International Journal of Financial Markets and Derivatives (7 papers in press)
Closed-form solution for the critical stock price and the price of perpetual American call options via the improved Mellin transforms
by Sunday Emmanuel Fadugba, Chuma Nwozo
Abstract: This paper presents the closed-form solution for the critical stock price also known as the free boundary and the price of the perpetual American call options by means of the improved Mellin transforms. The expression for the price of the perpetual American call options with non-dividend yield is obtained as a steady-state solution to the non-homogeneous Black-Scholes partial differential equation for the American call options, rather than as a solution to the static problem. The result shows that the critical stock price for the American call option is infinite and the price of the option coincides with the underlying asset price. For better accuracy, we have shown that our integral representation for the price of the American call option can be evaluated by means of a N-point Gauss-Laguerre quadrature method. To determine the performance of the improved Mellin transforms, we have compared the results generated by the improved Mellin transforms with the binomial model and the Black-Scholes model for the valuation of the American call option with non-dividend yield. The numerical results show that the improved Mellin transforms agrees with the Black-Scholes model and performs better than the binomial model as shown in Figure 3 below.
Keywords: American call option; Black-Scholes equation; Critical stock price; Gauss-Laguerre quadrature method; Improved Mellin transforms; Non-dividend yield; Perpetual American call option.
DYNAMICS OF RANDOMNESS AND EFFICIENCY IN THE INDIAN STOCK MARKETS
by Sujeesh Kumar, Nanda Mohan
Abstract: This paper analysed the behaviour of randomness and efficiency in the Indian stock markets in view of the efficient market hypothesis (EMH) and adaptive market hypothesis (AMH). We have examined the randomness in detail and found that there has been no uniformity or trend in randomness and further, efficiency is time varying. Although inefficiencies were evidenced during the period of study (19902014), improvement in efficiencies has been observed in some pockets of time, implying greater adaptability in the markets-BSE Sensex and NSE Nifty. Based on the Lyapunov exponent, indication of nonlinear deterministic chaos also detected. The extent of randomness has been compared between both the markets using an entropy measure.
Keywords: Randomness; Runs; Variance ratio; Market efficiency; Chaos; and Entropy.
Assessing the power of VaR: New empirical evidence
by Andrei Rusu
Abstract: Risk and uncertainty are concepts found in every financial environment. In order to anticipate and prevent their losses, financial market participants use various measures to quantify risk. One frequently used measure is value at risk (VaR). This study is focused on comparing and assessing the performance for a set of parametric and semi-parametric methods of estimating VaR, highlighting some of the less investigated approaches in empirical literature, which have significant proven performance nonetheless. In order to evaluate the out-of-sample performance of this measure, we considered the evolution of stock indexes from 14 international markets, between years 2006-2016. Thus, the data covers periods characterized by stability and also periods of extreme events like the financial crisis which started in 2007-2008. The results showed that filtered historical simulation performed best on all indexes. It was also found that taking into account the asymmetric character of financial information leads to more accurate predictions.
Keywords: Value at risk; APARCH; Generalized Pareto distribution; Backtesting; Financial markets.
An Equilibrium Pricing for OTC Derivatives with Non-Cash Collateralization
by Kazuhiro Takino
Abstract: In this study, we propose an equilibrium pricing rule for contingent claims traded in over-the-counter (OTC) markets with non-cash collateralization. Owing to counterparty risks in OTC markets, collateral is required to create a derivative contract. In 2017, Osaka Exchange decided to expand the type of collateral asset, while cash has always been used as a collateral. In this study, we consider a market model in which the required collateral is not cash, and is instead assets with a senior credit class, such as a US government bond. We further assume that market participants source collateral from the repurchase market (SC repo), where investors can borrow assets. Therefore, we provide an equilibrium pricing model that includes the repo market under counterparty risk. Our pricing rule also determines an equilibrium volume for the derivative contract. This enables us to examine the effects of the repo market on the price and volume for OTC derivative transactions.
Keywords: OTC derivative pricing; counterparty risk; collateral; pricing kernel; repo market.
Comparison of Determinants in the Different Property Sectors of Japanese REIT Market under Non-Traditional Monetary Policy Regimes
by Takayasu Ito
Abstract: Stock price has a positive impact on the Real Estate Investment Trust (REIT) Property Sector Index Series (Office, Residential, and Retail & Logistics) in all three sample periods. Interest rate has no significant impact on any of the sectors in the REIT Property Sector Index Series under the comprehensive easing policy regime. On the other hand, interest rate has a negative impact on each of the sectors in the REIT Property Sector Index Series under the quantitative and qualitative easing and the negative interest rate policy regimes. The negative impact of interest rate on the REIT market is larger under the quantitative and qualitative policy regime than it is under the negative interest rate policy regime. As regards the sensitivity of the three REIT property sectors to stock price and interest rate, no significant differences are found in any of the samples; the three different sectors are almost equally influenced by stock price and long-term interest rate in each sample.
Keywords: REIT Property Sector; Stock Price; Swap Rate; Non-Traditional Monetary Policy.
VOLATILITY ESTIMATION FOR CRYPTOCURRENCIES USING MARKOV-SWITCHING GARCH MODELS
by Paulo Vitor Jordão Da Gama Silva, Marcelo Cabus Klotzle, Antonio Carlos Figueiredo Pinto, Leonardo Lima Gomes
Abstract: In the 21st century, digital currencies have become a disruptive technology that is shaking up both financial markets and academic environment. Investors, politicians, companies, and academics are attempting to improve their understanding of these currencies for future investment possibilities and technological applications. This study aims to evaluate changes in different volatility states of eight digital currencies (BTC, ETH, LTC, XRP, XMR, NEM, LISK, and STEEM) that showed the highest liquidity and market capitalization from 2013 to 2017. The methodology involved the MSGARCH model, using SGARCH, EGARCH, GJRGARCH, and TGARCH models. Our study demonstrated that two volatility regimes, that is, one with a larger volatility and another with a smaller one, clearly exist for all the analyzed cryptocurrencies. What differs between the currencies is the probability of a second regime occurring. Moreover, we concluded that for both the first and second state, the asymmetry coefficient (gamma) is positive for all currencies.
Keywords: Cryptocurrencies; GARCH; Markov-switching model; Volatility.
Post Global Financial Crisis Modelling: Credit Risk For Firms That Are Too Big To Fail
by Ephraim Clark, Sovan Mitra, Octave Jokung
Abstract: rnSince the start of the Global Financial Crisis the validity of all financial models have come under serious questioning, with firms that are `too big to fail' being frequently discussed in the media. Such firms are systemically too important to the economy to allow them to fail, as well as posing significant contagion risk. In such firms, the standard credit risk models are not sufficient because systemically important firms do not default under standard circumstances. In fact it was frequently observed during the Global Financial Crisis that such firms were able to continue borrowing when other firms would normally default.rnrnrnIn this paper we propose a new model for credit risk for firms that are too big to fail. We propose a structural model of credit risk but model credit risk as a real option. We derive a closed form solution for the option to default and take into account the borrowing practices of systemically important firms. We develop our model to take into account economic factors using regime switching, and derive an option pricing solution under such a process. Finally we obtain solutions for hedging the option to default, which takes into account the market incompleteness of such options. We conduct numerical experiments to calculate the option to default at different debt values and volatility.
Keywords: credit risk; real options; too big to fail; financial crisis; hedging.