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Dive into the research topics where L. C. G. Rogers is active.

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Featured researches published by L. C. G. Rogers.


Journal of Applied Probability | 1995

The value of an Asian option

L. C. G. Rogers; Z. Shi

This paper approaches the problem of computing the price of an Asian option in two different ways. Firstly, exploiting a scaling property, we reduce the problem to the problem of solving a parabolic PDE in two variables. Secondly, we provide a lower bound which is so accurate that it is essentially the true price.


Mathematical Finance | 2002

Monte Carlo Valuation of American Options

L. C. G. Rogers

This paper introduces a dual way to price American options, based on simulating the paths of the option payoff, and of a judiciously chosen Lagrangian martingale. Taking the pathwise maximum of the payoff less the martingale provides an upper bound for the price of the option, and this bound is sharp for the optimal choice of Lagrangian martingale. As a first exploration of this method, four examples are investigated numerically; the accuracy achieved with even very simple choices of Lagrangian martingale is surprising. The method also leads naturally to candidate hedging policies for the option, and estimates of the risk involved in using them.


Mathematical Finance | 1997

Arbitrage with Fractional Brownian Motion

L. C. G. Rogers

Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long–range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motion to model long–range dependence of returns while avoiding arbitrage.


Mathematical Finance | 1998

Complete Models with Stochastic Volatility

David Hobson; L. C. G. Rogers

The paper proposes an original class of models for the continuous-time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log-price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference-independent options prices. Copyright Blackwell Publishers 1998.


Finance and Stochastics | 2002

Optimal capital structure and endogenous default

Bianca Hilberink; L. C. G. Rogers

Abstract. In a sequence of fascinating papers, Leland and Leland and Toft have investigated various properties of the debt and credit of a firm which keeps a constant profile of debt and chooses its bankruptcy level endogenously, to maximise the value of the equity. One feature of these papers is that the credit spreads tend to zero as the maturity tends to zero, and this is not a feature which is observed in practice. This defect of the modelling is related to the diffusion assumptions made in the papers referred to; in this paper, we take a model for the value of the firms assets which allows for jumps, and find that the spreads do not go to zero as maturity goes to zero. The modelling is quite delicate, but it just works; analysis takes us a long way, and for the final steps we have to resort to numerical methods.


Mathematical Finance | 1997

The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates

L. C. G. Rogers

It is possible to specify a model for interest rates in various ways, by giving the dynamics of the spot rate or of the forward rates, for example. A less well-developed approach is to specify the law of the state-price density process directly. In abstract, the state-price density process is a positive supermartingale, and the theory of Markov processes provides a rich framework for the generation of examples of such things. We show how this can be done, and provide simple examples (some familiar, some new) where prices of derivatives can be computed very easily. One benefit of the potential approach is that it becomes very easy to model the yield curve in many countries at once, together with the exchange rates between them. Copyright Blackwell Publishers Inc. 1997.


Mathematical Finance | 2001

Robust Hedging of Barrier Options

Haydyn Brown; David Hobson; L. C. G. Rogers

This article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behavior of the underlying assets are in some sense incorporated into the hedge and do not need to be specified exogenously. Thus we are able to find prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying assets follow an exponential Brownian motion. We find model‐independent upper and lower bounds on the prices of knock‐in and knock‐out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating profits at zero risk. Examples illustrate that the bounds we give can be fairly tight.


Finance and Stochastics | 2001

The relaxed investor and parameter uncertainty

L. C. G. Rogers

Abstract. We firstly consider an investor faced with the classical Merton problem of optimal investment in a log-Brownian asset and a fixed-interest bond, but constrained only to change portfolio (and, if relevant, consumption) choices at times which are a multiple of h. We show that the cost of this constraint can be well described by a power series expansion in h, the first few terms of which we determine explicitly. Typically, this cost is not too large. We then compare this with the cost of parameter uncertainty, as modelled by supposing that the rate of return on the share has a prior Gaussian distribution. We find that the effect of parameter uncertainty is typically bigger than the effects of infrequent policy review.


Management Science | 2013

Failure and Rescue in an Interbank Network

L. C. G. Rogers; Luitgard A. M. Veraart

This paper is concerned with systemic risk in an interbank market, modelled as a directed graph of interbank obligations. This builds on the modelling paradigm of Eisenberg and Noe [Eisenberg L, Noe TH 2001 Systemic risk in financial systems. Management Sci. 472:236--249] by introducing costs of default if loans have to be called in by a failing bank. This immediately introduces novel and realistic effects. We find that, in general, many different clearing vectors can arise, among which there is a greatest clearing vector, arrived at by letting banks fail in succession until only solvent banks remain. Such a collapse should be prevented if at all possible. We then study situations in which consortia of banks may have the means and incentives to rescue failing banks. This again departs from the conclusions of the earlier work of Eisenberg and Noe, where in the absence of default losses there would be no incentive for solvent banks to rescue failing banks. We conclude with some remarks about how a rescue consortium might be constructed. This paper was accepted by Wei Xiong, finance.


Stochastics and Stochastics Reports | 1994

Equivalent martingale measures and no-arbitrage

L. C. G. Rogers

We give here an elementary proof of the fundamental theorem of discrete-time asset pricing, due originally to Dalang, Morton and Willinger. The essence is a simple utility-maximisation argument, and no deep results from functional analysis are required

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John B. Walsh

University of British Columbia

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A. Jobert

University of Cambridge

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Liang Zhang

University of Cambridge

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Umut Çetin

London School of Economics and Political Science

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