Axel Wåhlin

Estimation, Examination and Extensions of SPDs Empirical
Study on The Nordic Option Market

Abstract

Different methods of estimating the implied state price densities
(SPDs) are reported and compared. SPD meaning a risk-neutral
density. A crosssection of option prices on the OMXS30 index is used
to estimate the option implied SPD, which is compared to a SPD implied
by the time-series of the returns of the index. If the compared SPDs
have the same attributes, implications of the rationality of investors
option pricing can be made. Interesting results from SPD estimation
comes from identifying the prices of risks in the market that are
taken on by investors. The observed market inferred SPD is
risk-neutral and cannot be directly compared with the observed
time-series density. The time-series SPD has an actual (historical)
density. The latter is therefore transformed with Girsanov s
transformation before it is examined. Two methods are used in the
comparison, a hypothesis test, and a trading strategy test that
exploits possible di erences. The results are contradicting, the
hypothesis test cannot reject the hypothesis that both SPDs are indeed
identical when the trading strategy employed yield large
returns. Analysis of SPDs is suggested for usage within risk
management.