2. Your option portfolio has European style put options on stock of ABC Ltd. with a notional value of $10 million. You are asked to mark-to- market the option portfolio using the Finite difference schemes under the Black-Scholes framework. The trade terms specify the following additional information: Initial Stock Price (ABC Ltd.) = $40 (as of Today) Strike = $40 Time to Maturity = 1 Year (12 months expiry) Risk free rate = 0.10 Volatility = 0.30 For the grid discretization scheme the following parameters can be set as follows: Smax = 100; Step size for Stock Price (M) = 400; Step size for time (N) = 400. a. As shown in class, use implicit Euler method to solve the above pricing PDE and calculate the price. b. Comment on the stability of FDS scheme used and its convergence. c. The trader added another barrier style (down and out) option to the portfolio with the same trade terms as above and the additional barrier level specified at B = $30. You are asked to price this trade using the finite difference scheme as above. (Note - you need to apply the appropriate boundary conditions for barrier style exercise as discussed in the class)