Statistical & Financial Consulting by Stanford PhD
OPTION PRICING

Option Pricing is part of financial engineering that focuses on pricing vanilla options (European style, American style) and exotic options (knockouts, double knockouts, basket options, Asian options). Option pricing rests on two techniques:

1] perfect or imperfect replication of the option with simpler assets whose prices are known,

2] pricing an option by modeling its underlying asset(s) as a complex stochastic process whose parameters are calibrated to the market.

Option pricing involves relatively little statistics. Typically, we are not fitting the model to historical data. We are not concerned with identifying the most statistically efficient technique making use of every observation in a long historical time window. We are fitting the model to one observation only but that fit must be perfect or nearly perfect. The observation represents the most recent prices of the liquid products in the same market. These prices are taken as an axiom and, for that reason, option pricing employs many more results from probability theory than from applied or theoretical statistics.

Option pricing is one the greatest successes of mathematics in the world of finance. Surprisingly many options can be priced relatively accurately by the methods of stochastic calculus, partial differencial equations, numerical methods and Monte Carlo.

OPTION PRICING REFERENCES

Hull, J. (2011), Options, Futures, and Other Derivatives (8th ed), Pearson / Prentice Hall.

Brigo, D., & Mercurio, F. (2006). Interest Rate Models - Theory and Practice (2nd ed). Springer-Verlag Berlin Heidelberg.

Duffie, D. (2001), Dynamic Asset Pricing Theory (3rd ed), Princeton University Press.

Bjork, T. (2009), Arbitrage Theory in Continuous Time (3rd ed), Oxford University Press.

Lipton, A. (2001). Mathematical Methods for Foreign Exchange: A Financial Engineer's Approach. World Scientific.

Bouzoubaa, M. (2010). Exotic Options and Hybrids: A Guide to Structuring, Pricing and Trading. Wiley.

de Weert, F. (2008). Exotic Options Trading. Wiley.

Nelken, I., ed (1996). The Handbook of Exotic Options: Instruments, Analysis and Applications. McGraw-Hill.

Gatheral, J. (2006). The Volatility Surface. John Wiley & Sons, New Jersey.

Clark, I. J. (2011). Foreign Exchange Option Pricing: A Practitioner's Guide. Wiley.

Glasserman, P. (2003). Monte Carlo Methods in Financial Engineering. Springer-Verlag New York.

Haug, E. G. (2006). The Complete Guide to Option Pricing Formulas (2nd ed). McGraw-Hill.

Cochrane, J. H. (2003). Asset Pricing (revised ed). Princeton University Press.

Passarelli, D. (2008). Trading Option Greeks: How Time, Volatility, and Other Pricing Factors Drive Profit. Bloomberg Press, New York.

OPTION PRICING RESOURCES

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