Most classical models for derivatives prices focus on prescribing the time evolution of the underlying stochastic factors. The prices of derivatives are then computed, for example, via the risk-neutral expectations. As markets developed and many derivative contracts became liquidly traded, it appeared necessary, in order to avoid creating arbitrage opportunities and to fully exploit the information given by the market, to calibrate such models so that they reproduce the observed derivatives prices. However, the results of the calibration may vary significantly from day to day, implying that none of the calibrated models can be used to describe the future time evolution of the derivatives prices and, in particular, study the risks associated with them.
The idea of the market-based approach is to model the derivatives prices directly, as the prices of generic financial assets. This approach allows starting the model from an arbitrary combination of derivatives prices currently observed in the market, without having to change (recalibrate) the model. In this presentation, I will outline the main difficulties associated with the construction of market-based models and will present a general methodology that bypasses these difficulties. I will also present an overview of the existing families of market-based models, starting with the famous Heath-Jarrow-Morton theory, and show how these results can be obtained via the general methodology. Finally, I will illustrate the theory by constructing (both mathematically and numerically) a family of market-based models for the European call options of multiple strikes and maturities.
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