Nomura Seminar
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Tue, 03/05/2011 14:15 |
Lioudmilla Vostrikova (University of Angers) |
Nomura Seminar  |
Oxford-Man Institute |
| We study exponential Levy models with change-point which is a random variable, independent from initial Levy processes. On canonical space with initially enlarged filtration we describe all equivalent martingale measures for change- point model and we give the conditions for the existence of f-minimal equivalent martingale measure. Using the connection between utility maximisation and f-divergence minimisation, we obtain a general formula for optimal strategy in change-point case for initially enlarged filtration and also for progressively enlarged filtration when the utility is exponential. We illustrate our results considering the Black-Scholes model with change-point. Key words and phrases: f-divergence, exponential Levy models, change-point, optimal portfolio MSC 2010 subject classifications: 60G46, 60G48, 60G51, 91B70 | |||
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Fri, 06/05/2011 14:15 |
Prof Emmanuel Gobet (Ecole Polytechnique) |
Nomura Seminar |
DH 1st floor SR |
| We derive a general methodology to approximate the law of the average of the marginal of diffusion processes. The average is computed w.r.t. a general parameter that is involved in the diffusion dynamics. Our approach is suitable to compute expectations of functions of arithmetic or geometric means. In the context of small SDE coefficients, we establish an expansion, which terms are explicit and easy to compute. We also provide non asymptotic error bounds. Applications to the pricing of basket options, Asian options or commodities options are then presented. This talk is based on a joint work with M. Miri. | |||
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Wed, 18/05/2011 12:45 |
Robert Elliott (University of Adelaide and University of Calgary) |
Nomura Seminar |
Oxford-Man Institute |
| We discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer's risk process is modeled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth. The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. This leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases. | |||
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Fri, 20/05/2011 14:15 |
Prof Tom Hurd (McMaster University) |
Nomura Seminar |
DH 1st floor SR |
| We argue that a natural extension of the well known structural credit risk framework of Black and Cox is to model both the firm's assets and liabilities as correlated geometric Brownian motions. This financially reasonable assumption leads to a unification of equity derivatives (written on the stock price), and credit securities like bonds and credit default swaps (CDS), nesting the Black-Cox credit model with a particular stochastic volatility model for the stock. As we will see, it yields reasonable pricing performance with acceptable computational efficiency. However, it has been well understood how to extend a credit framework like this quite dramatically by the trick of time- changing the Brownian motions. We will find that the resulting two factor time-changed Brownian motion framework can encompass well known equity models such as the variance gamma model, and at the same time reproduce the stylized facts about default stemming from structural models of credit. We will end with some encouraging calibration results for a dataset of equity and credit derivative prices written on Ford Motor Company. | |||
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Mon, 23/05/2011 17:00 |
Marco Avellaneda (Courant Institute, NYU) |
Nomura Seminar |
Oxford-Man Institute |
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Leveraged ETFs are funds that target a multiple of the daily return of a reference asset; eg UYG (Proshares) targets twice the daily return of XLF (Financial SPDR) and SKF targets minus twice the daily return of XLF. It is well known that these leveraged funds have exposure to realized volatility. In particular, the relation between the leveraged and the unleveraged funds over a given time-horizon (larger than 1 day) is uncertain and will depend on the realized volatility. This talk examines this phenomenon theoretically and empirically first, and then uses this to price options on leveraged ETFs in terms of the prices of options on the underlying ETF. The resulting model allows to model the volatility skews of the leveraged and unleveraged funds in relation to each other and therefore suggest an arbitrage relation that could prove useful for traders and risk-managers. |
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Tue, 24/05/2011 14:15 |
Prof Costis Skiadas (NorthwesternUniversity) |
Nomura Seminar |
Oxford-Man Institute |
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Wed, 25/05/2011 12:45 |
Dr Umut Cetin (London School of Economics) |
Nomura Seminar |
Oxford-Man Institute |
| Given a deterministically time-changed Brownian motion Z starting from 1, whose time-change V (t) satisfies V (t) > t for all t > 0, we perform an explicit construction of a process X which is Brownian motion in its own filtration and that hits zero for the first time at V (S), where S := inf {t > 0 : Z_t = 0}. We also provide the semimartingale decomposition of X under the filtration jointly generated by X and Z. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process X may be viewed as the analogue of a 3-dimensional Bessel bridge starting from 1 at time 0 and ending at 0 at the random time V (S). We call this a dynamic Bessel bridge since S is not known at time 0 but is slowly revealed in time by observing Z. Our study is motivated by insider trading models with default risk. (this is a joint work with Luciano Campi and Albina Danilova) | |||
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Fri, 27/05/2011 14:15 |
Dr Harry Zheng (Imperial College London) |
Nomura Seminar |
DH 1st floor SR |
| In this talk we show that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions | |||
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Fri, 03/06/2011 14:15 |
Prof Stefan Ankirchner (University of Bonn) |
Nomura Seminar |
DH 1st floor SR |
| When managing risk, frequently only imperfect hedging instruments are at hand. We show how to optimally cross-hedge risk when the spread between the hedging instrument and the risk is stationary. At the short end, the optimal hedge ratio is close to the cross-correlation of the log returns, whereas at the long end, it is optimal to fully hedge the position. For linear risk positions we derive explicit formulas for the hedge error, and for non-linear positions we show how to obtain numerically effcient estimates. Finally, we demonstrate that even in cases with no clear-cut decision concerning the stationarity of the spread it is better to allow for mean reversion of the spread rather than to neglect it. The talk is based on joint work with Georgi Dimitroff, Gregor Heyne and Christian Pigorsch. | |||
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Tue, 07/06/2011 14:15 |
Prof Freddy Delbaen (ETH Zurich) |
Nomura Seminar |
Oxford-Man Institute |
