scholarly journals Pricing Stock Loans with the CGMY Model

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Congyin Fan ◽  
Chunhao Zhou
Keyword(s):  
Stock Price ◽  
Asymmetric Distribution ◽  
Pricing Model ◽  
Fractional Partial Differential Equation ◽  
Penalty Term ◽  
First Order ◽  
Fully Implicit ◽  
Condition Problem ◽  
Implicit Difference Schemes ◽  
Stock Loan

The empirical research shows that the log-return of stock price in finance market rejects the normal distribution and admits a subclass of the asymmetric distribution. Hence, the pricing problem of stock loan is investigated under the assumption that the log-return of stock price follows the CGMY process in this work. Under this framework, the pricing model of stock loan can be described by a free boundary condition problem of space-fractional partial differential equation (FPDE). First of all, in order to change the original model defined in a fixed domain, a penalty term is introduced, and then a first order fully implicit difference schemes is developed. Secondly, based on the numerical scheme, we prove the stock loan value generated by our method does not fall below the value obtained when the contract of stock loan is exercised early. Finally, the numerical experiments are implemented and the impacts of key parameters in the CGMY model on the value and optimal redemption price of stock loan are analyzed, and some reasonable explanation should be given.

scholarly journals Pricing of Margin Call Stock Loan Based on the FMLS

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Kaili Xiang ◽  
Peng Hu ◽  
Xiao Li
Keyword(s):  
Free Boundary ◽  
Normal Distribution ◽  
Stock Price ◽  
Empirical Test ◽  
Stable Process ◽  
Standard Normal Distribution ◽  
Asymmetric Distribution ◽  
Finite Moment ◽  
The Impact ◽  
Stock Loan

In common stock loan, lenders face the risk that their loans will not be repaid if the stock price falls below loan, which limits the issuance and circulation of stock loans. The empirical test suggests that the log-return series of stock price in the US market reject the normal distribution and admit instead a subclass of the asymmetric distribution. In this paper, we investigate the model of the margin call stock loan problem under the assumption that the return of stock follows the finite moment log-stable process (FMLS). In this case, the pricing model of the margin call stock loan can be described by a space-fractional partial differential equation with a time-varying free boundary condition. We transform the free boundary problem to a linear complementarity problem, and the fully-implicit finite difference method that we used is unconditionally stable in both the integer and fractional order. The numerical experiments are carried out to demonstrate differences of the margin call stock loan model under the FMLS and the standard normal distribution. Last, we analyze the impact of key parameters in our model on the margin call stock loan evaluation and give some reasonable explanation.

scholarly journals Estimasi Bullish dan Bearish dengan Model Perpindahan Markov dan Risiko Sistematis (beta) dengan Model Penilaian Modal Sharpe dalam Investasi Saham di Bursa Efek Indonesia, Tahun 2011 - 2016

2018 ◽  
Vol 8 (3) ◽  
pp. 221
Author(s):  
Prima Respati ◽  
Budi Purwanto ◽  
Abdul Kohar Irwanto
Keyword(s):  
Interest Rates ◽  
Capital Market ◽  
Stock Price ◽  
Markov Switching ◽  
Systematic Risk ◽  
Risk Identification ◽  
Pricing Model ◽  
Markov Switching Model ◽  
Switching Model ◽  
Capital Assets

