Davydov, Dmitry; PhD
UNIVERSITY OF MICHIGAN, 2000
ECONOMICS, FINANCE (0508); POLITICAL SCIENCE, GENERAL (0615)
The dissertation is a collection of four papers. The papers utilize the common
technique of modeling
political and financial variables as Markov diffusion processes. In the first
chapter we build a model of a
political system, in which the ruling party chooses the time of election. We
demonstrate that such a
system significantly prolongs the expected duration of the ruling party's stay
in power. The time value of
the right crucially depends on the volatility of the public opinion. We show
how to express the ruling
party's expected duration of stay in power as a solution to a free-boundary
problem that we solve
numerically. In the second chapter we generalize the Black-Scholes-Merton option
pricing model to a
wide class of Markov diffusion processes, including the constant elasticity
of variance (CEV) process.
The CEV model exhibits an implied volatility smile that is a convex and monotonically
decreasing function
of strike. We derive closed-form solutions for the prices of barrier and lookback
options and demonstrate
that, in the presence of a CEV-based volatility smile, barrier and lookback
prices and hedge ratios can
deviate dramatically from the values under a lognormal specification. The third
chapter we analyze double
barrier step options with the payoff dependent on the occupation time outside
the prespecified price
range during the life of the option. Occupation time-based contracts are easier
to hedge than standard
barrier options and, therefore, smaller bid-ask spreads over the theoretical
price are required. We obtain
the price and hedge ratios of occupation-time derivatives under assumption of
lognormal process. The
solutions are represented in the form of single or double inverse Laplace transforms.
In the fourth
chapter, we build a bond-pricing model with a positive probability of default.
A firm may suffer a
random-size loss that occurs at the first jump of a Poisson process with random
intensity. The default
happens only if the firm's equity, which is assumed to follow the lognormal
process, is not large enough
to cover the loss. The analytical tractability is achieved through the approximation
of the hazard rate. We
derive the analytical formulae for the price of the risky bonds and the spread.
Social
Systems Simulation Group
P.O. Box 6904 San Diego, CA 92166-0904 Roland Werner, Principal Phone/FAX (619) 660-1603 |