It can be great if someone can help me to solve this questions. It is from part a to part f. Thanks!

You are attempting to value a structured note with current value W5", 1) by using a nite-difference method. QR and are USD ad EUR risk-free money market account, S: is the price of the Euro Winder: (denominated in Euros) and et is the USDIEUR exchange rate. These prices follow the processes dIiEi't = rBtdt dBEt = TEBEtdt d3, = (,u - 6)S,dt + aSthl de = peedt + agedXz. Where X1, X2 are correlated Brownian motions with correlation p. w, r, p, p, 6', s, and 6e are constants. As S: is usually denominated in Euros then it is appropriate to value this product as a sguanto. According to a standard derivation, V(S, t) is dened by the following partial differential equation: 6V 1 , 262V ("W + s + 5 s V=0 a: 20 6S2 ("3 'me) as r The details for the structured note are on page 23 (you may remove this page). You may assume that the volatility of the EURO STOXX index is 30%. We will attempt to solve this option problem using an Crank-Nicolson finite difference scheme where we havemmeps in S, so AS = (WWand msteps in r, so that At = 17% a) Choosing 1096 time steps (imax = 1096) or one step per day, what is the maximum number of S steps, w you would wish to use? Explain. [1 point] b) Based on the details of the product what is your choice of Smax, Smin and AS? Please explain your reasoning. [2 points] c) By using central difference approximations for the derivatives in S and a forward difference approximation for the derivative in L311 calculated at i9; + Atf2 for i: 0,..., m write the nite difference equations as follows: b0 qJ 0 0 . . 0 V5: d5 31 b1 C1 0 - ' Vi- di- 0 32 b2 C2 0 . V2l dill a3 b3 C3 ' V3: : a; b; 9' - ' - . . . . - it/_I,"llrria:v(1 ' _ 0 . . 0 aj max bj max l/jlmax I'll-"ax Determine the expressions for 31; 912 aand g'lforj = l, ..., imax 1. [3 Points] d) Write down the nal condition V(S, I). Also find appropriate upper and lower boundary conditions. Use these boundary conditions to derive the appropriate values of be, cu, aimax? bjmax, for all t. [3 Points] e) Explain how you would use the CN nite difference scheme to price the Structured note, V(S,0)? You may assume that you know how to solve the system of equations. I am mainly interested in what you do at maturity, on coupon payment and autocall dates. [3 Points] f) You also Wish to calculate the risk-neutral probability that your product is NOT W Explain how you could adapt your nite-difference methodology to determine this probability? (3 points)