<p><em>ABSTRACT</em></p><p><em>Various research including Panggabean (2010) and Usman (2016) show that the long-term trend of Indonesia's capital market is on an uptrend, marked by more bullish periods and longer duration than bearish; and the development determined by rising rates of return rather than interest rates and exchange rates (Defrizal et al, 2015). However, the research has not determined yet whether there are any difference risks in bullish and bearish conditions, especially for systematic or market risk. This study aims to 1) identify the bullish and bearish segmentation period using the Markov Switching Model, and 2) measure systematic risk using the capital assets pricing model (CAPM) with the Sharpe beta indicator. Using the composite stock price index (JCI) and trading data from TICMI (The Indonesia Capital Market Institute) period 2011-2016, consists of 560 issuers, it was found that there were 10 segments that could be identified as 5 bullish periods for 30 weeks , and 5 bearish periods for 8 weeks. Other finding indicates that the probability of switching from bullish to bearish is 3.33% and from bearish to bullish is 12.14%. That means there are positive sentiments that the market tends to be bullish rather than vice versa. The result of beta or systematic risk identification indicates that during bullish and bearish period the market proved to be different risk. Other interesting findings, in both these two different conditions there are negative betas exist that still gives a positive yield.</em></p><p> </p><p>ABSTRAK</p><p>Berbagai riset termasuk Panggabean (2010) dan Usman (2016) menunjukkan bahwa kecenderungan jangka panjang pasar modal Indonesia berada pada kecenderungan naik (uptrend), ditandai dengan periode bullish lebih banyak, dan durasi lebih panjang, daripada bearish.  Perkembangan perkembangan itu dipicu oleh kenaikan tingkat imbalan, alih-alih suku bunga dan nilai tukar (Defrizal et al 2015). Namun riset-riset tersebut tidak mengidentifikasi eksistensi kondisi bullish dan bearish dan berdampak perbedaan risiko, terutama risiko sistematis atau risiko pasar, kecuali mengasumsikan saja keberadaannya.  Penelitian ini bertujuan 1) mengidentifikasi segmentasi periode bullish dan bearish dengan menggunakan model perpindahan Markov (Markov Switching), dan mengukur risiko sistematis menggunakan model penilaian modal (capital assets pricing model, CAPM) dengan indikator beta Sharpe.  Menggunakan data indeks harga saham gabungan (IHSG) serta data perdagangan bersumber dari TICMI (The Indonesia Capital Market Institute) periode 2011-2016 yang mencakup 560 emiten, diperoleh hasil bahwa dalam periode tersebut terdapat 10 segmen yang dapat diidentifikasi sebagai 5 periode bullish selama 30 pekan, dan 5 periode bearish selama 8 pekan.  Temuan lain menunjukkan bahwa peluang perpindahan dari kondisi bullish ke bearish sebesar 3,33% dan dari kondisi bearish ke bullish sebesar 12,14%. Artinya terdapat sentimen positif bahwa pasar cenderung menjadi bullish daripada sebaliknya.  Hasil identifikasi risiko sistematis menunjukkan, berbeda dengan konsep dasar CAPM, bahwa beta pada periode bullish dan bearish tidak sama.  Temuan menarik lainnya, pada kedua kondisi tersebut terdapat beta negatif yang dapat memberikan tingat imbalan positif.</p>

scholarly journals Good Volatility, Bad Volatility, and Option Pricing

2018 ◽  
Vol 54 (2) ◽  
pp. 695-727 ◽  
Author(s):  
Bruno Feunou ◽  
Cédric Okou
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Asset Price ◽  
Jump Diffusion ◽  
Quadratic Variation ◽  
Pricing Model ◽  
Economic Gain ◽  
Underlying Asset ◽  
Model Free ◽  
Option Pricing Model

Advances in variance analysis permit the splitting of the total quadratic variation of a jump-diffusion process into upside and downside components. Recent studies establish that this decomposition enhances volatility predictions and highlight the upside/downside variance spread as a driver of the asymmetry in stock price distributions. To appraise the economic gain of this decomposition, we design a new and flexible option pricing model in which the underlying asset price exhibits distinct upside and downside semivariance dynamics driven by the model-free proxies of the variances. The new model outperforms common benchmarks, especially the alternative that splits the quadratic variation into diffusive and jump components.

ORDER AND CONVERGENCE OF THE ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING INITIAL VALUE PROBLEM

2021 ◽  
Vol 5 (2) ◽  
pp. 442-446
Author(s):  
Muhammad Abdullahi ◽  
Hamisu Musa
Keyword(s):  
Initial Value Problem ◽  
Initial Value Problems ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Differentiation Formula ◽  
Stiff Initial Value Problems ◽  
First Order ◽  
Backward Differentiation Formula ◽  
Fully Implicit ◽  
Necessary And Sufficient

This paper studied an enhanced 3-point fully implicit super class of block backward differentiation formula for solving stiff initial value problems developed by Abdullahi & Musa and go further to established the necessary and sufficient conditions for the convergence of the method. The method is zero stable, A-stable and it is of order 5. The method is found to be suitable for solving first order stiff initial value problems

Predicting the stock price of frontier markets using machine learning and modified Black–Scholes Option pricing model

