## Implementation and Algorithm

Functions and market data are stored in the folder BetaEstimation. Before running the code, you must include this folder and its subfolders in the MATLAB directory list. To do so select Set Path from the File Menu and follow the instructions. The Beta Estimation folder contains the following MATLAB scripts to estimate the beta according to the different procedures ParlOLS, ParlEWMa, ParlBetaBAYES, ParlBetaTrimming, ParlBetaMedRobust, ParlBetaRobust, ParOlBetaKALMAN, KalmanRunOpt,...

## Solution Methodology

A possible way out is to derive a function c -,t by interpolating observed option prices. As observed by McCauley and Melick 1996a, 1996b and Campa, Chang and Reider 1997, 1998 the most binding limitations of this approach occur on the over-the-counter OTC currency market where prices for very few strikes, say three to five, are usually quoted. Several approaches to extract an implied density from option prices have been proposed in the literature. A comparison of different approaches can be...

## Den Iseger Transform

These examples have been obtained writing the Matlab functions AWSR spot, strike, expiry, sg, rf, aa, terms, extraterms The function AWSR performs the numerical inversion of the Laplace transform according to the Abate-Whitt algorithm. The function ltsr returns the quantity v x, t y Y2. The complete code is given here below. function optprice AWSR spot, strike, expiry, sg, rf, aa, terms, extraterms X strike expiry sum 0 compute the LT at gamma aa 2 strike lt ltsr spot , expiry , sg , rf , aa 2...

## Info

G 0,z ez - K , G t, ln U 0, G t, ln L 0. G 0,z ez - K , G t, ln U 0, G t, ln L 0. As described in the Appendix on the MATLAB solver, we need to define functions describing a the PDE, b the initial condition, c the boundary conditions. This has been done in the M-file pdeBSDoubleBarrierExample.m, where the function pdepe is called using the structure sigma,strike . Notice the presence of the parameters riskfree,sigma,strike as additional inputs in the function pdepe. The functions pdefun,...

## Contents

xv 1 Static Monte 1.1 Motivation and 1.1.1 Issue 1 Monte Carlo 1.1.2 Issue 2 Efficiency and Sample 1.1.3 Issue 3 How to Simulate 1.1.4 Issue 4 How to Evaluate Financial Derivatives 9 1.1.5 The Monte Carlo Simulation 1.2 Simulation of Random 1.2.1 Uniform Numbers 1.2.2 Transformation Methods 1.2.3 Acceptance-Rejection 1.2.4 Hazard Rate Function Method 1.2.5 Special Methods 1.3 Variance Reduction 1.3.1 Antithetic 1.3.2 Control 1.3.3 Importance Sampling 1.4 Comments 2 Dynamic Monte 2.1 Main...