International Journal of Financial Engineering

A method for feedback control of the multi-asset Black–Scholes PDE is developed. By applying semi-discretization and a finite differences scheme the multi-asset Black–Scholes PDE is transformed into a state-space model consisting of ordinary nonlinear differential equations. For this set of differential equations it is shown that differential flatness properties hold. This enables to solve the associated control problem and to succeed stabilization of the options’ dynamics. It is shown that the previous procedure results into a set of nonlinear ordinary differential equations (ODEs) and to an associated state equations model. For the local subsystems, into which a Black–Scholes PDE is decomposed, it becomes possible to apply boundary-based feedback control. The controller design proceeds by showing that the state-space model of the Black–Scholes PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem’s dynamics and can eliminate the subsystem’s tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the multi-asset Black–Scholes PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the Black–Scholes PDE system so as to assure that all its state variables will converge to the desirable setpoints.

The Gaussian affine interest rate models are widely used in the financial industry for pricing, hedging and also risk management purposes. We consider the multifactor models with time dependent parameters. Usually the models are simulated using some appropriate discretization schema because the joint distribution of the stochastic and discounting factors is not known. We derive the exact joint conditional distribution of the stochastic and discounting factors. Additionally we show how an efficient and exact Monte Carlo simulation of the Gaussian affine interest rate models could be performed.

This article aims to estimate the fair-value of flexi-forwards, popular financial instruments on currencies, through Leisen–Reimer trees. The first part of paper deals with Markov chains suitable for pricing American options: Cox–Ross–Rubinstein, Jarrow–Rudd, Tian, Leisen–Reimer Trees. The correctness of the implementation in Matlab has been tested by comparing their prices with those obtained through approximated closed-formulas. The second part highlights the better performance of Leisen–Reimer trees in terms of convergence speed and sensitivity. Finally, flexi-forward contracts have been priced by using the numerical methodologies which have outperformed in the previous parts.

We consider the valuation of single name CDS options (CDSO) and related optionalities, particularly extension risk, in the structural default model introduced by Chen and Kou (2009). This jump-diffusion based model is able to generate realistic dynamics for CDS spreads and has decent calibration performance. Due to the European character of the considered options, they can be valued with an efficient Monte Carlo algorithm based on Brownian bridges, adapted from Ruf and Scherer (2011). In contrast to the intensity approach, structural models offer a link to the equity side of a firm’s capital structure, possibly enabling to hedge CDS options with instruments other than CDS.

Hull and White approach to Wrong Way Risk in the computation of Credit Value Adjustment (CVA) is considered the most straightforward generalization of the standard Basel approach. The model is financially intuitive and it can be implemented by a slight modification of existing algorithms for CVA calculation. However, path dependency in the key quantities has non-elementary consequences in the calibration of model parameters. We propose a simple and fast approach for computing these quantities via a recursion formula. We show in detail the calibration methodology on market data and CVA computations in two relevant cases: a FX forward and an interest rate swap.

In a continuous-in-time model, there is an important financial quantity called Loan which cannot be determined directly in terms of algebraic spending but has a major impact on the financial strategy. In this paper, we use a mathematical framework to discuss an inverse problem of determining the implied Loan Measure from Algebraic Spending Measure when it is possible. In addition, we build a numerical method to concentrate a measure as a sum of Dirac masses.

Stochastic volatility model of the Gamma Ornstein–Uhlenbeck possess authentic capability of both capturing some stylized features of financial time series and pricing European options. In this work we modify the Gamma OU model from the viewpoint of Monte Carlo simulation, which is crucial in both model inference and exotic option pricing. We discuss topics related to the measure transformation between objective and risk-neutral measures, arbitrage-free and market incompleteness of the new model. Furthermore, we investigate the performance of this model in European options pricing and an empirical application is presented.

This study is based on positivism research philosophy and utilizes deductive approach. The study uses a dataset of 117 firms listed on KSE-100 Index from 2005 to 2012 to analyze the predictability of capital asset pricing model (CAPM) under different data frequencies and time frames. Six months daily data, in contradiction to the recommended five years monthly data, provides the best estimates. However, the performance of model can be regarded poor as it only explains 7.39% difference in returns.