Question 4. (25 marks) The instantaneous interest rate is assumed to follow the risk-neutral dynamics drt = (0 - rt)dt + odWt, ro: given, (1) where K, 0, and o are positive constants. (This is the well-known Vasicek for the instantaneous interest rate.) Consider a T-maturity zero-coupon bond that pays $1 at time T. It can be shown that the arbitrage-free price of the bond, denoted by Ct, satisfies the Partial Differential Equation (PDE) ac ac opac + (0-2) at 2C, (x,t) Rx (0,7), 2 222 (2) aar C(2,7) + = 1. In this question, you are asked to develop a fully explicit finite difference scheme for the above PDE. Following steps discussed in class, for computational purposes, we truncate the infinite domain Rx [0,T) to (2 min; Imax] * [0,T), where Imax > 0 and I'min