# L22 - Lecture 22 More on Monte Carlo Methods in Finance...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 22 More on Monte Carlo Methods in Finance Monte Carlo methods apply to several aspects in mathematical finance, which we will briefly describe in what follows. 1 Simulation of SDEs Consider an Itˆo process X defined as a solution to the SDE dX t = μ t dt + σ t dW t , t ∈ [0 ,T ] , with X = x. (22.1) For simplicity, assume μ t = a ( X t ) and σ t = b ( X t ) for some deterministic functions a ( · ) and b ( · ). The Euler discretization scheme (see [2] or [3]) provides a first-order approximation to (22.1) as follows: For a small time increment Δ > 0, suppose T/ Δ = n (a positive integer). Let Y i = X i Δ , i = 0 , 1 ,...,n . Then (22.1) is approximated by the (discrete) time series Y i = Y i- 1 + a ( Y i- 1 ) Δ + b ( Y i- 1 ) √ Δ ² i , i = 1 ,...,n, with Y = x, (22.2) where ² 1 ,² 2 ,... are iid N (0 , 1) random variables. An obvious way to simulate the sequence { Y i } would start with generating the sequence { ² i } then follow the iterations in (22.2)....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

L22 - Lecture 22 More on Monte Carlo Methods in Finance...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online