发帖
雷达卡
The purpose of this paper is to be an introduction to Monte Carlo techniques used in nance, mainly to price complicated products, called exotics. This paper has been designed for a on-expert public and focuses on giving a broad overview of Monte Carlo techniques from a practical point of view and presents also some improvements that can be done to increase the e ciency.
Contents
1 Origin 3
1.1 Geometrical application . . . . . . . . . . . . . . . . . . . . . 3
2 Financial modelling 5
2.1 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Classic Call case . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Results obtained . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Why does this work ? . . . . . . . . . . . . . . . . . . . . . . 7
2.5 Asian options . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.6 General case for 1 asset . . . . . . . . . . . . . . . . . . . . . 8
2.7 General case for n assets . . . . . . . . . . . . . . . . . . . . . 8
3 How to build a Monte Carlo pricer 9
3.1 Approach used . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Generation of random numbers . . . . . . . . . . . . . . . . . 9
3.2.1 Introduction to the problem . . . . . . . . . . . . . . . 9
3.2.2 The dierent types of generators . . . . . . . . . . . . 9
3.2.3 From uniform to normal . . . . . . . . . . . . . . . . . 10
3.3 How to build correlated arrays . . . . . . . . . . . . . . . . . 11
4 Greek computation 12
4.1 What are these greeks ? . . . . . . . . . . . . . . . . . . . . . 12
4.2 Simple approach . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3 More advanced methods . . . . . . . . . . . . . . . . . . . . . 13
4.3.1 Path dierenciation . . . . . . . . . . . . . . . . . . . 13
4.3.2 Other methods . . . . . . . . . . . . . . . . . . . . . . 14
5 Conclusion 14
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