## BACHELIER FINANCE SOCIETY

 ABSTRACTS -Submitted Posters
 Presenting Posters June 23 Presenting Poster June 24 24 Konstantinides, Dimitrios --University of the Aegean 27 Lee, Hyo Seob KAIST --Business School 42 Zhao, Hongbiao --London School of Economics 44 He, Tony --University of Technology, Sydney 44 Shi, Lei-- University of Technology, Sydney 47 Song, Qingshuo --City University of Hong Kong 50 Jessen, Cathrine --Copenhagen Business School 82 Koos, Birgit-- University of Bonn 93 Goldammer, Verena --Vienna University of Technology 143 Callegaro, Giorgia --Université d'Evry 146 Walker, Michael --University of Toronto 147 Li, Jing --University of Bonn 153 Kim, Kyu Yoon --Yonsei University 156 Zhang, Kai --University of Warwick 157 Jonen, Christian --University of Cologne 158 Xing, Hao --Boston University 180 Loebnitz, Kolja --University of Twente 183 Goetz, Barbara --TU Muenchen 184 Sadefo Kamdem, Jules --Université de Montpellier 1 - UFR d'économie 140 Kato, Takashi --Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd (unable to attend). 186 Wei, Xiangwei --Chinese University of Hong Kong 225 Li, Duan --Chinese University of Hong Kong 233 Peng, Xiaohu-- University of Western Ontario 261 Broni-Mensah, Edwin-- University of Manchester 301 Kenyon, Chris --DEPFA Bank Plc. 315 Wopperer, Christoph-- University of Ulm 332 Wojakowski, Rafal --Lancaster University 356 Lim, Byung Hwa-- KAIST 360 Oh, Gabjin --Chosun University 367 Uratani, Tadashi --Hosei University 369 Muromachi, Yukio --Tokyo Metropolitan University 382 Possamaï, Dylan --Ecole Polytechnique 397 Kunz, Andreas --MunichRE 407 Ferrando, Sebastian/Olivares, Pablo --Ryerson University 415 Cerny, Ales --Cass Business School 429 Hanzon, Bernard --University College Cork 436 Hägnesten, Stefan --Lund University 447 Kim, Hwa-Sung --Kyung Hee University 459 Eisenberg, Larry-- New Jersey Institute of Technology 469 Valov, Angel --Scotiabank

Poster Number 24
Konstantinides, Dimitrios
, (University of the Aegean)
Coauthors, Konstantinides D. G., Kountzakis C. E.
Risk measures in ordered normed linear spaces with non-empty cone-interior
In this paper, we use tools from the theory of partially ordered normed linear spaces, especially the bases of cones. This work extends the well-known results for convex and coherent risk measures. Its linchpin consists in the replacement of the riskless bond by some interior point in the cone of the space of risks, which stands as the alternative numeraire.

Poster Number 27
Lee, Hyo Seob
Coauthors, Hyo Seob Lee, Tong Suk Kim
Robust Portfolio Choice with External Habit Formation and Equilibrium Asset Prices
This paper examines optimal consumption and portfolio choice for the agent concerned about a worst-case scenario with respect to external habit formation. We theoretically derive the countercyclical uncertainty aversion, which is disentangled from the risk aversion. The better the economy, the lower the uncertainty aversion. We obtain both the Lucas style equilibrium asset price and risk-free rate, and we provide more plausible parameter choices to explain both the equity premium puzzle and the low risk-free rate puzzle.

Poster Number 42
Zhao, Hongbiao
, (London School of Economics)
Coauthors, Angelos Dassios and Hongbiao Zhao
Point Processes with Contagion and an Application to Credit Risk
We introduce a new point process, the dynamic contagion process, by generalising the Hawkes process and the Cox process with shot noise. Our process includes self excited and externally excited jumps, which can be used to model the dynamic contagion impact from endogenous and exogenous factors. The analytic expressions of the Laplace transform of the intensity process and probability generating function of the point process have been derived. The object of this study is to produce a general mathematical framework for modelling the dependence structure of arriving events, which has the potential to be applicable to a variety of problems in finance. We provide an application to credit risk, and the simulation algorithm for industrial implementation.

Poster Number 44
Shi, Lei (He, Tony)
, (University of Technology, Sydney)
Coauthors, Xue-Zhong He, Lei Shi
Difference in Opinions and Risk Premium
When people agree to disagree, this paper examines the impact of the disagreement among agents on market equilibrium and equity premium. Within the standard mean variance framework, we consider a market of two risky assets, a riskless asset and two (and then a continuum of) agents who have different preferences and heterogeneous beliefs in the means and variance/covariances of the asset returns. By constructing a consensus belief, we introduce a boundedly rational equilibrium (BRE) to characterize the market equilibrium and derive a CAPM under heterogeneous beliefs. When the differences in opinion are formed as mean-preserving spreads of a benchmark homogeneous belief, we analyze explicitly the impact on the market equilibrium and risk premium, showing that the risk tolerance, optimism/pessimism and confidence/doubt can jointly generate high risk premium and low risk-free rate.

Poster Number 47
Song, Qingshuo
, (City University of Hong Kong)
Coauthors, Erhan Bayraktar, Qingshuo Song, and Jie Yang
On The Continuity of Stochastic Exit Time Control Problems
In general one can show that the value function is a viscosity solution of a fully non-linear Hamilton-Jacobi-Bellman equation given that it is a continuous function. However, when the domain is bounded, it is not always the case that the value function is continuous due to tangency problem. A sufficient condition for the continuity of the value function is provided in Theorem 5.2.1 in Fleming and Soner (2006) for the continuity of the value functions. In this paper we improve this condition using a probabilistic argument by observing the sample path behavior of the controlled processes.

Poster Number 50
Jessen, Cathrine
Coauthors, Cathrine Jessen and Rolf Poulsen
Empirical Performance of Models for Barrier Option Valuation
The empirical performance of five models for barrier option valuation is investigated: Black-Scholes, the constant elasticity of variance, Heston's stochastic volatility, Merton's jump-diffusion, and the Variance Gamma models. We use time-series data from the USD/EUR exchange rate market. The models are calibrated to plain vanilla option prices, and prediction errors at different horizons for plain vanilla and barrier options are investigated. For plain vanilla options, the Heston and Merton models have similar and superior performance for prediction horizons up to one week. For barrier options, the continuous-path models do almost equally well, while both models with jumps perform markedly worse.

Poster Number 82
Koos, Birgit
, (University of Bonn)
Coauthors, Dirk Broeders, An Chen
A utility-based comparison of pension funds and life insurance companies under regulatory constraints
This paper compares two diff erent types of annuity providers, i.e. defined benefi t pension funds and life insurance companies. It employs a contingent claim approach to evaluate the risk return trade-off for annuitants. For that, we take into account the differences in contract speci fications and in regulatory regimes. Mean-variance-skewness analysis is conducted to determine annuity choices of consumers. We calibrate the regulatory default probabilities such that the consumer is indi fferent between a pension fund and a life insurer. The consumer's risk aversion level appears to play a crucial rule in this.

Poster Number 93
Goldammer, Verena
, (Vienna University of Technology)
Coauthors, Verena Goldammer
Modeling and Estimation of Dependent Credit Rating Transitions
Simultaneous defaults in large portfolios of credit derivatives can induce huge losses. To take this into account, we model the credit rating transitions of firms by an interacting particle system that allows the firms to change their credit rating at the same time. We provide a general model, where all firms may change their credit rating simultaneously and then restrict the possible transitions. Simulation results demonstrate the influence of dependence between the firms. To estimate the parameters the maximum likelihood function is provided for the general model. In case of the strongly coupled random walk we state the maximum likelihood estimators and show consistency and asymptotic normality.

Poster Number 140
Kato, Takashi
, (Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd.)
Coauthors, Takashi Kato
How to Model and Measure Market Impact
We study an optimal execution problem in consideration of market impact. To formulate a mathematical model, we derive a continuous-time model as a limit of discrete-time models. We study some properties of its value function, especially a characterization as a viscosity solution of HJB. Next we consider a case where essential effects of market impact appear. We show that a trader should execute gradually when a market impact function is non-linear or there is price recovery effect of a security. In these cases, we see that total market impact cost induced by an optimal execution policy is concave.

Poster Number 143
Callegaro, Giorgia
, (Université d'Evry)
Coauthors, Giorgia Callegaro
Optimal consumption problems in discontinuous markets
We study an extension of Merton's classical portfolio optimization problem to a particular case of discontinuous market, with a single jump. The market consists of a non-risky asset, a "standard risky" asset and a risky asset with discontinuous price dynamics. We consider three different problems of maximization of the expected utility from consumption, in the cases when the investment horizon is fixed, finite (but possibly uncertain) and infinite. We solve the problems by means of a direct approach and of the Dynamic Programming Principle. In the logarithmic, power and exponential utility cases, we compare the obtained explicit solutions.

Poster Number 146
Walker, Michael
, (University of Toronto)
Coauthors, Michael B Walker
Hedging and Valuation of Seasoned CDSs: a Numerical Example
Seasoned CDS contracts can not, in general, be perfectly hedged using CDSs from the current CDS market. Such contracts are often approximately hedged in terms of a single CDS from the market. (This hedge will be called a vanilla hedge.) The first contribution of this poster is to demonstrate by a numerical example how an appropriately chosen multi-CDS hedge (made up of CDSs from the market of several different maturities) can give the hedger a net position with a lower risk than that achieved with the vanilla hedge. Seasoned CDSs are commonly valued in terms of a procedure designed for complete markets, and based on a risk-neutral measure uniquely determined by a calibration process; this procedure does not take into account the cost of hedging, the fact that the risk of the hedged position has an impact on its value, or the fact that the CDS market is in reality incomplete. The second contribution of this report is to take the point of view of a dealer taking over an investor's illiquid seasoned CDS position, and to show by an example how to establish good-deal bid and ask prices for the seasoned CDS using an incomplete-market approach. This approach supposes that the dealer will require to make a minimum expected profit, which must be positive, in order to agree to the deal.

Poster Number 147
Li, Jing
, (University of Bonn)
Coauthors, Jing Li, Alexander Szimayer
The Uncertain Force of Mortality Framework: Pricing Unit-Linked Life Insurance Contracts
Unit-linked life insurance contracts link the financial market and the insurance market together. In a complete and arbitrage-free financial market, financial risk can be hedged perfectly, but perfect hedging is not possible when mortality risk is embedded in a financial product. For many years, this problem was ignored by assuming that the force of mortality is deterministic. Under this assumption, an insurance company can hedge against mortality risk by pooling a large number of policyholders together. It then only needs to deal with the financial risk. However, in recent years it has been acknowledged that the force of mortality is actually stochastic and researchers have tried to model this stochastic process. The drawback of this procedure is that it cannot provide a nearly perfect hedge against mortality risk unless a large number of mortality-linked financial products are liquidly traded. In contrast to specifying a stochastic model for the force of mortality, we provide a framework where the force of mortality is uncertain but stays within lower and upper bounds. Within this framework, we obtain upper and lower price bounds for European-style unit-linked life insurance contracts by applying optimal control theory and PDE methods. In particular, the upper and lower price bounds are obtained by seeking out the worst and best scenarios for varying forces of mortality. The PDE formulation of the pricing problem is solved with finite difference methods. The upper and lower price bounds enable us to enhance hedging strategies and reduce exposure to financial and mortality risks.

Poster Number 153
Kim, Kyu Yoon
, (Yonsei University)
Coauthors, Kyu-Yoon Kim, Jeong-Hoon KIm, So-Young Sohn, Won-Sang Lee
Real options under the CEV Diffusion with Stochastic Volatility
As empirical tests on finacial option has shown the non-constant features of the implied volatility, an extension to the real option needs a same analysis with different financial circumstances. Here, we consider a real option pricing model with stochastic volatility for the first time, and a goal of this research is providing CEV diffusion with stochastic volatility(SVCEV) into the real option especially for Technology Financing. Furthermore, an empirical test with dicrete annual Technology Financing Data is examined with interesting analogies.

Poster Number 156
Zhang, Kai
, (University of Warwick)
Coauthors, Kai Zhang
Weak and Strong Numerical Schemes for the LIBOR Market Model in the Terminal Measure
This paper investigates the convergence properties of various methods for drift approximation in the LIBOR market model in the terminal measure. The methods we consider are Ito-Taylor schemes and strong Taylor approximations based on perturbed stochastic differential equations. We propose an improvement of the latter. The pricing errors of various methods are compared in both single and multiple step cases. We criticize that the strong Taylor approximation approaches do not converge as the number of time steps increases and therefore should not be used for discretization.

Poster Number 157
Jonen, Christian
, (University of Cologne)
Coauthors, Christian Jonen
A Robust Regression Monte Carlo Method for Pricing High-Dimensional American-Style Options
We present a new regression-based Monte Carlo method for pricing multi-asset American-style options. The key idea is to fit the model function for the continuation value at every exercise date by robust regression rather than least squares. Furthermore, we suggest a new technique for calculating the coefficients of the model function to decrease the number of basis functions and to enable the parallelization of our approach. In addition, we extend earlier results for variance reduction via importance sampling for American-style options. In comparison to existing Monte Carlo methods, we can improve convergence significantly by implementing our proposed approaches.

Poster Number 158
Xing, Hao
, (Boston University)
Coauthors, Erhan Bayraktar, Constantinos Kardaras, and Hao Xing
Valuation equations for stochastic volatility models
We study the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models. The standard Feynman-Kac theorem cannot be directly applied because the diffusion coefficients may degenerate on the boundaries of the state space and grow faster than linearly. We allow for various types of model behavior; for example, the volatility process in our model can potentially reach zero and either stay there or instantaneously reflect, and asset-price processes may be strict local martingales under a given risk-neutral measure. Our main result is an extension of the standard Feynman-Kac theorem in the context of stochastic volatility models. Sharp results on the existence and uniqueness of classical solutions to the valuation equation are obtained using a combination of probabilistic and analytical techniques. The role of boundary conditions is also discussed.

Poster Number 180
Loebnitz, Kolja
, (University of Twente)
Coauthors, Kolja Loebnitz and Berend Roorda
A simple framework to adjust EC and RAROC for liquidity risk
Banks can default because of illiquidity, despite being technically solvent and having adequate capital. However, regulators and banks have focused primarily on measuring and managing solvency risk, not liquidity risk. We introduce a nonlinear value deflator that allows banks to adjust their Economic Capital and RAROC for a combination of market liquidity risk and funding risk. We go on to examine the problem of allocating the overall liquidity-adjusted EC and RAROC to business units. Finally, we show that, under moderate assumptions, coherent liquidity adjusted risk measures are convex, positively scale-supervariant, and cash-equity translational subvariant in asset liability pairs.

Poster Number 183
Goetz,Barbara
, (TU Muenchen)
Coauthors, Barbara Goetz, Marcos Escobar, Rudi Zagst
Two asset-barrier option within stochastic volatility models.
Financial products which depend on hitting times for two underlying assets have become very popular in the last years, for example double-digital barrier options, two-asset barrier spread options and double lookback options. Analytical expressions of the joint distribution of the maximum and/or minimum values of two assets have been derived by He et al. (1998) and Zhou (1997, 2001) leading to closed-form pricing of those derivatives in the context of constant volatility and correlation. The financial crisis has shown that constant covariances are an assumption which is not valid. Thus, we introduce a third stochastic factor to the geometric Brownian model governing the covariance and derive closed-form expressions for some two-asset barrier options.

Poster Number 184
Sadefo Kamdem, Jules (Université de Montpellier 1 - UFR d'économie)
This paper provides explicit expression for the lower bound and the upper bound of the overall VaR of a portfolio of business units when the joint risks factors of each business unit follows a mixture of multivariate elliptic distributions with dynamic conditional correlation matrix. We use copula to measure the dependance between the pro ts and losses (P&Ls) of di erent

Poster Number 186
Wei, Xiangwei
, (The Chinese University of Hong Kong)
Coauthors, Ning Cai, Nan Chen, Xiangwei Wan
Pricing and Hedging Occupation-Time-Related Options
In this paper, we provide Laplace transform-based analytical solutions to pricing problems of various occupation-time-related derivatives such as step options, corridor options, and quantile options under Kou's double-exponential jump diffusion model. These transforms can be inverted numerically via the Euler Laplace inversion algorithm, and the numerical results illustrate that our pricing methods are accurate and efficient. The analytical solutions can be obtained primarily because we derive the closed-form Laplace transform of the joint distribution of the occupation time and the terminal value of the double-exponential jump diffusion process.

Poster Number 225
Li, Duan
, (The Chinese University of Hong Kong)
Coauthors, Duan Li, Xiangyu Cui and Jiaan Yan
Classical Mean Variance Model Revisited: Pseudo Efficiency
Almost all literatures on mean-variance portfolio selection adhere their investigation to a binding budget spending assumption. In the mean-variance world for a market of all risky assets, however, the common belief of monotonicity does not hold, i.e., not the larger the funding level, the better the outcome. We introduce in this paper the concept of pseudo efficiency to remove from the candidates such efficient mean-variance policies which can be achieved by less initial investment level. By relaxing the binding budget spending restriction in investment, we derive an optimal scheme in managing initial wealth which dominates the traditional mean-variance efficient frontier.

Poster Number 233
Peng, Xiaohu
, (University of Western Ontario)
Coauthors, Xiaohu Peng, Tyson Whitehead, Mark Reesor
Pricing and Optimal Management of a Retail Debt Portfolio
Often retail debt products are priced and sold before they are issued to individual investors. This sales strategy makes pricing and management of the retail debt portfolio interesting. In this paper we present a general simulation framework in which one can account for this price-commitment risk and define objective functions suitable for the seller. Retail debt products having embedded features similar to Canada Savings Bonds are considered. A pricing methodology using least-squares Monte Carlo is developed for these bonds. Examples are presented showing the optimal initial coupon (bond price) for three different objective functions that sellers may consider for this type of sales strategy.

Poster Number 261
Broni-Mensah, Edwin
, (University of Manchester)
Coauthors, Edwin K. Broni-Mensah, Peter W. Duck, David P. Newton
A simple and generic methodology to suppress Non-linearity' error in lattice-based option pricing
We propose and develop a generic methodology for overcoming non-linearity' errors often found in lattice-based option pricing. The approach can readily be applied to a broad class of numerical schemes to improve convergence, including binomial trees, quadrature and nite-di erence schemes. The methodology, which utilises the least-squares method on raw output data, is powerful, as it overcomes non-monotonic convergence behaviour that is present due to the misalignment of node points. The methodology enables extrapolation techniques to be employed on non-monotonic data sets, is equally applicable to pricing options with early exercise features, and produces signi cant improvements in accuracy.

Poster Number 301
Kenyon, Chris
, (DEPFA Bank Plc.)
Coauthors, Donal Gallagher, James P. Gleeson, Chris Kenyon, Roland Lichters
Valuation of a Cashflow CDO Without Monte Carlo Simulation
Unlike tranches of synthetic CDOs, that depend only on defaults of underlying securities, tranches of cashflow CDOs also depend on interest cash flows from coupons. Whilst fast, accurate, (semi-)analytic methods exist for pricing synthetic CDO tranches, no equivalent methods exist for pricing cashflow CDO tranches because of their dependence on both principal and interest waterfalls. We introduce an analytical approximation that renders cashflow CDOs amenable to (semi-)analytic pricing. The complication of needing the joint distribution of interest and outstanding notional is reduced to needing only marginal distributions. We show that our analytic approximation is globally valid with bounded errors.

Poster Number 315
Wopperer, Christoph
, (University of Ulm)
Coauthors, Christoph Wopperer
Robust portfolio optimization for HARA-utility and stochastic coefficients by BSDEs
Continuous-time portfolio optimization problems with stochastic coefficients are treated by BSDE techniques among others in Hu, Imkeller and Müller (2005), Lim and Quenez (2008) and Ferland and Watier (2008). Here we consider robust consumption-investment problems with uncertain drift process under general HARA-utility and stochastic coefficients. From the martingale optimality principle we derive a stochastic Hamilton-Jacobi-Bellman equation for the robust optimal value function. Using a separation ansatz, we obtain a linear BSDE for the robust optimal value function and compute a robust optimal policy. Moreover, we present explicit solutions for logarithmic and exponential utility. The main mathematical tools are BSDEs.

Poster Number 332
Wojakowski, Rafal
, (Lancaster University)
Coauthors, M. Shahid Ebrahim, Mark B. Shackleton, Rafal M. Wojakowski
On Pricing Continuous Workout Mortgages
This paper offers a method to reduce vulnerability of the financial architecture to banking crisis by employing Continuous Workout Mortgages (CWMs). CWMs enable the financial system to absorb shocks better than the rigid plain vanilla Fixed Rate Mortgages, Adjustable Rate Mortgages (ARMs) and their hybrids. We model CWMs by employing a market-observable variable such as the house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable "workout proportion" and adjustable "workout threshold." These results are of importance as they not only help understanding the mechanics of CWMs and estimating key contract parameters. Our results also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk.

Poster Number 356
Lim, Byung Hwa
, (KAIST)
Coauthors, Bong-Gyu Jang
Robust Portfolio Rules with a New State Variable
In the paper, we solve a robust control problem in the line of Gilboa and Schmeidler [Gilboa, I., and D. Schmeidler, 1989, Maxmin expected utility with non-unique prior, Journal of Mathematical Economics 18, 141-153]'s work. By using a continuation entropy as a new state variable, we convert the constraint robust control problem in Hansen and Sargent [Hansen, L.P., and T.J. Sargent, 2001, Robust control and model uncertainty, American Economic Review 91, 60-66] into a robust control problem which can be interpreted as a two player zero-sum game. Under the problem setup, we show that the Bellman-Isaacs condition is satisfied, thus the time inconsistency issue is not a trouble any more. We find the optimal consumption and portfolio strategies of an individual with a CRRA utility, which can give an alternative explanation for the famous under-diversification puzzle and equity premium puzzle.

Poster Number 360
Oh, Gabjin
, (Chosun University)
Coauthors, Gabjin Oh, Jaewook Lee
The nonlinear and statistical properties of the implied volatility for index option
In this paper, we analyze the statistical and non-linear properties of the log-variations in implied volatility for CAC40, DAX, S&P500 daily index options. The price of index option is generally represented by its implied volatility surface, existing the smile and skew properties. We utilize the Levy process as underlying asset in order to understand an intrinsic property of implied volatility in the index options and estimate the implied volatility surface. We have found that the option pricing models used in this paper can produce the smile or sneer features of implied volatility observed in the real option markets. We study the variation of implied volatility for at-the-money index call and put options and find that its distribution function follows a power-law behavior with an exponent within 3.5 < gamma <4.5. In particular, the variation of implied volatility show multifractal spectrum characteristics for all data sets used.

Poster Number 367
, (Hosei University)
We study the self-annuitization and the dynamic optimal portfolio selection to minimize the probability of lifetime ruin. To avoid the risk of living after spending out his wealth, there are three financial instruments, a risky asset like corporate stock, risk free asset like bank account, and annuity which guarantee fixed income until death. As a retiree is getting older, the annuity price is becoming cheaper to purchase it. The problem is to find the optimal portfolio of three financial assets and the timing to buy annuity. Bayraktar solved the problem by borrowing constraint or by introducing borrowing rate. The optimal solution is holding only the risky asset afterwards his wealth equals to the risky investment. When we take an annuity into portfolio on these setting, it is generally difficult to solve it. Because the price of annuity depends on his remaining year of life. We assume firstly that consumption plan is based on the optimal investment policy of Bayraktar,and secondly that the annuity price is exponentially decreasing. We obtain the optimal portfolio strategy and the average timing to purchase annuity by Laplace transform.

Poster Number 369
Muromachi, Yukio
, (Tokyo Metropolitan University)
Coauthors, An application of the implied copula model to the risk evaluation of a portfolio
Yukio Muromachi
We propose a simple application of the implied copula model, proposed by Hull and White (2006), to the risk evaluation of a portfolio. In the implied copula model, the hazard rates of the entities have a distribution, and the default times are conditionally independent. Additionally we assume that the normalized hazard rates under the risk neutral probability measure and the physical measure have the same distribution. Then, the risk calculated by our model can reflect the latent fear of the major market participants. We will show a practical and simple example.

Poster Number 382
Possamaï, Dylan
, (Ecole Polytechnique)
Coauthors, Umut Cetin, Dylan Possamaï, Mete Soner and Nizar Touzi
Large Liquidity Expansion of the super-hedging costs
We consider a financial market with liquidity cost as in \c{C}etin, Jarrow and Protter where the supply function $\mathbf{S}^\eps(s,\nu)$ depends on a parameter $\eps\ge 0$ with $\mathbf{S}^0(s,\nu)$ corresponding to the perfect liquid situation. Using the PDE characterization of \c{C}etin, Soner and Touzi, we provide a Taylor expansion of the super-hedging price in powers of $\eps$. In particular, we explicitly compute the first term in the expansion for a Call option and give bounds for the order of the expansion for a Digital Option, pointing out a subtle change of regime for discontinuous payoffs.

Poster Number 397
Kunz, Andreas
, (MunichRE)
Coauthors, Andreas Kunz, Lothar Kruppok
Valuation and Hedging of With-Profit Insurance Policies with Interest Rate Guarantees
We analyze a with-profit life insurance product of universal life type with a bonus contribution mechanism that is indexed to interest rates in the following way: the crediting rate is floored by a guaranteed rate; to allow for outperformance in case of rising interest rates, it is indexed to the average of observed long-term interest rates. Financially rational surrender behavior of policy holders is explicitly taken into account. We will analyze the capital market sensitivities of the crediting mechanism using the LIBOR market interest rate model and derive a hedging strategy. We find that the constant maturity swap feature dominates the crediting rate mechanism. A hedging strategy for this product would use interest rate swaptions to match the non-linear profile and the volatility exposure. This shows that the naive investment strategy motivated from an accounting point of view, would lead to completely wrong hedging results.

Poster Number 407
Ferrando, Sebastian (Olivares, Pablo)
, (Ryerson University)
Coauthors, Alexander Alvarez, Sebastian Ferrando, Pablo Olivares
Non-Probabilistic Hedging and Pricing. Applications to Probabilistic Models
The paper studies several aspects of a non-probabilistic approach to hedging and pricing. In order to illustrate some of the differences with the classical probabilistic approach, we use our setup to derive new hedging and pricing results in probabilistic models. Besides dealing with classes of continuous paths, we also incorporate jumps; for some of our deterministic classes this leads to incompleteness and, in order to achieve perfect replication of options in such a setting, we allow hedging with options to take place. In this setup, our results provide a path-wise and discrete approach, with explicit expressions for the hedging portfolio, to a result of Mancini on perfect hedging with European calls in a Poisson-Gaussian model.

Poster Number 415
Cerny, Ales
Coauthors, Sara Biagini and Ales Cerny
Admissible Strategies in Semimartingale Portfolio Optimization
The choice of admissible trading strategies in mathematical modeling of financial markets is a delicate issue. We propose a novel notion of admissibility that has many pleasant features: admissibility is characterized purely under the objective measure; each admissible strategy can be approximated by simple strategies; the wealth of any admissible strategy is a supermartingale under all pricing measures; local boundedness of the price process is not required. For utility functions finite on the real line our class represents a minimal set containing simple strategies which also contains the optimizer, under conditions that are milder than the celebrated reasonable asymptotic elasticity condition on the utility function.

Poster Number 429
Hanzon, Bernard
, (University College Cork)
Coauthors, Bernard Hanzon and Finbarr Holland
Non-negativity of exponential polynomials and EPT functions
The class of exponential-polynomial-trigonometric (EPT) functions is the class of functions that appear as a solution to some linear differential equation with constant coefficients; here we consider these functions on [0, infinity). Examples are the exponential functions, the polynomials and sin(t) and cos(t). We consider the question how to determine whether such a function is non-negative on a given finite interval [0,T]. We solve this by presenting a so-called generalized Budan-Fourier sequence for any given EPT function. Using this the number of sign-changing zeros of the function can be determined. As an application we present a parametrization of all non-negative Nelson-Siegel forward rate curves.

Poster Number 436
Hägnesten, Stefan
, (Lund University)
Coauthors, Stefan Hägnesten, MSc., Jimmy Olsson, PhD, Assistant professor
Option-based Maximum Likelihood Estimation in Stochastic Volatility Models
In this note we apply the particle-based iterated filtering algorithm proposed by Ionides et al. (2009) to the problem of calibration of stochastic volatility models. We assume that the underlying asset follows the Heston stochastic volatility dynamics and consider a hidden Markov model formulation of the observed option prices where the volatility of the underlying asset is treated as a latent signal. In this setting, robust approximations of the maximum likelihood estimator (MLE) are obtained by introducing a time varying parameter process following a random walk dynamics with decreasing size of the increments. The technique is demonstrated on simulated data.

Poster Number 447
Kim, Hwa-Sung
, (Kyung Hee University)
Coauthors, Bara Kim and Hwa-Sung Kim
Parabolic approximation method for option pricing and applications to compound options
This paper provides an efficient and accurate approximation of European-style option values. We propose that any payoff of an option is approximated by a piecewise quadratic function of the underlying asset price. Our approximation method is applicable easily to European options with any payoffs as well as under various stochastic process encompassing the jump-diffusion and stochastic volatility models.

Poster Number 459
Eisenberg, Larry
, (New Jersey Institute of Technology)
Coauthors, Larry Eisenberg
The short and longer-term consequences of VaR and probability-of-ruin with normal risks
Despite the use of VaR as a means to control risk, VaR regulations can have the opposite effect. A manager who maximizes his firm's expected equity value subject to a VaR constraint, when the firm is in bad financial health, on its constraint pays a premium for financial instruments that increase his firm's volatility and does the opposite when the firm is in good financial health. Basel II regulations encourage banks with greater systemic risk to use VaR constraints thereby encouraging banks to which the financial system is most exposed to increase risk when it is most vulnerable. The firm in bad financial health will pay a premium to increase its variance, and the firm in good financial health will do the opposite.

Poster Number 469
Valov, Angel
, (Scotiabank)
Coauthors, S. Jaimungal, A. Kreinin, A. Valov
Generalyzed Shiryaev's Embedding and Skorohod Problem
We consider a connection between the famous Skorohod stopping problem and an inverse problem for the first hitting time distribution for the Brownian motion: given a probability distribution, F, find a boundary such that the first hitting time distribution is F. We show that randomization of the initial state of the process makes the inverse problem analytically tractable. The idea of randomization of the initial state allows us to significantly extend the class of distribution in the case of a linear boundary and helps to establish connection with the Skorohod stopping problem.