Artificial Neural Networks Performance in WIG20 Index Options Pricing

In this paper, the performance of artificial neural networks in option pricing was analyzed and compared with the results obtained from the Black–Scholes–Merton model, based on the historical volatility. The results were compared based on various error metrics calculated separately between three moneyness ratios. The market data-driven approach was taken to train and test the neural network on the real-world options data from 2009 to 2019, quoted on the Warsaw Stock Exchange. The artificial neural network did not provide more accurate option prices, even though its hyperparameters were properly tuned. The Black–Scholes–Merton model turned out to be more precise and robust to various market conditions. In addition, the bias of the forecasts obtained from the neural network differed significantly between moneyness states. This study provides an initial insight into the application of deep learning methods to pricing options in emerging markets with low liquidity and high volatility.

Probability of Default Bank Umum di Indonesia: Alternatif dalam Implementasi Sisitem Premi Deferensial

The Indonesian Deposit Insurance Corporation (LPS) initially imposed the flat rate premium system, the same premium rate for all banks, which is 0.2% of the total third party funds (DPK) of commercial banks. However; when there is a change in the value of deposits guaranteed, LPS needs to change from the flat rate premium system to the Differential Premium System. This study uses Probability of Default (PoD), derived from the Merton Model (1974), for each individual Commercial Bank in Indonesia in implementing the Differential Premium System as the mandate of Article 15 paragraph (1) of the Law. Thus, each individual bank will pay a premium in accordance with the probability of default to LPS. This study finds that the average of probability of default of all commercial banks in the period 2002-2014 reaches 57.12%. Bank that has the smallest average Probability of Default (PoD) is Bank 151Â with a PoD of 14.10% and an AA category rating. The second position is Bank 427 with a PoD of 18.20% and a rating of A. While the third position is Bank 14 with a PoD of 18.70% also with a rating of A. This study finds that the Differential Premium System in Indonesia can be implemented, given that LPS revenue will not be reduced much or at least close to the flat rate premium system, when LPS imposes the Differential Premium System.

Determining the Credit Score and Credit Rating of Firms using the Combination of KMV-Merton Model and Financial Ratios

Credit risk management has become a must in this era due to the increase in the number of businesses defaulting. Building upon the legacy of Kealhofer, McQuown, and Vasicek (KMV), a mathematical model is introduced based on Merton model called KMV-Merton model to predict the credit risk of firms. The KMV-Merton model is commonly used in previous default studies but is said to be lacking in necessary detail. Hence, this study aims to combine the KMV-Merton model with the financial ratios to determine the firms’ credit scores and ratings. Based on the sample data of four firms, the KMV-Merton model is used to estimate the default probabilities. The data is also used to estimate the firms’ liquidity, solvency, indebtedness, return on asset (ROA), and interest coverage. According to the weightages established in this analysis, scores were assigned based on those estimates to calculate the total credit score. The firms were then given a rating based on their respective credit score. The credit ratings are compared to the real credit ratings rated by Malaysian Rating Corporation Berhad (MARC). According to the comparison, three of the four companies have credit scores that are comparable to MARC’s. Two A-rated firms and one D-rated firm have the same ratings. The other receives a C instead of a B. This shows that the credit scoring technique used can grade the low and the high credit risk firms, but not strictly for a firm with a medium level of credit risk. Although research on credit scoring have been done previously, the combination of KMV-Merton model and financial ratios in one credit scoring model based on the calculated weightages gives new branch to the current studies. In practice, this study aids risk managers, bankers, and investors in making wise decisions through a smooth and persuasive process of monitoring firms’ credit risk.

What Do We Know About Corporate Bond Returns?

Recently, there has been a fast-growing literature on the determinants of corporate bond returns, in particular, the driving force of cross-sectional return variation. In this review, we first survey recent empirical studies on this important topic. We discuss cross-sectional evidence as well as time-series evidence. We then present a model-based analysis of individual corporate bond returns using the structural approach for credit risk modeling. We show, among other things, that the expected corporate bond return implied by the Merton model predicts 1-month-ahead corporate bond returns in the cross section. Expected final online publication date for the Annual Review of Financial Economics, Volume 13 is November 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A Comparative Study of Pricing Option with Efficient Methods

Our main objective of this paper is to introduce four individual techniques of pricing options; the techniques are Binomial method, Trinomial method, Monte Carlo simulation and Black-Scholes-Merton model. Because they play a significant role in option valuation of stock price dynamics, risk managements as well as stock market. In this paper, we briefly discuss all these four methods with their properties and behavior. We also focused on numerical technique for the higher accuracy of option pricing and compare them graphically. We use the Computer Algebra System (CAS) Python (Edition 2019.3.1) for this purpose. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 1-7

Volatility morphology of asset value and credit spread puzzle

Merton model has provided a classic theoretical framework for explaining credit spreads. This paper extends Merton model by introducing morphology factor of asset value volatility in the model, and conducts empirical studies on the effect of asset volatility morphology on credit spreads in China’s bond market. The results show that asset volatility morphology is economically important and can explain credit spreads well. Furthermore, this paper analyzes the asymmetric influences of monetary policy on credit spreads and asset volatility morphology. This paper points out that the responses of credit spreads and asset volatility morphology to monetary policy are consistent in the tight liquidity environments. To this end, monetary policy and liquidity, which are two factors that have been ignored by classic Merton model but proved to have significant influences on credit spreads, play roles in influencing credit spreads by changing volatility morphology of asset value. Since asset volatility morphology can reflect the change of investors’ expectation on the default probability of asset, the argument mentioned in the credit spread puzzle that the fundamentals related to bond default probability cannot explain credit spreads needs to be reexamined.

Option pricing: a yet simpler approach

We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox–Ross–Rubinstein (CRR) pricing model. The main tool used in this paper for simplifying the reasoning is applying static hedging arguments. In applying the static hedging principle, we consider Arrow–Debreu securities and digital options, or backward random processes. In the last case, the CRR model is extended to an infinite state space which leads to an interesting new phenomenon not present in the classical CRR model. At the end, we discuss the paradox involving the drift parameter $$\mu $$ μ in the Black–Scholes–Merton model pricing. We provide sensitivity analysis and an approximation of the speed of convergence for the asymptotically vanishing effect of drift in prices.

PROBABILITY OF DEFAULT MEASUREMENT MODELS OF MERTON ON SHARIAH BANKS AND CONVENTIONAL BANKS IN INDONESIA FOR 2011-2017 PERIOD

This paper provides empirical evidence of the comparison default risk in Islamic banks and conventional banks in Indonesia over the 2011 to 2017 period. The calculation of bank default risk using a Merton Model has allowed the measure of the Distance-to-Default (DD) and Default probability (DP). This study was extended to investigate the differences of bank default risk between Islamic banks and conventional banks with the employ of T-test. The evidence shows Islamic banks as banks that are far from the Possibility of Default Risk rather than conventional banks. The T-test indicates that there are significant differences in the Probability of Default values between Islamic banks and conventional banks. These findings could be relevance to regulators in Indonesia to support the growth of Islamic, which helps in maintaining financial system stability and avoiding systemic risk.