# Value at Risk

Topic: Discuss and investigate VaR and its characteristics when applied to options. You must produce example calculations on:

European and American style options

Long and short positions in these

Portfolio of at least three different options (more is better)

Introduction

All financial institutions bear some sort of risk while dealing with different financial instruments, whether it be corporate treasurers, fund managers or financial institutions, they are all exposed to a certain market risks while carrying out their daily trading activities. There is a possibility that the institution makes a blunder in forecasting the future value of its trade and this may lead to major losses that have to be

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For a description of the other methods one can refer to the chapter on value at risk in Hull,J(2010).

The Monte Carlo simulation method

The Monte Carlo method is a technique which used random numbers and probability to solve problems. The term Monte Carlo was coined by S. Ulam and Nicholas Metropolis(…….) in conjunction with the game of gambling at a casino called Monte Carlo. They referred the process to a game to roulette in which the chances of the number striking are probable and random. It uses the

To calculate a 1-day VaR for a portfolio using Monte-Carlo simulation we follow the following steps(Hull,J.C, 2010):

Step 1: value the portfolio today in the usual way using the current values of market variable

Step 2: sample once from the multivariate normal probability distribution of the ∆xi

Step 3: use the value of the ∆xi that are sampled to determine the value of each market variable at the end of one day.

Step 4: Revalue the portfolio at the end of the day in the usual way.

Step 5: subtract the value calculated in step 1 from the value in step 4 to determine a sample ∆P.

Step 6: repeat steps 2 to 5 many times to build up a probability distribution for ∆P.

Antithetic variables can be used while using the Monte Carlo simulation which would reduce the variance. While using antithetic variable, the simulation produces two values of the derivative. The first value (f1) is