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1546 KiB

Open AccessArticle

Inflation and Speculation in a Dynamic Macroeconomic Model

by Matheus R. Grasselli and Adrien Nguyen Huu

J. Risk Financial Manag. 2015, 8(3), 285-310; https://doi.org/10.3390/jrfm8030285 - 06 Jul 2015

Cited by 11 | Viewed by 6146

We study a monetary version of the Keen model by merging two alternative extensions, namely the addition of a dynamic price level and the introduction of speculation. We recall and study old and new equilibria, together with their local stability analysis. This includes [...] Read more.

We study a monetary version of the Keen model by merging two alternative extensions, namely the addition of a dynamic price level and the introduction of speculation. We recall and study old and new equilibria, together with their local stability analysis. This includes a state of recession associated with a deflationary regime and characterized by falling employment but constant wage shares, with or without an accompanying debt crisis. Full article

(This article belongs to the Special Issue Selected Papers from the Fifth International Conference on Mathematics in Finance (MiF) 2014, Organized by North-West University, University of Cape Town and University of Johannesburg, South Africa)

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691 KiB

Open AccessArticle

Quantification of VaR: A Note on VaR Valuation in the South African Equity Market

by Lesedi Mabitsela, Eben Maré and Rodwell Kufakunesu

J. Risk Financial Manag. 2015, 8(1), 103-126; https://doi.org/10.3390/jrfm8010103 - 13 Feb 2015

Cited by 4 | Viewed by 6026

Abstract

The statistical distribution of financial returns plays a key role in evaluating Value-at-Risk using parametric methods. Traditionally, when evaluating parametric Value-at-Risk, the statistical distribution of the financial returns is assumed to be normally distributed. However, though simple to implement, the Normal distribution underestimates [...] Read more.

The statistical distribution of financial returns plays a key role in evaluating Value-at-Risk using parametric methods. Traditionally, when evaluating parametric Value-at-Risk, the statistical distribution of the financial returns is assumed to be normally distributed. However, though simple to implement, the Normal distribution underestimates the kurtosis and skewness of the observed financial returns. This article focuses on the evaluation of the South African equity markets in a Value-at-Risk framework. Value-at-Risk is estimated on four equity stocks listed on the Johannesburg Stock Exchange, including the FTSE/JSE TOP40 index and the S & P 500 index. The statistical distribution of the financial returns is modelled using the Normal Inverse Gaussian and is compared to the financial returns modelled using the Normal, Skew t-distribution and Student t-distribution. We then estimate Value-at-Risk under the assumption that financial returns follow the Normal Inverse Gaussian, Normal, Skew t-distribution and Student t-distribution and backtesting was performed under each distribution assumption. The results of these distributions are compared and discussed. Full article

(This article belongs to the Special Issue Selected Papers from the Fifth International Conference on Mathematics in Finance (MiF) 2014, Organized by North-West University, University of Cape Town and University of Johannesburg, South Africa)

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352 KiB

Open AccessArticle

Quadratic Hedging of Basis Risk

by Hardy Hulley and Thomas A. McWalter

J. Risk Financial Manag. 2015, 8(1), 83-102; https://doi.org/10.3390/jrfm8010083 - 02 Feb 2015

Cited by 7 | Viewed by 6007

Abstract

This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging [...] Read more.

This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach. Full article

(This article belongs to the Special Issue Selected Papers from the Fifth International Conference on Mathematics in Finance (MiF) 2014, Organized by North-West University, University of Cape Town and University of Johannesburg, South Africa)

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1173 KiB

Open AccessArticle

Implied and Local Volatility Surfaces for South African Index and Foreign Exchange Options

by Antonie Kotzé, Rudolf Oosthuizen and Edson Pindza

J. Risk Financial Manag. 2015, 8(1), 43-82; https://doi.org/10.3390/jrfm8010043 - 26 Jan 2015

Cited by 4 | Viewed by 10004

Abstract

Certain exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility. Many exotics are priced in a local volatility framework. Pricing under local volatility has become a field of extensive research in finance, and various models are [...] Read more.

Certain exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility. Many exotics are priced in a local volatility framework. Pricing under local volatility has become a field of extensive research in finance, and various models are proposed in order to overcome the shortcomings of the Black-Scholes model that assumes a constant volatility. The Johannesburg Stock Exchange (JSE) lists exotic options on its Can-Do platform. Most exotic options listed on the JSE’s derivative exchanges are valued by local volatility models. These models needs a local volatility surface. Dupire derived a mapping from implied volatilities to local volatilities. The JSE uses this mapping in generating the relevant local volatility surfaces and further uses Monte Carlo and Finite Difference methods when pricing exotic options. In this document we discuss various practical issues that influence the successful construction of implied and local volatility surfaces such that pricing engines can be implemented successfully. We focus on arbitrage-free conditions and the choice of calibrating functionals. We illustrate our methodologies by studying the implied and local volatility surfaces of South African equity index and foreign exchange options. Full article

