The price of a financial asset can be conceived as the risk-neutral expectation of its random payoff. When the payoff has an exponential form as well as known distribution, the moment generating function and its analytical counterpart (the Laplace transform) become an important instrument for calculation purposes. This article shows the effectiveness of the Laplace technique in pricing options in the classic Black Scholes (1973) setting. In particular, options endowed with the "bull-bear" clause are priced.
Sbuelz, A., Moment Generating Function and Asset Pricing: A note, <<GIORNALE DELL'ISTITUTO ITALIANO DEGLI ATTUARI>>, 1998; LXI (1/2): 55-64 [http://hdl.handle.net/10807/22758]
Moment Generating Function and Asset Pricing: A note
Sbuelz, Alessandro
1998
Abstract
The price of a financial asset can be conceived as the risk-neutral expectation of its random payoff. When the payoff has an exponential form as well as known distribution, the moment generating function and its analytical counterpart (the Laplace transform) become an important instrument for calculation purposes. This article shows the effectiveness of the Laplace technique in pricing options in the classic Black Scholes (1973) setting. In particular, options endowed with the "bull-bear" clause are priced.
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