M.Sc Student | Geidman Denis |
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Subject | Change of Stochastic Parameters in Derivative Assets |

Department | Department of Industrial Engineering and Management |

Supervisors | ASSOCIATE PROF. Haim Reisman |

PROF. Rann Smorodinsky | |

Full Thesis text |

Derivative assets are financial contracts whose value is determined by some underlying entity. The dependence of the derivative asset on the underlier is defined in the contract through various parameters, such as strike prices, delivery dates, contract size etc. These parameters are set at the creation of the contract and stay unchanged until its expiration. It is a common practice among both academics and practitioners to use alternative parameters when examining certain types of derivative assets. The most trivial example of this practice is the use of time to maturity as a parameter for bonds while the actual parameter in the bond contract is a maturity date. This alternative parametrization describes a financial instrument that is not traded in the real market and therefore standard financial methodologies cannot be applied to it.

In this thesis, we formalize a framework under which alternatively parametrized derivative assets can be studied, in a similar manner to real traded assets. In this framework, familiar financial techniques such as the fundamental theorem of asset pricing can be expanded and applied to a variety of financial entities for which conventional approaches may not apply.

We define a no arbitrage condition over a market of traded derivative assets and then we expand the definition to include markets of non-traded, alternatively parametrized assets. We show two methods for replicating alternatively parametrized assets using the original, traded assets. We show how one of the replication methods can be used to model the market of traded assets, using a market model of our choice for the alternatively parametrized assets. Our main result is the introduction of martingale pricing to alternatively parametrized asset markets - markets that are not necessarily comprised of real traded securities. Finally, we demonstrate an application of the methodology on a model of the implied volatility surface of a stock index.