Forthcoming Seminars › Seminar Series

Mathematical Finance Internal Seminar

Thu, 17/01/2008
12:00 		Michael Monoyios Mathematical Finance Internal Seminar Add to calendar DH 1st floor SR
Optimal hedging of basic risk with partial information
The setting is a lognormal basis risk model. We study the optimal hedging of a claim on a non-traded asset using a correlated traded asset in a partial information framework, in which trading strategies are required to be adapted to the filtration generated by the asset prices. Assuming continuous observations, we take the assets' volatilites and the correlation as known, but the drift parameters are not known with certainty. We assume the drifts are random variables with a Gaussian prior distribution, derived from data prior to the hedging timeframe. This distribution is updated via a Kalman-Bucy filter. The result is a basis risk model with random drift parameters. Using exponsntial utility, the optimal hedging problem is attacked via the dual to the primal problem, leading to a representation for the hedging strategy in terms of derivatives of the indifference price. This representation contains additional terms reflecting uncertainty in the assets' drifts, compared with the classical full information model. An analytic approximation for the indifference price and hedge is developed, for small positions in the claim, using elementary ideas of Malliavin calculus. This is used to simulate the hedging of the claim over many histories, and the terminal hedging error distribution is computed to determine if learning can counteract the effect of drift parameter uncertainty.
Thu, 14/02/2008
12:00 		Mile Giles (Oxford) Mathematical Finance Internal Seminar Add to calendar DH 1st floor SR
Smoking adjoints
This talk will be about the mathematics and computer science behind my "Smoking Adjoints: fast Monte Carlo Greeks" article with Paul Glasserman in Risk magazine. At a high level, the adjoint approach is simply a very efficient way of implementing pathwise sensitivity analysis. At a low level, reverse mode automatic differentiation enables one to differentiate a "black-box" to get the sensitivity of a single output to multiple inputs at a cost no more than 4 times greater than the cost of evaluating the black-box, regardless of the number of inputs

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