Editorial

4 pages, 180 KiB

Open AccessEditorial

by Lars Stentoft

J. Risk Financial Manag. 2020, 13(7), 145; https://doi.org/10.3390/jrfm13070145 - 04 Jul 2020

Cited by 1 | Viewed by 2109

The field of computational finance is evolving ever faster. This book collects a number of novel contributions on the use of computational methods and techniques for modelling financial asset prices, returns, and volatility, and on the use of numerical methods for pricing, hedging, [...] Read more.

The field of computational finance is evolving ever faster. This book collects a number of novel contributions on the use of computational methods and techniques for modelling financial asset prices, returns, and volatility, and on the use of numerical methods for pricing, hedging, and risk management of financial instruments. Full article

(This article belongs to the Special Issue Computational Finance)

Research

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31 pages, 413 KiB

Open AccessArticle

Forest of Stochastic Trees: A Method for Valuing Multiple Exercise Options

by R. Mark Reesor and T. James Marshall

J. Risk Financial Manag. 2020, 13(5), 95; https://doi.org/10.3390/jrfm13050095 - 13 May 2020

Cited by 1 | Viewed by 2473

Abstract

We present the Forest of Stochastic Trees (FOST) method for pricing multiple exercise options by simulation. The proposed method uses stochastic trees in place of binomial trees in the Forest of Trees algorithm originally proposed to value swing options, hence extending that method [...] Read more.

We present the Forest of Stochastic Trees (FOST) method for pricing multiple exercise options by simulation. The proposed method uses stochastic trees in place of binomial trees in the Forest of Trees algorithm originally proposed to value swing options, hence extending that method to allow for a multi-dimensional underlying process. The FOST can also be viewed as extending the stochastic tree method for valuing (single exercise) American-style options to multiple exercise options. The proposed valuation method results in positively- and negatively-biased estimators for the true option value. We prove the sign of the estimator bias and show that these estimators are consistent for the true option value. This method is of particular use in cases where there is potentially a large number of assets underlying the contract and/or the underlying price process depends on multiple risk factors. Numerical results are presented to illustrate the method. Full article

(This article belongs to the Special Issue Computational Finance)

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21 pages, 853 KiB

Open AccessArticle

Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method

by Pascal Létourneau and Lars Stentoft

J. Risk Financial Manag. 2019, 12(4), 190; https://doi.org/10.3390/jrfm12040190 - 15 Dec 2019

Cited by 3 | Viewed by 3085

Abstract

This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross-sectional regressions to the fullest [...] Read more.

This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross-sectional regressions to the fullest by averaging the individually obtained estimates at each early exercise step, starting from just before maturity, in the backwards induction algorithm. With this method, less errors are accumulated, and as a result of this, the price estimate is essentially unbiased even for long maturity options. Numerical results demonstrate the improvements from our method and show that these are robust to the choice of simulation setup, the characteristics of the option, and the dimensionality of the problem. Finally, because our method naturally disassociates the estimation of the optimal early exercise boundary from the pricing of the option, significant efficiency gains can be obtained by using less simulated paths and repetitions to estimate the optimal early exercise boundary than with the regular method. Full article

(This article belongs to the Special Issue Computational Finance)

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21 pages, 2547 KiB

Open AccessArticle

Generalized Mean-Reverting 4/2 Factor Model

by Yuyang Cheng, Marcos Escobar-Anel and Zhenxian Gong

J. Risk Financial Manag. 2019, 12(4), 159; https://doi.org/10.3390/jrfm12040159 - 08 Oct 2019

Cited by 7 | Viewed by 4179

Abstract

This paper proposes and investigates a multivariate 4/2 Factor Model. The name 4/2 comes from the superposition of a CIR term and a 3/2-model component. Our model goes multidimensional along the lines of a principal component and factor covariance decomposition. We find conditions [...] Read more.

