lévy model.
In the first part, we consider pricing of various types of exotic discrete variance
swaps, like the gamma swaps and corridor swaps, under the 3/2-stochastic
volatility models with jumps as this model has been shown to fit the market data
better than the popular Heston model. By using the partial integro-differential
equation formulation, we manage to derive quasi-closed form pricing formulas for
the fair strike values of various types of discrete variance swaps. Pricing properties
of these exotic discrete variance swaps under different market conditions
are explored. The second part suggests a numerical method of pricing options
on discretely sampled variance swaps under the time-changed Lévy processes.
We construct numerical algorithm that relies on the computation of the moment
generating function of the realized variance under the time-changed Lévy models.
By using the randomization of the Laplace transform of the discrete log
return with a standard normal random variable, recursive quadrature algorithm
can be derived to compute the moment generating function. The option prices
are computed by inverse Laplace transform method. The fair strikes of discrete
volatility swaps are also obtained by a similar method.
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