We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the the joint distribution of any finite sequence of log returns admits a Gram-Charlier A expansion in closed-form . We use this to derive closed-form series representations for option prices whose payoff is a function of the underlying asset price trajectory at finitely many time points. This includes European call, put, and digital options, forward start options, and forward start optionson the underlying return. We derive sharp analytical and numerical bounds on the series truncation errors. We illustrate the performance by numerical examples, which show that our approach offers a viable alternative to Fourier transform techniques .
We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns admits a Gram-Charlier A expansion with closed-form coefficients. We derive closed-form series representations for option prices whose discounted payoffs are functions of the asset price trajectory at finitely many time points. This includes European call, put, and digital options, forward start options, and can be applied to discretely monitored Asian options. In a numerical analysis we find that the price approximations become accurate within short CPU time .
R
the joint distribution
joint density
R
in
with
R
. We use this to
coefficients. We
R
payoff is a function of the underlying
discounted payoffs are functions of the
R
forward start optionson the underlying return. We derive sharp analytical and numerical bounds on the series truncation errors. We illustrate the performance by numerical examples, which show that our approach offers a viable alternative to Fourier transform techniques
can be applied to discretely monitored Asian options. In a numerical analysis we find that the price approximations become accurate within short CPU time