Jon M. Huntsman School of Business Master of Science in Financial Economics August 2013

Pricing and Hedging Asian Options
By Vineet B. Lakhlani

Pricing and Hedging Asian Options

Table of Contents

Table of Contents 1. Introduction to Derivatives 2. Exotic Options
2.1.
Introduction to Asian Options 3.1. Binomial Option Pricing Model 3.2. Black-Scholes Model 3.2.1. Black-Scholes PDE Derivation 3.2.2. Black-Scholes Formula

1 2 3 4
4 5 6 7 3

3. Option Pricing Methodologies

4. Asian Option Pricing
4.1. 4.2. 4.3. 4.4. Closed Form Solution (Black-Scholes Formula) QuantLib/Boost Monte Carlo Simulations Price Characteristics

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8 10 11 14

5. Hedging
5.1. Option Greeks 5.2. Characteristics of Option Delta (Δ) 5.3. Delta Hedging 5.3.1. Delta-Hedging for 1 Day 5.4. Hedging Asian Option 5.5. Other Strategies 6. Conclusion

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17 17 19 20 22 25

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27 32 34

Appendix
i. ii. iii. Tables References Code: Black-Scholes Formula For European & Asian (Geometric) Option

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Pricing and Hedging Asian Options

1. Introduction to Derivatives:
Financial derivatives have been in existence as long as the invention of writing. The first derivative contracts—forward contracts—were written in cuneiform script on clay tablets. The evidence of the first written contract was dates back to in nineteenth century BC in Mesopotamia on a tablet that promised delivery of 30 wooden [planks] of specific dimension to client at a future date. [11] There are many other written accounts of such contracts in various pre BC civilizations in Indus Valley, Greece and Rome. [11] Financial derivatives are used extensively in various financial markets to effectively and economically hedge different risks. The semiannual