This paper proposes and investigates a multivariate 4/2 Factor Model. The name 4/2 comes from the superposition of a CIR term and a 3/2-model component. Our model goes multidimensional along the lines of a principal component and factor covariance decomposition. We find conditions for well-defined changes of measure and we also find two key characteristic functions in closed-form, which help with pricing and risk measure calculations. In a numerical example, we demonstrate the significant impact of the newly added 3/2 component (parameter b) and the common factor (a), both with respect to changes on the implied volatility surface (up to 100%) and on two risk measures: value at risk and expected shortfall where an increase of up to 29% was detected. Full article

(This article belongs to the Special Issue Computational Finance)

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27 pages, 603 KiB

Open AccessArticle

Defined Contribution Pension Plans: Who Has Seen the Risk?

by Peter A. Forsyth and Kenneth R. Vetzal

J. Risk Financial Manag. 2019, 12(2), 70; https://doi.org/10.3390/jrfm12020070 - 24 Apr 2019

Cited by 5 | Viewed by 4035

Abstract

The trend towards eliminating defined benefit (DB) pension plans in favour of defined contribution (DC) plans implies that increasing numbers of pension plan participants will bear the risk that final realized portfolio values may be insufficient to fund desired retirement cash flows. We [...] Read more.

The trend towards eliminating defined benefit (DB) pension plans in favour of defined contribution (DC) plans implies that increasing numbers of pension plan participants will bear the risk that final realized portfolio values may be insufficient to fund desired retirement cash flows. We compare the outcomes of various asset allocation strategies for a typical DC plan investor. The strategies considered include constant proportion, linear glide path, and optimal dynamic (multi-period) time consistent quadratic shortfall approaches. The last of these is based on a double exponential jump diffusion model. We determine the parameters of the model using monthly US data over a 90-year sample period. We carry out tests in a synthetic market which is based on the same jump diffusion model and also using bootstrap resampling of historical data. The probability that portfolio values at retirement will be insufficient to provide adequate retirement incomes is relatively high, unless DC investors adopt optimal allocation strategies and raise typical contribution rates. This suggests there is a looming crisis in DC plans, which requires educating DC plan holders in terms of realistic expectations, required contributions, and optimal asset allocation strategies. Full article

(This article belongs to the Special Issue Computational Finance)

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11 pages, 2451 KiB

Open AccessArticle

The Impact of Algorithmic Trading in a Simulated Asset Market

by Purba Mukerji, Christine Chung, Timothy Walsh and Bo Xiong

J. Risk Financial Manag. 2019, 12(2), 68; https://doi.org/10.3390/jrfm12020068 - 20 Apr 2019

Cited by 10 | Viewed by 5248

Abstract

In this work we simulate algorithmic trading (AT) in asset markets to clarify its impact. Our markets consist of human and algorithmic counterparts of traders that trade based on technical and fundamental analysis, and statistical arbitrage strategies. Our specific contributions are: (1) directly [...] Read more.

In this work we simulate algorithmic trading (AT) in asset markets to clarify its impact. Our markets consist of human and algorithmic counterparts of traders that trade based on technical and fundamental analysis, and statistical arbitrage strategies. Our specific contributions are: (1) directly analyze AT behavior to connect AT trading strategies to specific outcomes in the market; (2) measure the impact of AT on market quality; and (3) test the sensitivity of our findings to variations in market conditions and possible future events of interest. Examples of such variations and future events are the level of market uncertainty and the degree of algorithmic versus human trading. Our results show that liquidity increases initially as AT rises to about 10% share of the market; beyond this point, liquidity increases only marginally. Statistical arbitrage appears to lead to significant deviation from fundamentals. Our results can facilitate market oversight and provide hypotheses for future empirical work charting the path for developing countries where AT is still at a nascent stage. Full article

(This article belongs to the Special Issue Computational Finance)

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26 pages, 609 KiB

Open AccessArticle

Efficient Numerical Pricing of American Call Options Using Symmetry Arguments

by Lars Stentoft

J. Risk Financial Manag. 2019, 12(2), 59; https://doi.org/10.3390/jrfm12020059 - 09 Apr 2019

Cited by 5 | Viewed by 3197

Abstract

This paper demonstrates that it is possible to improve significantly on the estimated call prices obtained with the regression and simulation-based least-squares Monte Carlo method by using put-call symmetry. The results show that, for a large sample of options with characteristics of relevance [...] Read more.

