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It turns out that in the bivariate Black-Scholes economy Margrabe type options exhibit symmetry properties leading to semi-static hedges of rather general barrier options. Some of the results are extended to variants obtained by means of Brownian subordination. In order to increase the liquidity of the hedging instruments for certain currency options, the duality principle can be applied to set up hedges in a foreign market by using only European vanilla options sometimes along with a risk-less bond. Since the semi-static hedges in the Black-Scholes economy are exact, closed form valuation formulas for certain barrier options can be easily derived.
We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investors beliefs, risk preferences and f
We study indifference pricing of exotic derivatives by using hedging strategies that take static positions in quoted derivatives but trade the underlying and cash dynamically over time. We use real quotes that come with bid-ask spreads and finite qua
The portfolio optimization problem is a basic problem of financial analysis. In the study, an optimization model for constructing an options portfolio with a certain payoff function has been proposed. The model is formulated as an integer linear prog
In this paper, we are concerned with the valuation of Guaranteed Annuity Options (GAOs) under the most generalised modelling framework where both interest and mortality rates are stochastic and correlated. Pricing these type of options in the correla
In this paper we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage probability.