Fin & math doc seminar

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Spring Semester 2014

Date / Time

Speaker

Title

Location

18 March 2014
12:15-13:00

Chris Bardgett
UZH

Event Details

Fin & Math Doc Seminar

Title	A parsimonious stochastic correlation framework to model the joint dynamics of assets
Speaker, Affiliation	Chris Bardgett, UZH
Date, Time	18 March 2014, 12:15-13:00
Location	KOL G 212
Abstract	We introduce a novel and flexible stochastic correlation framework for asset returns. The system of stochastic differential equations satisfied by the correlation processes is proven to admit a unique strong solution and the correlation matrix is shown to be positive semidefinite over time. We investigate the case of correlated returns each of them following a stochastic volatility model and argue that our setup presents two main advantages compared to existing ones. First, the stochastic dependence structure is specified independently of the asset's individual dynamics, which makes it possible to estimate separately each asset's dynamics and their dependence structure. Second, our framework is parsimonious in the number of stochastic factors which is proportional to the number $n$ of assets, as opposed to quadratic in $n$. Finally, in an numerical experiment we examine the impact of stochastic correlations on the steepness of the implied volatility smile of index options. To avoid the curse of dimensionality when pricing basket options, we investigate two alternative solutions. The first one is to use standard Monte Carlo techniques. The second one is to solve the high dimensional partial differential equation that option prices satisfy using the Quantized Tensor Train representation for large matrices entering in the Finite Difference discretization. This low parametric format for high dimensional tensors is designed to make the storage cost and computational complexity grow linearly with the number of assets.

A parsimonious stochastic correlation framework to model the joint dynamics of assetsread_more

KOL G 212

29 April 2014
12:15-13:00

Dr. Kai Du
ETH

Event Details

Fin & Math Doc Seminar

Title	On solvability conditions for backward stochastic Riccati equations
Speaker, Affiliation	Dr. Kai Du, ETH
Date, Time	29 April 2014, 12:15-13:00
Location	KOL F 104
Abstract	This talk concerns a special class of matrix-valued quadratic BSDEs, called backward stochastic Riccati equations (SREs), arising in stochastic LQ optimal control problems. In a classical setting proposed by Bismut (’76), a complete solvability result was established by Tang (’03), depending on a definiteness assumption on certain coefficients. The general form, usually called indefinite SREs, releasing the definite condition but instead involving an algebraic constraint in addition to the backward equation, has not been solved completely, but only for several very special cases. In this talk, we give some novel sufficient conditions for the solvability of indefinite SREs, including a very practicable criterion, based on a new-defined notion named “subsolution”. These results seemed to cover almost all existing ones on the solvability of indefinite SREs. Several examples will be presented to illustrate the results.

On solvability conditions for backward stochastic Riccati equationsread_more

KOL F 104

27 May 2014
12:15-13:00

Robert Huitema
UZH

Event Details

Fin & Math Doc Seminar

Title	Risk premiums in a multi-factor jump-diffusion model for the joint dynamics of equity options and their underlying
Speaker, Affiliation	Robert Huitema, UZH
Date, Time	27 May 2014, 12:15-13:00
Location	KOL F 109
Abstract	This paper proposes a new approach to measure premiums for volatility and jump risks in option markets. These risks are captured by a multi-factor jump-diffusion model for the joint evolution of the underlying and the implied volatility surface. This market-based approach enables us to carefully test and select the most relevant risk factors in option markets. We extend the approach of Schonbucher (1998) to processes that include jumps and derive a condition that ensures absence of dynamic arbitrage. As this condition is derived under the physical measure, it incorporates a premium for each risk factor in the model. We then interpret the no-arbitrage condition as a noisy measurement of these risk premiums and other latent variables such as the volatility and jump-intensity of the underlying. This allows us to dynamically calibrate these variables to data from several markets using Bayesian filtering methods. The results shed new light on how option risk premiums vary over time and across markets. As our approach provides an accurate and arbitrage-free description of option price dynamics it can also be used for risk management of portfolios of options and for testing dynamic option strategies.

Risk premiums in a multi-factor jump-diffusion model for the joint dynamics of equity options and their underlyingread_more

KOL F 109

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Organizers: Martin Herdegen

Archive: SS 15 AS 14 SS 14 AS 13 SS 13 AS 12