Aleš Černý

On the Structure of General Mean-Variance Hedging Strategies

We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure

An improved convolution algorithm for discretely sampled Asian options

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Mean Variance Hedging and Optimal Investment in Heston's Model with Correlation

which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to

Hedging by Sequential Regressions Revisited

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Risk, Return and Portfolio Allocation Under Alternative Pension Systems With Incomplete and Imperfect Financial Markets

coincides with the variance-optimal martingale measure relative to the original probability measure

Optimal Continuous-Time Hedging with Leptokurtic Returns

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Admissible Strategies in Semimartingale Portfolio Selection

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The Impact of Changing Demographics and Pensions on The Demand for Housing and Financial Assets

We suggest an improved FFT pricing algorithm for discretely sampled Asian options with general independently distributed returns in the underlying. Our work complements the studies of Carverhill and Clewlow [Risk, 1990, 3(4), 25-29], Benhamou [J. Comput. Finance, 2002, 6(1), 49-68], and Fusai and Meucci [J. Bank. Finance, 2008, 32(10), 2076-2088], and, if we restrict our attention only to log-normally distributed returns, also Vecer [Risk, 2002, 15(6), 113-116]. While the existing convolution algorithms compute the density of the underlying state variable by moving forward on a suitably defined state space grid, our new algorithm uses backward price convolution, which resembles classical lattice pricing algorithms. For the first time in the literature we provide an analytical upper bound for the pricing error caused by the truncation of the state space grid and by the curtailment of the integration range. We highlight the benefits of the new scheme and benchmark its performance against existing finite difference, Monte Carlo, and forward density convolution algorithms.

The Risk of Optimal, Continuously Rebalanced Hedging Strategies and It's Efficient Evaluation via Fourier Transform

This paper solves the mean-variance hedging problem in Hestons model with a stochastic opportunity set moving systematically with the volatility of stock returns. We allow for correlation between stock returns and their volatility (so-called leverage effect). Our contribution is threefold: using a new concept of opportunity-neutral measure we present a simplified strategy for computing a candidate solution in the correlated case. We then go on to show that this candidate generates the true variance-optimal martingale measure; this step seems to be partially missing in the literature. Finally, we derive formulas for the hedging strategy and the hedging error.

Currency crises: introduction of spot speculators

Almost 20 years ago Foellmer and Schweizer (1989) suggested a simple and influential scheme for the computation of hedging strategies in an incomplete market. Their approach of local risk minimization results in a sequence of one-period least squares regressions running recursively backwards in time. In the meantime there have been significant developments in the global risk minimization theory for semimartingale price processes. In this paper we revisit hedging by sequential regression in the context of global risk minimization, in the light of recent results obtained by Cerny and Kallsen (2007). A number of illustrative numerical examples is given.