Question: (c) Write the Euler scheme for the linear SDE dXt=(Xt+)dt+XtdWt,X0=1 ( 4 marks) (d) State the Central Limit Theory (CLT) and demonstrate its application in

(c) Write the Euler scheme for the linear SDE dXt=(Xt+)dt+XtdWt,X0=1 ( 4 marks) (d) State the Central Limit Theory (CLT) and demonstrate its application in construction of the confidence bounds for Monte Carlo simulations. (4 marks) (e) Boundary conditions establish the uniqueness of the solution to a partial differential equation. For a put option with payoff (KST)+, write down the respective boundary conditions for the Black-Scholes PDE and give their economic interpretation. (6 marks) (f) Distinguish between the two sources of errors when approximating the solution of partial differential equations. (4 marks)

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