arXiv subjects
Publications and source records attributed to Travis Fisher.
Financial models are studied where each asset may potentially lose value relative to any other. Conditioning on non-devaluation, each asset can serve as proper numéraire and classical valuation rules can be formulated. It is shown when and how these local valuation rules can be aggregated to obtain global arbitrage-free valuation formulas.
We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a change of numéraire (change of currency) technique when the underlying is only a local martingale modelling for example an exchange rate. The new pricing operator assigns prices to contingent claims according to the minimal cost for superreplication strategies that succeed with probability one for both currencies as numéraire. Within this context, we interpret the lack of the martingale property of an exchange-rate as a reflection of the possibility that the numéraire currency may devalue completely against the asset currency (hyperinflation).
We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that only depends on the terminal value of the stopped Brownian motion. This explains the existence of explicit analytic formulas for option prices within Quadratic Normal Volatility models in the academic literature.