The aim of this paper is to develop a hedging methodology for making a portfolio of options delta, vega and gamma neutral by taking positions in other available options, and simultaneously minimizing the net premium to be paid for the hedging. A quadratic programming solution for the problem is...

This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses. It introduces the theory of interest, discrete and continuous random variables and probability,...

This paper uses a dynamic optimization model to quantify the potential welfare gains of hedging against commodity price risk for commodity-exporting countries. We show that hedging enhances domestic welfare through two channels: first, by reducing export income volatility; and second, by...

We study the valuation and hedging of unit-linked life insurance contracts in a setting where mortality intensity is governed by a stochastic process. We focus on model risk arising from different specifications for the mortality intensity. To do so we assume that the mortality intensity is...

We propose a simplified approach to mean-variance portfolio problems by changingtheir parametrisation from trading strategies to final positions. This allows us to treat,under a very mild no-arbitrage-type assumption, a whole range of quadratic optimisationproblems by simple mathematical tools...

This paper discusses how to achieve the optimal hedging of a cash flow when facing price risk of the product the company sells, when we are also in the presence of cost and quantity uncertainty. We present an analytical solution to the optimal hedging strategy in the general case and in some...

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their "distance" to a reference local volatility model. In...

We study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this vanilla option, delta-vega hedging is asymptotically optimal...

Investors have long debated what fraction, if any, of their portfolio's currency exposure they should hedge. Although the answers cover a broad range, often with dubious rationale, most informed investors agree that the solution should be based on mean-variance optimization, deployed either to...

We consider the problem of hedging a European contingent claim in a Bachelier model with transient price impact as proposed by Almgren and Chriss. Following the approach of Rogers and Singh [24] and Naujokat and Westray, the hedging problem can be regarded as a cost optimal tracking problem of...