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State price density, Esscher transforms, and pricing options on stocks, bonds, and foreign exchange rates. (English) Zbl 1083.62548

Summary: The state price density is modeled as an exponential function of the underlying state variables, and the Esscher transform is used to specify the forward-risk-adjusted measure. With the aid of state price densities, Esscher transforms, and characteristic functions, this paper provides a consistent framework for pricing options on stocks, interest rates, and foreign exchange rates. The framework discussed is quite general and is related to many popular models.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B28 Finance etc. (MSC2000)
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