Seminarium i matematisk statistik
måndagen den 10 januari 13.15 i MH:227

Mogens Bladt
IIMAS, National University of Mexico
Mexico City

Titel:
Extending Samuelson's option pricing formula

Abstract:
We study the pricing of derivatives in a simple two--period model with a
continuous payoff distribution. This corresponds to a financial model
where intermidate hedging or movement is not allowed (buy-and-hold
strategy).
Such a model cannot be priced within the framework of arbitrage theory
though it is clear that any contingent claim should have a ``fair''
price which compensates the risk of the payoff distribution. We call
this price the buy-and-hold price of the derivative and show that it
coincides with a formula proposed by Samuelson in 1965. The buy-and-hold
price will not always coincide with the corresponding arbitrage price.
The arbitrage price, as opposed to the buy-and-hold price, is dependent
on a dynamic model specification in a continuous time environment. We
are able to recover Black--Scholes formula as a special case of the
buy-and-hold prices. Finally we investigate the relation between the
buy-and-hold prices and arbitrage prices; it turns out that an extention
of the Samuelson 1965 formula is consistent to arbitrage pricing.
Markov--modulation will be the main vehicle for establishing Samuelson's
formula and as a by--product we obtain explicit formulas for the
two--state model, which may be of interest on its own.