PT - JOURNAL ARTICLE
AU - Shimko, David C.
TI - Simplified Option Price Derivations
AID - 10.3905/jod.2022.1.160
DP - 2022 May 25
TA - The Journal of Derivatives
PG - 9--19
VI - 29
IP - 5
4099 - http://jod.pm-research.com/content/29/5/9.short
4100 - http://jod.pm-research.com/content/29/5/9.full
AB - Previous academic research reveals that mean-variance asset pricing (MVAP) models such as the single-period capital asset pricing model (CAPM) fail to produce rational European option prices. This article shows two adaptations of MVAP models that may be used to value derivatives with nonlinear payouts. The first removes static option arbitrage in investorsâ€™ optimized aggregate portfolio selection. The second linearizes the pricing kernel, using a static version of the self-financing condition applied in dynamic option modeling. Both adaptations produce risk-neutral derivative prices in equilibrium for all finite-moment probability distributions of underlying asset prices with compact support. The derivation does not require stochastic calculus, frictionless continuous trading assumptions, or the solution of differential equations. The resulting model is a hybrid of equilibrium and arbitrage techniques that rationally values assets and derivatives.