(This article belongs to the Special Issue Selected Papers from the Fifth International Conference on Mathematics in Finance (MiF) 2014, Organized by North-West University, University of Cape Town and University of Johannesburg, South Africa)

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2172 KiB

Open AccessArticle

Pricing a Collateralized Derivative Trade with a Funding Value Adjustment

by Chadd B. Hunzinger and Coenraad C.A. Labuschagne

J. Risk Financial Manag. 2015, 8(1), 17-42; https://doi.org/10.3390/jrfm8010017 - 26 Jan 2015

Cited by 4 | Viewed by 5835

Abstract

The 2008 credit crisis changed the manner in which derivative trades are conducted. One of these changes is the posting of collateral in a trade to mitigate the counterparty credit risk. Another is the realization that banks are not risk-free and, as a [...] Read more.

The 2008 credit crisis changed the manner in which derivative trades are conducted. One of these changes is the posting of collateral in a trade to mitigate the counterparty credit risk. Another is the realization that banks are not risk-free and, as a result, cannot borrow at the risk-free rate any longer. The latter led banks to introduced the controversial adjustment to derivative prices, known as a funding value adjustment (FVA), which is interlinked with the posting of collateral. In this paper, we extend the Cox, Ross and Rubinstein (CRR) discrete-time model to include collateral and FVA. We prove that this derived model is a discrete analogue of Piterbarg’s partial differential equation (PDE), which describes the price of a collateralized derivative. The fact that the two models coincide is also verified by numerical implementation of the results that we obtain. Full article

(This article belongs to the Special Issue Selected Papers from the Fifth International Conference on Mathematics in Finance (MiF) 2014, Organized by North-West University, University of Cape Town and University of Johannesburg, South Africa)

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313 KiB

Open AccessArticle

State Prices and Implementation of the Recovery Theorem

by Alex Backwell

J. Risk Financial Manag. 2015, 8(1), 2-16; https://doi.org/10.3390/jrfm8010002 - 19 Jan 2015

Cited by 8 | Viewed by 5854

Abstract

It is generally held that derivative prices do not contain useful predictive information, that is, information relating to the distribution of future financial variables under the real-world measure. This is because the market’s implicit forecast of the future becomes entangled with market risk [...] Read more.

It is generally held that derivative prices do not contain useful predictive information, that is, information relating to the distribution of future financial variables under the real-world measure. This is because the market’s implicit forecast of the future becomes entangled with market risk preferences during derivative price formation. A result derived by Ross [1], however, recovers the real-world distribution of an equity index, requiring only current prices and mild restrictions on risk preferences. In addition to being of great interest to the theorist, the potential practical value of the result is considerable. This paper addresses implementation of the Ross Recovery Theorem. The theorem is formalised, extended, proved and discussed. Obstacles to application are identified and a workable implementation methodology is developed. Full article

(This article belongs to the Special Issue Selected Papers from the Fifth International Conference on Mathematics in Finance (MiF) 2014, Organized by North-West University, University of Cape Town and University of Johannesburg, South Africa)

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264 KiB

Open AccessArticle

Exact Fit of Simple Finite Mixture Models

by Dirk Tasche

J. Risk Financial Manag. 2014, 7(4), 150-164; https://doi.org/10.3390/jrfm7040150 - 20 Nov 2014

Cited by 7 | Viewed by 4406

Abstract

How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score [...] Read more.

How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year’s portfolio-wide default rate. We point out that the maximum-likelihood (ML) approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fixed. From this observation we can conclude that the standard default rate forecast based on last year’s conditional default rates will always be located between last year’s portfolio-wide default rate and the ML forecast for next year. As an application example, cost quantification is then discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem. Full article

(This article belongs to the Special Issue Selected Papers from the Fifth International Conference on Mathematics in Finance (MiF) 2014, Organized by North-West University, University of Cape Town and University of Johannesburg, South Africa)

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132 KiB

Open AccessBrief Report

Report on the Fifth International Mathematics in Finance (MiF) Conference 2014, Skukuza, Kruger National Park, South Africa

by Michael McAleer

J. Risk Financial Manag. 2014, 7(3), 110-112; https://doi.org/10.3390/jrfm7030110 - 19 Sep 2014

Viewed by 4498

Abstract

The Journal of Risk and Financial Management was first published in 2008, and, since its inception, has published a number of theoretical and empirical papers on various topics in risk and financial management, in pursuit of its stated goal of advancing knowledge and [...] Read more.

The Journal of Risk and Financial Management was first published in 2008, and, since its inception, has published a number of theoretical and empirical papers on various topics in risk and financial management, in pursuit of its stated goal of advancing knowledge and understanding in the practice of risk and financial management through the publication of high quality papers that are relevant to practitioners in the field.[...] Full article

(This article belongs to the Special Issue Selected Papers from the Fifth International Conference on Mathematics in Finance (MiF) 2014, Organized by North-West University, University of Cape Town and University of Johannesburg, South Africa)

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