On changes of measure in stochastic volatility models

By Bernard Wong, Chris C. Heyde. 2006

60 citations recorded by the source corpus.

Pricing in mathematical finance often involves taking expected values under different equivalent measures. Fundamentally, one needs to first ensure the existence of ELMM, which in turn requires that the stochastic exponential of the market price of risk process be a true martingale. In general, however, this condition can be hard to validate, especially in stochastic volatility models. This had led many researchers to “assume the condition away,” even though the condition is not innocuous, and nonsensical results can occur if it is in fact not satisfied. We provide an applicable theorem to check the conditions for a general class of Markovian stochastic volatility models. As an example we will also provide a detailed analysis of the Stein and Stein and Heston stochastic volatility models.

Subfields: Demography, Finance

View Paper: https://www.semanticscholar.org/paper/e9bb8589f36ab89305deb4f819568256e11f2db1

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Citations in the corpus

• The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Withdrawal Benefit Guarantees in Variable Annuities (2011, background): “Wong and Heyde (2006) also show that the equivalent ocal martingale measure that corresponds to the market price of volatility risk, )(tVλ , exists if the inequality ∞ ≤− λσκ v/ is fulfilled.”