We consider that the price of a firm follows a non linear stochastic delay differential equation. We also assume that any claim value whose value depends on firm value and time follows a non linear stochastic delay differential equation. Using self-financed strategy and duplication we are able to derive a Random Partial Differential Equation (RPDE) that any claim whose value depends on firm value and time should satisfy. We solve the RPDE for debt and loan guarantees under the assumption that there are no coupon payment nor dividends prior to the maturity of the debt.
We consider that the price of a firm follows a non linear stochastic delay differential equation. We also assume that any claim value whose value depends on firm value and time follows a non linear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a Random Partial Differential Equation (RPDE) satisfied by any corporate claim whose value is a function of firm value and time . Under specific final and boundary conditions, we solve the RPDE for the debt value and loan guarantees within a single period and homogeneous class of debt.
R
duplication
replication
R
that any
satisfied by any corporate
R
depends on
is a function of
R
should satisfy. We
. Under specific final and boundary conditions, we
R
debt
the debt value
R
under the assumption that there are no coupon payment nor dividends prior to the maturity of the
within a single period and homogeneous class of