This paper demonstrates that it is possible to improve significantly on the estimated call prices obtained with the regression and simulation-based least-squares Monte Carlo method by using put-call symmetry. The results show that, for a large sample of options with characteristics of relevance in real-life applications, the symmetric method performs much better on average than the regular pricing method, is the best method for most of the options, never performs poorly and, as a result, is extremely efficient compared to the optimal, but unfeasible method that picks the method with the smallest Root Mean Squared Error (RMSE). A simple classification method is proposed that, by optimally selecting among estimates from the symmetric method with a reasonably small order used in the polynomial approximation, achieves a relative efficiency of more than

98 %

. The relative importance of using the symmetric method increases with option maturity and with asset volatility. Using the symmetric method to price, for example, real options, many of which are call options with long maturities on volatile assets, for example energy, could therefore improve the estimates significantly by decreasing their bias and RMSE by orders of magnitude. Full article

(This article belongs to the Special Issue Computational Finance)

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25 pages, 1179 KiB

Open AccessArticle

Positive Liquidity Spillovers from Sovereign Bond-Backed Securities

by Peter G. Dunne

J. Risk Financial Manag. 2019, 12(2), 58; https://doi.org/10.3390/jrfm12020058 - 09 Apr 2019

Cited by 3 | Viewed by 2699

Abstract

This paper contributes to the debate concerning the benefits and disadvantages of introducing a European Sovereign Bond-Backed Securitisation (SBBS) to address the need for a common safe asset that would break destabilising bank-sovereign linkages. The analysis focuses on assessing the effectiveness of hedges [...] Read more.

This paper contributes to the debate concerning the benefits and disadvantages of introducing a European Sovereign Bond-Backed Securitisation (SBBS) to address the need for a common safe asset that would break destabilising bank-sovereign linkages. The analysis focuses on assessing the effectiveness of hedges incurred while making markets in individual euro area sovereign bonds by taking offsetting positions in one or more of the SBBS tranches. Tranche yields are estimated using a simulation approach. This involves the generation of sovereign defaults and allocation of the combined credit risk premium of all the sovereigns, at the end of each day, to the SBBS tranches according to the seniority of claims under the proposed securitisation. Optimal hedging with SBBS is found to reduce risk exposures substantially in normal market conditions. In volatile conditions, hedging is not very effective but leaves dealers exposed to mostly idiosyncratic risks. These remaining risks largely disappear if dealers are diversified in providing liquidity across country-specific secondary markets and SBBS tranches. Hedging each of the long positions in a portfolio of individual sovereigns results in a risk exposure as low as that borne by holding the safest individual sovereign bond (the Bund). Full article

(This article belongs to the Special Issue Computational Finance)

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31 pages, 3292 KiB

Open AccessArticle

Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time

by Vladimir Petrov, Anton Golub and Richard Olsen

J. Risk Financial Manag. 2019, 12(2), 54; https://doi.org/10.3390/jrfm12020054 - 01 Apr 2019

Cited by 3 | Viewed by 9907

Abstract

We propose a novel intraday instantaneous volatility measure which utilises sequences of drawdowns and drawups non-equidistantly spaced in physical time as indicators of high-frequency activity of financial markets. The sequences are re-expressed in terms of directional-change intrinsic time which ticks only when the [...] Read more.

