Financial/Actuarial Mathematics Seminar

Option pricing in the broadest sense of pricing contingent cash flows is clearly a major focus of Actuarial Science. Most of this actuarial pricing work is done using realistic probability distributions and realistic return expectations, yet one of the cornerstones of modern finance, the Black-Scholes equation, uses unrealistic probabilities and the risk free rate. This paper provides a methodology for pricing options using realistic probabilities (P-Space) and state price deflators. It also shows that these P-Space option prices match Black-Scholes option prices when stock returns are assumed to be normally distributed, and proves that in this case the P-Space call equation is equivalent to the Black-Scholes call equation. The paper also provides the connection among the key option pricing variables: expected return, standard deviation, and the risk free rate.