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A simplified Capital Asset Pricing Model
Vladimir Vovk
We consider a Black-Scholes market in which a number of stocks and an index are traded. The simplified Capital Asset Pricing Model is the conjunction of the usual Capital Asset Pri…
The Capital Asset Pricing Model as a corollary of the Black-Scholes model
Vladimir Vovk
We consider a financial market in which two securities are traded: a stock and an index. Their prices are assumed to satisfy the Black-Scholes model. Besides assuming that the inde…
The efficient index hypothesis and its implications in the BSM model
Vladimir Vovk
This note studies the behavior of an index I_t which is assumed to be a tradable security, to satisfy the BSM model dI_t/I_t = μdt + σdW_t, and to be efficient in the following sen…
Losing money with a high Sharpe ratio
Vladimir Vovk
A simple example shows that losing all money is compatible with a very high Sharpe ratio (as computed after losing all money). However, the only way that the Sharpe ratio can be hi…
Probability-free pricing of adjusted American lookbacks
A. Philip Dawid, Steven de Rooij, Peter Grunwald +5
Consider an American option that pays G(X^*_t) when exercised at time t, where G is a positive increasing function, X^*_t := \sup_{s\le t}X_s, and X_s is the price of the underlyin…
Ito calculus without probability in idealized financial markets
Vladimir Vovk
We consider idealized financial markets in which price paths of the traded securities are cadlag functions, imposing mild restrictions on the allowed size of jumps. We prove the ex…