With the success of variable annuities, insurance companies are piling up large risks in terms of both equity and fixed income assets. These risks should be properly modeled as the resulting dynamic hedging strategy is very sensitive to the modeling assumptions. The current literature has been...

With the success of variable annuities, insurance companies are piling up large risks in terms of both equity and fixed income assets. These risks should be properly modeled as the resulting dynamic hedging strategy is very sensitive to the modeling assumptions. The current literature has been...

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...

In this paper, we investigate the following problem: How can a financial institution, which has sold an option to a client, optimally hedge the payoff of this option by investing into a stock and into the option itself? Optimality is measured in terms of minimal variance and the associated...

Classical quantitative finance models such as the Geometric Brownian Motion or its later extensions such as local or stochastic volatility models do not make sense when seen from a physics-based perspective, as they are all equivalent to a negative mass oscillator with a noise. This paper...

Mathematical finance explores the consistency relationships between the prices of securities imposed by elementary economic principles. Commonplace among these are replicability and the absence of arbitrage, both essentially algebraic constraints on the valuation map from a security to its...

Derivatives pricing can be seen as extrapolation of the present (fit existing tradeable products like vanilla options to price new ones like barrier options) and thatquantitative investment is an extrapolation of the past (fit past patterns to predictthe future). In this book, we argue that...

An example is used to show that efficient market expectations are not the same as expectations in a stochastic process. An implication is that efficient market expectations need not have stochastic properties like orthogonality and variance bounds. Failure to recognize this fact has led to bad...

We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied...