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by Tim Bogomolov Abstract: Pairs trading is a market neutral investment strategy that attracts attention of academics and practitioners. Despite that, very little testing on the real market data has been published. This research considers three the most cited methods of pairs trading, two of them had never been tested on the real market data. Clear trading rules have been defined for all methods and their performance has been empirically assessed using the daily data covering 12 years history of the Australian stock exchange.
All three methods demonstrate statistically significant excess returns from 5% to 12% per year. However, after accounting for the transaction costs, two methods became unprofitable, and one earned minimal profit. These results demonstrate limited practical value of these strategies on the Australian stock market in their current form, suggesting the need for substantial improvements. Discuss this paper
Much of the work on path-dependent options assumes that the underlying asset price follows geometric Brownian motion with constant volatility. This paper uses a more general assumption for the asset price process that provides a better fit to the empirical observations. We use the so-called constant elasticity of variance (CEV) diffusion model where the volatility is a function of the underlying asset price. We derive analytical formulae for the prices of important types of path-dependent options under this assumption. We demonstrate that the prices of options, which depend on extrema, such as barrier and lookback options, can be much more sensitive to the specification of the underlying price process than standard call and put options and showthat a financial institution that uses the standard geometric Brownian motion assumption is exposed to significant pricing and hedging errors when dealing in path-dependent options.(Path-Dependent Options; Barrier Options; Lookback Options; Diffusion Processes; CEV Mode Generalized Bessel Process; Radial Ornstein-Uhlenbeck Process
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by Arlen David Schmidt This study uses the Johansen test for cointegration to select trading pairs for use within a pairs trading framework. A long-run equilibrium price relationship is then estimated for the identified trading pairs, and the resulting mean-reverting residual spread is modeled as a Vector-Error-Correction model (VECM). The study uses 5 years of daily stock prices starting from the beginning of July, 2002. The search for trading pairs is restricted to 17 financial stocks listed on the ASX200. The results show that two cointegrated stocks can be combined in a certain linear combination so that the dynamics of the resulting portfolio are governed by a stationary process. Although a trading rule is not employed to access the profitability of this trading strategy, plots of the residual series show a high rate of zero crossings and large deviations around the mean. This would suggest that this strategy would likely be profitable. It can also be concluded that in the presence of cointegration, at least one of the speed of adjustment coefficients must be significantly different from zero. Discuss this paper
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by Michael C. Fu, Dilip B. Madan, and Tong Wang In this paper, we investigate two numerical methods for pricing Asian options: Laplace transform inversion and Monte Carlo simulation. In attempting to numerically invert the Laplace transform of the Asian call option that has been derived previously in the literature, we point out some of the potential difficulties inherent in this approach. We investigate the effectiveness of two easy-to-implement algorithms, which not only provide a cross-check for accuracy, but also demonstrate superior precision to two alternatives proposed in the literature for the Asian pricing problem. We then extend the theory of Laplace transforms for this problem by deriving the double Laplace transform of the continuous arithmetic Asian option in both its strike and maturity. We contrast the numerical inversion approach with Monte Carlo simulation, one of the most widely used techniques, especially by practitioners, for the valuation of derivative securities. For the Asian option pricing problem, we show that this approach will be effective for cases when numerical inversion is likely to be problematic. We then investigate ways to improve the precision of the simulation estimates through the judicious use of control variates. In particular, in the problem of correcting the discretization bias inherent in simulation when pricing continuous-time contracts, we find that the use of suitably biased control variates can be beneficial. This approach is also compared with the use of Richardson extrapolation. Discuss this paper
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Thesis by Antti Eloranta The popularity of exotic foreign exchange rate options has grown rapidly during the past decade. High profit margins and rapid market growth have made the market particularly lucrative for banks. On the other hand, the correct pricing of exotic options requires more sophisticated models than traditional Black-Scholes. The objective of this thesis is to build, implement, and validate a pricing model for exotic foreign exchange rate options. Based on previous research, this thesis models the stochastic behavior of foreign exchange rates as stochastic volatility Discuss this paper
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NATALIA BELIAEVA SANJAY NAWALKHA GLORIA M. SOTO Abstract: This paper shows how to price American interest rate options under the exponential jumps-extended Vasicek model, or the Vasicek-EJ model. We modify the Gaussian jump-diffusion tree of Amin [1993] and apply to the exponential jumps-based short rate process under the Vasicek-EJ model. The tree is truncated at both ends to allow fast computation of option prices. We also consider the time-inhomogeneous version of this model, denoted as the Vasicek-EJ model that allows exact calibration to the initially observable bond prices. We provide an analytical solution to the deterministic shift term used for calibrating the short rate process to the initially observable bond prices, and show how to generate the jump-diffusion tree for the Vasicek-EJ model. Our simulations show fast convergence of European option prices obtained using the jump-diffusion tree, to those obtained using the Fourier inversion method for options on zero-coupon bonds (or caplets), and the cumulant expansion method for options on coupon bonds (or swaptions).
Keywords: Bond options, Interest Rate Trees, Jumps, Vasicek Model, American options Discuss this paper
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Author : Gohou Ferdinand DANON As popular vehicles for trading a portfolio of credit risks, we focus on a Synthetic Collateralized Debt Obligation swaps (Synthetic CDOs), in terms of pricing and risk analysis. Our purpose is not to create a new concept in these stylised facts of correlation products. Instead, we attempt to assess the key idea behind the standard credit derivatives pricing model in order to fully capture the essential of the risk of a synthetic CDO swaps. To this end, we provide a step by step description of the one factor Gaussian Copula model which is said to overcome computation costs inherent to the use of Monte Carlo simulation in the standard Gaussian copula model. This thesis also presents the double-t distribution suggested by Hull and White (2004) as an extension of the one factor Gaussian copula where they used a multi factor framework. For practical purpose, we use Microsoft Excel to calculate a synthetic CDO tranche price based on the computation of a homogenous portfolio of credit defaults under the one factor Gaussian copula model. We compared our empirical results in terms of prices relative to our homogenous assumptions with the market quotes. We recognized that even if the CDO pricing theoretical side in terms of relationship between the default correlation risk and tranches prices is satisfied, our model prices do not match the market quotes. The thesis then goes on to present a way to assess the demanding credit risk analysis in light of such appealing issue. We also introduce other problems that we would like to understand better such as the implied and base correlations. We highlight the intuition behind them in terms of pricing and risk analysis. Finally the recent trouble of Bears Stearns funds Discuss this paper
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by George Papadakis and Peter Wysocki This paper examines the impact of accounting information events (i.e., earnings announcements and analysts Discuss this paper
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by Gwangheon Hong and Raul Susmel In this paper, we study pairs-trading strategies for 64 Asian shares listed in their local markets and listed in the U.S. as ADRs. Given that all pairs are cointegrated, they are logical choice for pairs-trading. We find that pairs-trading in this market delivers significant profits. The results are robust to different profit measures and different holding periods. For example, for a conservative investor willing to wait for a one-year period, before closing the portfolio pairs-trading positions, pairs-trading delivers annualized profits over 33%.
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ch. 10 of Brigo, Damiano book - Interest rate models - theory and practice. I was able to save it, hope this link stays there.. Discuss this paper
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1-2 pages are japanese and author is unknown abstract: Credit risk plays a very important role in the valuation of convertible bonds. In this study we use the model that was developed by Longsta and Schwartz (1995) to estimate the credit risk of convertible bonds. Moreover, the Least-Square-Method (LSM) proposed by Longsta and Schwartz (2001) is used to handle the hybrid features of convertible bonds. We also examine the e ect of volatility on the value of convertible bonds and the duration of convertible bonds for di erent parameters. The result shows that the value of convertible bonds may increase or decrease as the volatility of the rm's value increases. The price of the convertible bonds is the result of a combination of the debt part and the option part. Moreover, the duration of the convertible bonds, at low volatility, increases as the coupon rate increases when the other conditions are the same.
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by Adrian A Dragulescu1 and Victor M Yakovenko We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker Discuss this paper
In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model outperforms directly comparing bonds Discuss this paper
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by Angelos Dassios and Jayalaxshmi Nagaradjasarma
In this paper, we study the integral over time of the instantaneous rate, i.e the interest rate accrual, in the Cox Ingersoll Ross model. We derive distributional results for this process, including series representations for the density and probability distribution function. Applications to the valuation of derivatives, including Asian options prices in closed form, are presented here. Numerical examples are included to demonstrate the speed of convergence of the series. We also find that the series provide a more robust tool than numerical Laplace transform inversion for regions of high maturity and volatility. Given the versatility of the square-root process, the results derived in this paper are also of value for various others areas of finance, among which stochastic volatility and credit derivatives
KEY WORDS Derivatives, valuation, Square-root process, average-rate claims Discuss this paper
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Lorella Fatone Francesco Zirilli Abstract. This paper presents a numerical method to price European options on realized variance. A European realized variance option is an option where payoff depends on the time of maturity, on the observed variance of the log-returns of the stock prices in a preassigned sequence of time values ti, i = 0, 1, . . . ,N. The realized variance is the variance observed in the sample of the log-returns considered, so that the value at maturity of the realized variance option depends on the discrete sample of the log-returns of the stock prices observed at the preassigned dates ti, i = 0, 1, . . . ,N. The method proposed to approximate the price of these options is based on the idea of approximating the discrete sum that gives the realized variance with an integral, using as model of the dynamics of the log-return of the stock price the Heston stochastic volatility model. In this way the price of a realized variance option is approximated with the price of an integrated stochastic variance option where payoff depends on the time of maturity and on the integrated stochastic variance. The integrated stochastic variance option is priced with the method of discounted expectations. We derive an integral representation formula for the price of this last kind of options. This integral formula reduces to a one dimensional Fourier integral in the case of the most commonly traded options that have a simple payoff function. The method has been validated on some test problems. The numerical experiments show that the approach suggested in this paper gives satisfactory approximations of the prices of the realized variance options (relative error 10−2, 10−3). This approach also allows substantial savings of computational time when compared with the Monte Carlo method used to evaluate with approximately the same accuracy. The website http://www.econ.univpm.it/recchioni/finance/w4 contains auxiliary material that can help in the understanding of this paper and makes available to the interested users the codes that implement the numerical method proposed here to price realized variance options. The use of these codes on a computing grid has been made user friendly developing a dedicated application using the software Symphony (that is, a Service Oriented Architecture (SOAM) software of Platform Computing Toronto, Canada). The website mentioned above makes this Symphony application available to the users.
Contents �� Problem definition �� The Black-Scholes case �� Pricing with characteristic functions �� Basket options in general models �� Swaptions in affine L Discuss this paper
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Schrager, D.F. and Pelsser A.A.J We propose an approach to find an approximate price of a swaption in Affine Term Structure Models. Our approach is based on the derivation of approximate dynamics in which the volatility of the Forward Swap Rate is itself an affine function of the factors. Hence we remain in the Affine framework and well known results on transforms and transform inversion can be used to obtain swaption prices in ways similar to bond options (i.e. caplets). We demonstrate that we can also obtain a closed form formula for the approximate price which is based on square-root dynamics for the swap rate. The latter approximation is extremely fast while remaining accurate. The method can be easily generalized to price options on coupon bonds. Computational time compares favorably with other approximation methods. Numerical results on the quality of the approximation are excellent. Our results show that in Affine models, analogously to the LIBOR Market Model, LIBOR and Swap rates are driven by approximately the same type of (in this case affine) dynamics Discuss this paper
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Alexey MEDVEDEV and Olivier SCAILLET In this paper we propose a new analytical approach that is both computational tractable and general enough to be successfully applied to a three-factor model. Our approach is based on the idea of substituting the optimal exercise rule with a simple one for which an approximate solution is easy to find. Similar ideas have already been explored in the literature (Broadie and Detemple (1996), Carr (1998), Ju (1998)). A typical rule is to exercise the option as soon as its moneyness measured in standard deviations reaches some predefined level. The price of such an option appears to have a regular asymptotic behavior near maturity with an asymptotic expansion available in a closed form for a broad class of models. The American option price is then approximated by the maximum over these option prices. In the paper we provide several numerical experiments showing that our method is competitive with existing ones with respect to computation time and accuracy. Under the Black-Scholes model our approximation is more accurate than a 1000-step binomial tree with a computational time equivalent to a 50-step tree. Discuss this paper
We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. We also explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is also computed using Monte Carlo simulation. This is made feasible by the representation of the American option price as a solution of a properly defined dual minimization problem, which is the main theoretical result of this paper. Our algorithm proves to be accurate on a set of sample problems where we price call options on the maximum and the geometric mean of a collection of stocks. These numerical results suggest that our pricing method can be successfully applied to problems of practical interest.
