Market consistent valuations with financial imperfection

Abstract

In this paper, we study market consistent valuations in imperfect markets. In the first part of the paper, we observe that in an imperfect market one needs to distinguish two type of market consistencies, namely types I and II. We show that while market consistency of type I holds without very strong conditions, market consistency of type II (which in the literature is known as the usual definition of market consistency) is only well defined in perfect markets. This is important since the existing literature on market consistency considers perfect markets where the two market consistencies are equivalent. In the second part of the paper, by introducing a best estimator we find strong connections between hedging and market consistency of either type. We show under very general conditions, the type I and the type II market consistent evaluators are best estimators, and establish a two-step representation for the market consistent risk evaluators. In the third part of the paper, we present several families of market consistent evaluators in imperfect markets.

A market- and time-consistent extension for the EIOPA risk-margin

“…They show that the fair hedge-based valuation is identical to the two-step actuarial valuation in Pelsser and Stadje [37]. Assa and Gospodinov [3] studied the market-consistent valuations in imperfect markets and showed that market-consistency of the type defined in this paper is only well-defined in a perfect market. They showed that market-consistency is strongly connected to hedging and all market-consistent evaluators are a kind of "best-estimate" that two-step valuations can represent.…”

“…Therefore, the insurer includes this cost-of-capital as risk loading in price to be paid by the policyholder. 3 The Solvency II framework advises to set the confidence level of the aR to 99.5% and the cost-of-capital to 6% . Suppose we only have the actuarial risk y t with payoff f (y T ) for t < T .…”

Insurance Valuation: A Two-Step Generalised Regression Approach

“…Karim Barigou acknowledges the financial support of the Joint Research Initiative on "Mortality Modeling and Surveillance" funded by AXA Research Fund. 4 We remark that our two-step approach should not be confused with the two-step mark etvaluation proposed by Pelsser and Stadje (2014) and the two-step evaluators of Assa and Gospodinov (2018) which have both different meanings.…”

“…We remark that our two-step approach should not be confused with the two-step market valuation proposed byPelsser and Stadje (2014) and the two-step evaluators ofAssa and Gospodinov (2018) which have both different meanings.…”

Learning agents in Black–Scholes financial markets

“…No single measure dominates. In fact, there are many models that are consistent with the observation of a finite number of strike volatilities in the market [38][39][40][41]. In practice, the choice of a correct probability measure such that a derivative contract is priced correctly is a subjective and quantitative exercise.…”