Recent Advances in Financial Engineering 2010

The following sections are included:

• PREFACE

• KIER-TMU International Workshop on Financial Engineering 2010

• PROGRAM

• CONTENTS

Longer horizon returns are constructed from data on daily returns. Observed drawbacks of a Lévy process are a sharp decrease in skewness and excess kurtosis. Drawbacks to scaling are a flat term structure of skewness and excess kurtosis. A strategy that combines some exposure to independent increments and some exposure to scaling is developed in the context of self decomposable daily return distributions. Estimations are conducted on 400 stocks and we report that a good strategy for constructing longer horizon returns can be that of accumulating as i.i.d. half the daily return while scaling the remainder at rate one half.

In a recent article [4], we have developed a market model where an insider trades using future information on the value of the underlying, through these trades it creates an effect on the drift of the underlying model. We find points of partial equilibria. That is, when the filtration is fixed the chosen portfolio is optimal, leads to finite utility of the insider and prices are semimartingales in their own filtration. In this article, we treat two explicit examples in detail. The first is an insider which has a medium term effect on the price. The second is an insider which has a long term effect on the price with memory effects. These examples were quoted in [4] but no details were given.

The purpose of this note is to describe a risk management procedure applicable to options on large credit portfolios, such as CDO tranches on iTraxx or CDX main indices. Credit spread risks are dynamically hedged using single name credit default swaps while default risk is kept under control thanks to diversification. The proposed risk management approach mixes ideas from finance and insurance and departs from standard approaches used in incomplete markets such as mean-variance hedging or expected utility maximisation. In order to ease the analysis and the exposure, default dates, within a reference credit portfolio, follow a multivariate Cox process. In such a framework, thanks to the no contagion property, i.e. default of a name does not trigger jumps in the credit spreads of the survivors and to the no simultaneous default property, i.e. the probability of joint defaults equals zero, we show that the hedging error can be kept under control. More specifically, by dynamically hedging of portfolio of single name credit default swaps, the hedging residual is bounded in . Moreover, the associated strategy corresponds to the mean variance hedging of a pseudo CDO tranche, where the actual portfolio loss is replaced by its projection on the background filtration.

We extend the Robust No Free Lunch (RNFL) theorem formulated for discrete-time models with proportional transaction costs to general continuous-time settings. We prove that the (RNFL) condition is equivalent to the existence of a strictly consistent price system, i.e. a martingale evolving in the interior of the solvency cone of all portfolio positions which can be changed into positive ones paying transaction costs.

In recent years, we have observed dramatic increase of collateralization as an important credit risk mitigation tool in over the counter (OTC) market [6]. Combined with the significant and persistent widening of various basis spreads, such as Libor-OIS and cross currency basis, the practitioners have started to notice the importance of difference between the funding cost of contracts and Libors of the relevant currencies. In this article, we integrate the series of our recent works [1, 2, 4] and explain the consistent construction of term structures of interest rates in the presence of collateralization and all the relevant basis spreads, their no-arbitrage dynamics as well as their implications for derivative pricing and risk management. Particularly, we have shown the importance of the choice of collateral currency and embedded "cheapest-to-deliver" (CTD) option in a collateral agreement.

In this paper we study conditional portfolio optimization problems when the conditional moments of returns are predictable. Our purpose is to investigate which state variables are statistically significant for the portfolio strategy in the Japanese market. By parametrizing the portfolio strategy, we transform the conditional problem into the unconditional problem and formulate the problem as a statistical estimation problem. This helps us determine the state variables which we should focus on.

In this paper, I study a noisy REE model of asset market with two types of costly private signals: a common signal with an identical error term and independent signals with dispersed error terms. Studying investors' endogenous information acquisition, I show that (i) investors observing the common signal and those observing the independent signals are likely to coexist in the equilibrium, (ii) at most, three equilibrium strategies can coexist, and (iii) when the equilibrium has three strategies, the evolutionary learning dynamics of investors can exhibit detours and cyclical oscillation.

In this paper, we present analytical solutions for the Laplace transforms of vanilla, barrier, and lookback options when the underlying process is a regime-switching jump-diffusion process. These closed-form solutions are possible due to the analytical characterization of the joint distribution of the underlying process with its running maximum or minimum under the regime-switching jump-diffusion model, developed in Kijima and Siu (2010). By performing the appropriate numerical Laplace inversion, we can recover the corresponding prices efficiently and stably.

This paper investigates market expectations of future equity prices using the probability distribution and the moments implied in equity option prices. We first conduct, without assuming a particular model, a nonparametric analysis of the development of market expectations in four major markets during the financial turmoil following the summer of 2007. We then conduct a parametric analysis to reconsider these expectations from the perspective of a stochastic process, assuming jump diffusion processes that configure the implied distribution. These analyses reveal that the possibility of discontinuous price jumps in each country increased downwards during the turmoil, while volatilities determining the dispersion of continuous price changes surged. Viewing the results from the perspective of a probability distribution, we find that kurtosis and the absolute value of skewness declined, while variance dramatically increased.

This paper investigates portfolio value behavior when the investors possessing the portfolio exhibit heterogeneous characteristics by altering the fraction of wealth invested by each investor and each investor's risk aversion. Portfolio value is investigated when these investors face trading restrictions and prices are observable. The behavior of the portfolio risk characteristics is examined for specific scenarios and price processes.

In this paper, we consider optimal hedges for a class of derivative securities whose underlyings are untraded using the additive sum of smooth functions of traded assets that minimizes their mean square errors. At first, we show that the general problem is reduced to a system of linear operator equations, and derive a methodology to obtain the optimal smooth functions efficiently based on suitable discretization. Then, we extend the idea to basket options consisting of the weighted sum of many stocks, where smooth payoff functions of individual assets are computed to approximate the terminal payoff of basket option as close as possible in the minimum mean square sense. Numerical experiments are also provided to illustrate our proposed methodology.