Past Mathematical Finance Internal Seminar

8 May 2008
13:00
Hanqing Jin
Abstract
In a financial market, the appreciate rates are very difficult to estimate precisely, and in general only some confidence interval will be estimated. This paper is devoted to the portfolio selection with the appreciation rates being in a certain closed convex set rather than some precise point. We study the problem in both expected utility framework and mean-variance framework, and robust solutions are given explicitly in both frameworks.
  • Mathematical Finance Internal Seminar
24 April 2008
13:00
Christopher Reisinger
Abstract
(based on joint work with Helen Haworth, William Shaw, and Ben Hambly) The simulation of multi-name credit derivatives raises significant challenges, among others from the perspective of dependence modelling, calibration, and computational complexity. Structural models are based on the evolution of firm values, often modelled by market and idiosyncratic factors, to create a rich correlation structure. In addition to this, we will allow for contagious effects, to account for the important scenarios where the default of a number of companies has a time-decaying impact on the credit quality of others. If any further evidence for the importance of this was needed, the recent developments in the credit markets have furnished it. We will give illustrations for small n-th-to-default baskets, and propose extensions to large basket credit derivatives by exploring the limit for an increasing number of firms
  • Mathematical Finance Internal Seminar
14 February 2008
12:00
Mile Giles
Abstract
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
  • Mathematical Finance Internal Seminar
17 January 2008
12:00
Michael Monoyios
Abstract
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.
  • Mathematical Finance Internal Seminar

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