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1. Evaluate the following European call options using FDM's Explicit, Implicit, and Crank-Nicolson methodologies. "Stock price =100, Strike price =100, interest rate =3.5%, Dividend =0.5%, Volatility =20%, expiry =0.5 2. The underlying asset and the time grid numbers M and N are increased to 200,250,300,400,500,1000 together Calculate the option price using FDM and compare it with the result using the Black-Scholes formula. ( However, comparing the Explicit, Implicit, and CrankNicolson methodologies) "Stock price =100, Strike price =100, interest rate =3.5%, Dividend =0.5%, Volatility =20%, expiry =0.5% 3 . Based on the result of #2, draw delta and gamma surface. "Stock price =100, Strike price =100, interest rate =3.5%, Dividend =0.5%, Volatility =20%, expiry =0.5 " [Note] In Matlab, the surface can be obtained using the "surf" function. 4. Use FDM to calculate the following American put option prices. (However, use the Implicit methodology only) "Stock price =100, Strike price =100, interest rate =3.5%, Dividend =0.5%, Volatility =20%, expiry =0.5" 1. Evaluate the following European call options using FDM's Explicit, Implicit, and Crank-Nicolson methodologies. "Stock price =100, Strike price =100, interest rate =3.5%, Dividend =0.5%, Volatility =20%, expiry =0.5 2. The underlying asset and the time grid numbers M and N are increased to 200,250,300,400,500,1000 together Calculate the option price using FDM and compare it with the result using the Black-Scholes formula. ( However, comparing the Explicit, Implicit, and CrankNicolson methodologies) "Stock price =100, Strike price =100, interest rate =3.5%, Dividend =0.5%, Volatility =20%, expiry =0.5% 3 . Based on the result of #2, draw delta and gamma surface. "Stock price =100, Strike price =100, interest rate =3.5%, Dividend =0.5%, Volatility =20%, expiry =0.5 " [Note] In Matlab, the surface can be obtained using the "surf" function. 4. Use FDM to calculate the following American put option prices. (However, use the Implicit methodology only) "Stock price =100, Strike price =100, interest rate =3.5%, Dividend =0.5%, Volatility =20%, expiry =0.5