We propose a novel intraday instantaneous volatility measure which utilises sequences of drawdowns and drawups non-equidistantly spaced in physical time as indicators of high-frequency activity of financial markets. The sequences are re-expressed in terms of directional-change intrinsic time which ticks only when the price curve changes the direction of its trend by a given relative value. We employ the proposed measure to uncover weekly volatility seasonality patterns of three Forex and one Bitcoin exchange rates, as well as a stock market index. We demonstrate the long memory of instantaneous volatility computed in directional-change intrinsic time. The provided volatility estimation method can be adapted as a universal multiscale risk-management tool independent of the discreteness and the type of analysed high-frequency data. Full article

(This article belongs to the Special Issue Computational Finance)

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19 pages, 974 KiB

Open AccessArticle

Statistical Arbitrage with Mean-Reverting Overnight Price Gaps on High-Frequency Data of the S&P 500

by Johannes Stübinger and Lucas Schneider

J. Risk Financial Manag. 2019, 12(2), 51; https://doi.org/10.3390/jrfm12020051 - 01 Apr 2019

Cited by 5 | Viewed by 7244

Abstract

This paper develops a fully-fledged statistical arbitrage strategy based on a mean-reverting jump–diffusion model and applies it to high-frequency data of the S&P 500 constituents from January 1998–December 2015. In particular, the established stock selection and trading framework identifies overnight price gaps based [...] Read more.

This paper develops a fully-fledged statistical arbitrage strategy based on a mean-reverting jump–diffusion model and applies it to high-frequency data of the S&P 500 constituents from January 1998–December 2015. In particular, the established stock selection and trading framework identifies overnight price gaps based on an advanced jump test procedure and exploits temporary market anomalies during the first minutes of a trading day. The existence of the assumed mean-reverting property is confirmed by a preliminary analysis of the S&P 500 index; this characteristic is particularly significant 120 min after market opening. In the empirical back-testing study, the strategy delivers statistically- and economically-significant returns of 51.47 percent p.a.and an annualized Sharpe ratio of 2.38 after transaction costs. We benchmarked our trading algorithm against existing quantitative strategies from the same research area and found its performance superior in a multitude of risk-return characteristics. Finally, a deep dive analysis shows that our results are consistently profitable and robust against drawdowns, even in recent years. Full article

(This article belongs to the Special Issue Computational Finance)

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23 pages, 455 KiB

Open AccessArticle

Between ℙ and ℚ: The ℙ^ℚ Measure for Pricing in Asset Liability Management

by Marcel T. P. Van Dijk, Cornelis S. L. De Graaf and Cornelis W. Oosterlee

J. Risk Financial Manag. 2018, 11(4), 67; https://doi.org/10.3390/jrfm11040067 - 24 Oct 2018

Cited by 5 | Viewed by 4561

Abstract

Insurance companies issue guarantees that need to be valued according to the market expectations. By calibrating option pricing models to the available implied volatility surfaces, one deals with the so-called risk-neutral measure

Q

, which can be used to generate market consistent values [...] Read more.

Insurance companies issue guarantees that need to be valued according to the market expectations. By calibrating option pricing models to the available implied volatility surfaces, one deals with the so-called risk-neutral measure

Q

, which can be used to generate market consistent values for these guarantees. For asset liability management, insurers also need future values of these guarantees. Next to that, new regulations require insurance companies to value their positions on a one-year horizon. As the option prices at

t = 1

are unknown, it is common practice to assume that the parameters of these option pricing models are constant, i.e., the calibrated parameters from time

t = 0

are also used to value the guarantees at

t = 1

. However, it is well-known that the parameters are not constant and may depend on the state of the market which evolves under the real-world measure

P

. In this paper, we propose improved regression models that, given a set of market variables such as the VIX index and risk-free interest rates, estimate the calibrated parameters. When the market variables are included in a real-world simulation, one is able to assess the calibrated parameters (and consequently the implied volatility surface) in line with the simulated state of the market. By performing a regression, we are able to predict out-of-sample implied volatility surfaces accurately. Moreover, the impact on the Solvency Capital Requirement has been evaluated for different points in time. The impact depends on the initial state of the market and may vary between −46% and +52%. Full article

(This article belongs to the Special Issue Computational Finance)

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