  A unified analytical pricing framework with involvement of the shot noise
random process has been introduced and elaborated. Two exactly solvable new
models have been developed. The first model has been designed to value options.
It is assumed that asset price stochastic dynamics follows a Geometric Shot
Noise motion. A new arbitrage-free integro-differential option pricing equation
has been found and solved. The put-call parity has been proved and the Greeks
have been calculated. Three additional new Greeks associated with market model
parameters have been introduced and evaluated. It has been shown that in
diffusion approximation the developed option pricing model incorporates the
well-known Black-Scholes equation and its solution. The stochastic dynamic
origin of the Black-Scholes volatility has been uncovered. The new option
pricing model has been generalized based on asset price dynamics modeled by the
superposition of Geometric Brownian motion and Geometric Shot Noise. To model
stochastic dynamics of a short term interest rate, the second model has been
introduced and developed based on Langevin type equation with shot noise. A new
bond pricing formula has been obtained. It has been shown that in diffusion
approximation the developed bond pricing formula goes into the well-known
Vasicek solution. The stochastic dynamic origin of the long-term mean and
instantaneous volatility of the Vasicek model has been uncovered. A generalized
bond pricing model has been introduced and developed based on short term
interest rate stochastic dynamics modeled by superposition of a standard Wiener
process and shot noise. Despite the non-Gaussianity of probability
distributions involved, all newly elaborated models have the same degree of
analytical tractability as the Black-Scholes model and the Vasicek model.
