Explain the programme of study of finite differences

Question

Explain the programme of study of finite differences.

Answer 1

When you are new to finite-difference methods and you really need to study them where a suggested programme of study is given

• Explicit method/European binaries, puts and calls: To get started you must learn the explicit way as applied to the Black–Scholes equation for a European option. It is very easy to program and you want not make many mistakes.

• Explicit method/American calls, binaries and puts: Not too much harder is the application of the explicit way to American options.

• Crank–Nicolson/European put, binaries and calls: Once you’ve determined the explicit method in your belt you must learn the Crank–Nicolson implicit method. It is harder to program, if you will get a better accuracy.

• Crank–Nicolson/American calls, puts and binaries: There’s not much more effort included in pricing American-style options than in the pricing of European-style options.

• Explicit method/path-dependent options: By now you will be fairly sophisticated and it is time to price a path-dependent contract. Begin with an Asian option with discrete sampling, and after that try a continuously-sampled Asian. At last, try your hand at look backs.

• Interest rate products: given programme repeated for non-path-dependent and after that path-dependent interest rate product. First price caps and floors and after that go on to the index amortizing rate exchange.

• Two-factor explicit: To find started on two-factor problems price a convertible bond by using an explicit way, with both the spot and the stock interest rate being stochastic.

• Two-factor implicit: The last stage is to implement the implicit two-factor method when applied to the convertible bond.