The Heston stochastic volatility model with volatility jumps can serve as a good tool for pricing and risk-managing derivatives on realized volatility and variance. In this paper, we derive analytical and approximate solutions for the values of contingent claims on realized variance and volatility under the Heston model with volatility jumps. By employing generalized Fourier transform we obtain analytical solutions (up to numerical inversion of Fourier integral) for swaps on realized volatility and variance with floor and cap protections, and for options on realized variance and volatility swaps. We also consider pricing forward-start claims on realized variance and volatility, including options on VIX, and obtain a closed-form solution and an accurate convexity adjustment formula for pricing these claims. Our solutions allow to unify pricing and risk managing of many volatility-dependent claims into one single framework. In addition, we derive a log-normal approximation to the density of the realized variance in the Heston model and obtain accurate approximate solutions for volatility- and variance-dependent claims with longer maturities. Discuss this paper
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Peter Meindl Abstract In this dissertation, we develop a new methodology to attack the two classic finance problems of portfolio optimization and dynamic hedging in an environment with a multi-period horizon, transaction costs, and dynamic asset parameters. Both of these problems would ideally be solved with dynamic programming, a methodology that would deliver the optimal solution. However, even problems that are much smaller than those of realistic size are computationally infeasible when formulated as a dynamic program. Thus, we propose a methodology to approximate the optimal solution to these computationally infeasible dynamic programming problems. Our methodology is based upon the optimization techniques of receding horizon control and stochastic programming. Bringing these methodologies together allows us to combine the long horizon of dynamic programming with computational feasibility. This methodology breaks down the monolithic dynamic programming problem into a sequence of smaller problems solved over time which allows us to incorporate changes in the system dynamics and to overcome issues of computational complexity. Our methodology has several key advantages. It can be applied to 1) a wide variety of asset dynamics, 2) more than just one or two assets (many competing v methodologies are limited to one or two assets along with a risk free asset), 3) different performance objectives, and 4) environments that include realistic factors such as transaction costs. Its final and perhaps most important advantage is 5) its strong level of performance vs. its competitors as we are able to show significantly superior results with our methodology. When applied to the dynamic hedging problem of hedging a short position on a derivative, this methodology is applicable to vanilla options, where analytical approximations exist, and to multi-dimensional options where no analytical solutions exist. Through simulation, empirical analysis, and a theoretical justification, we show our methodology significantly reduces expected absolute hedging error and increases expected utility on vanilla options vs. the classic analytical solutions as well as on multi-dimensional options vs. heuristic methodologies. For portfolio optimization, we focus mainly on optimizing a portfolio of defaultable bonds following a doubly stochastic reduced form model. Through Monte Carlo simulation we demonstrate results showing our methodology can significantly outperform the bond portfolio methodology of holding a constant percentage of the portfolio in each bond. Given the flexibility and high level of performance of this methodology in both portfolio optimization and dynamic hedging, we believe it is a positive contribution towards solving these two classic finance problems and perhaps to problems beyond this area.
Abstract This paper surveys the developments in the finance literature with respect to applying the Fourier transform for option pricing under affine jumpdiffusions. We provide a broad description of the issues and a detailed summary of the main points and features of the models proposed. First, we consider a wide class of affine jump-diffusions proposed for the asset price dynamics: jump-diffusions, diffusions with stochastic volatility, jump-diffusions with stochastic volatility, and jump-diffusions with stochastic volatility and jump intensity. Next we apply the Fourier transform for solving the problem of European option pricing under these price processes. We present two solution methods: the characteristic formula and the Black- Scholes-style formula. Finally, we discuss numerical implementation of pricing formulas and apply the considered processes for modeling the DAX options volatility surface.
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Authors Augusto Perilla & Diana Oancea This paper attempts to implement Monte Carlo simulations in order to price and hedge exotic options. Many exotic options have no analytic solutions, either because they are too complex or because the volatility specification is wrong. Consequently, numerical solutions are a necessity. We discuss the advantages and the drawbacks of such a pricing approach for the main exotic options. Given the strong assumptions of the Black-Scholes world, we attempt to relax them and, in particular, we focus on stochastic volatility models. After a review of the literature, we analyze via simulations the impact of stochastic volatility on the valuation of Asian and spread options. Next we construct and evaluate a dynamic hedging strategy for an exchange option under discrete rebalancing, stochastic volatility and transaction costs. We study the effect of each of these market imperfections on the hedge performance. Finally, we shortly discuss possible hedging approaches for various exotic options and compare static and dynamic hedging.
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