ABSTRACT
In the previous chapter, we saw how we could derive a closed-form formula for the price of a vanilla option (i.e. a call or a put) in the Black-Scholes environment. For more complex models, we are not able to find such explicit expressions. The same is true for American options, even in the Black-Scholes setting. That is why numerical methods are needed. The purpose of this chapter is to introduce the connection between diffusions and partial differential equations and to present some numerical methods based on this connection.
