Pricing swaptions and credit default swaptions in the quadratic Gaussian factor model
- Publication Type:
- Thesis
- Issue Date:
- 2007
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In this thesis we show how the multi-factor quadratic Gaussian model can be used
to price default free and defaultable securities. The mathematical tools used include
the theory of stochastic processes, the theory of matrix Riccati equations,
the change of measure technique, Ito's formula, use of Fourier Transforms in swaption
valuation and approximation methods based on replacing the values of some
stochastic processes by their time zero values.
The first chapter of the thesis deals with the derivation of efficient closed form
formulas for the price of zero coupon bonds in the multi-factor quadratic Gaussian
model and the calibration of the multi-factor quadratic Gaussian model to the
domestic and foreign forward rate term structures through closed form formulas.
In the second chapter of the thesis, we derive approximations for the price of
default free swaptions which are based on log-quadratic Gaussian processes. Using
numerical experiments, we show the limitations of these approximations. We also
give some numerical results for the pricing of a default free swaption using moment-based
density approximants of the probability density function of the swaption's
payoff.
The third chapter of the thesis deals with the calibration of a quadratic Gaussian
reduced form model of credit risk to the default free forward rate curve and to
the survival probability of an obligor. We also consider different approximations
for the price of credit default swaptions. Using numerical experiments, we show
the limitations of the approximations.
The final chapter of this thesis considers a two country reduced form model
of credit risk. We examine the relationship between the domestic forward credit
spread and the foreign forward credit spread of an obligor and provide quanto
adjustment formulas for the probability of survival of an obligor. In the final part
of this chapter, we show that the valuation of a quanto default swap is tractable in
a contagion type reduced form model of credit risk which assumes that underlying
processes are modelled by quadratic Gaussian processes.
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