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Graphical Representation of Option Price and Sensitivities

Mark Garman and Steven Kohlhagen were the founder of the Garman Kohlhagen model which is provided an analytic valuation model for European options on currencies using an approach similar to that used by Merton for European options on dividend-paying stocks.
It tries to evaluate a fair value of an option, and if it behaves well then the option's market price will equal the theoretical fair value.
The mathematics of their derivation is quite complex.
Interested readers can find it in the original paper Garman-Kohlhagen (1976), and the books by Hull (1993).

The Garman Kohlhagen model was developed to value European-style options on currencies. It is crucial to remember that the Garman Kohlhagen model is based on a number of assumptions.

  1. The distribution of terminal currency exchange rate (returns) is lognormal.
  2. There are no arbitrage possibilities.
  3. Transactions cost and taxes are zero.
  4. The risk-free interest rates, the foreign interest rates, and the exchange rate volatility are known functions of time over the life of the option.
  5. There are no penalties for short sales of currencies.
  6. The market operates continuously and the exchange rates follows a continuous Ito process.

Pricing Models Page Available is a Swing Java Jar File if you just wish to run the models.