2020 ◽  
Vol 555 ◽  
pp. 124444 ◽  
Author(s):  
Reaz Chowdhury ◽  
M.R.C. Mahdy ◽  
Tanisha Nourin Alam ◽  
Golam Dastegir Al Quaderi ◽  
M. Arifur Rahman
Keyword(s):  
Machine Learning ◽  
Option Pricing ◽  
Stock Price ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model

Dynamic Pricing Model of Power Options in a Fractional Market

2011 ◽  
Vol 225-226 ◽  
pp. 338-341
Author(s):  
Hui Zhang ◽  
Wen Yu Meng
Keyword(s):  
Option Pricing ◽  
Dynamic Pricing ◽  
Stock Price ◽  
Risk Preference ◽  
Conditional Density ◽  
Hurst Parameter ◽  
Pricing Model ◽  
Conditional Density Function ◽  
Price Process ◽  
Random Events

In this paper, we study the new method of option pricing based on the risk preference. We define the equivalent classes of random events based on the historical information and the risk preference. The dynamic pricing model of power options has been studied. Applying the conditional density function of the stock price process, we have given the explicit solution of the model. And we analyze the influence of Hurst parameter on pricing formula.

INELASTIC INTERACTION OF BOUSSINESQ SOLITONS

1994 ◽  
Vol 04 (05) ◽  
pp. 1095-1112 ◽  
Author(s):  
C.I. CHRISTOV ◽  
M.G. VELARDE
Keyword(s):  
Boussinesq Equation ◽  
Blow Up ◽  
Quantitative Agreement ◽  
Inelastic Interaction ◽  
Wave System ◽  
Residual Signal ◽  
Fully Implicit ◽  
Regularized Long Wave Equation ◽  
Implicit Difference Schemes ◽  
Negative Surface

Two improved versions of Boussinesq equation (Boussinesq paradigm) have been considered which are well-posed (correct in the sense of Hadamard) as an initial value problem: the Proper Boussinesq Equation (PBE) and the Regularized Long Wave Equation (RLWE). Fully implicit difference schemes have been developed strictly representing, on difference level, the conservation or balance laws for the mass, pseudoenergy or pseudomomentum of the wave system. Thresholds of possible nonlinear blow-up are identified for both PBE and RLWE. The head-on collisions of solitary waves of the sech type (Boussinesq solitons) have been investigated. They are subsonic and negative (surface depressions) for PBE and supersonic and positive (surface elevations) for RLWE. The numerically recovered sign and sizes of the phase shifts are in very good quantitative agreement with analytical results for the two-soliton solution of PBE. The subsonic surface elevations are found to be not permanent but to gradually transform into oscillatory pulses whose support increases and amplitude decreases with time although the total pseudoenergy is conserved within 10−10. The latter allows us to claim that the pulses are solitons despite their “aging” (which is felt on times several times the time-scale of collision). For supersonic phase speeds, the collision of Boussinesq solitons has inelastic character exhibiting not only a significant phase shift but also a residual signal of sizable amplitude but negligible pseudoenergy. The evolution of the residual signal is investigated numerically for very long times.

scholarly journals Valuing Coca-Cola And PepsiCo Options Using The Black-Scholes Option Pricing Model And Data Downloads From The Internet

2012 ◽  
Vol 8 (6) ◽  
pp. 559-564
Author(s):  
John C. Gardner ◽  
Carl B. McGowan Jr
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Option Price ◽  
Option Prices ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Risk Free Rate ◽  
Daily Returns ◽  
Free Rate

In this paper, we demonstrate how to collect the data and compute the actual value of Black-Scholes Option Pricing Model call option prices for Coca-Cola and PepsiCo.The data for the current stock price and option price are taken from Yahoo Finance and the daily returns variance is computed from daily prices.The time to maturity is computed as the number of days remaining for the stock option.The risk-free rate is obtained from the U.S. Treasury website.

Estimasi Bullish dan Bearish dengan Model Perpindahan Markov dan Risiko Sistematis (beta) dengan Model Penilaian Modal Sharpe dalam Investasi Saham di Bursa Efek Indonesia, Tahun 2011 - 2016

2018 ◽  
Vol 8 (3) ◽  
pp. 221
Author(s):  
Prima Respati ◽  
Budi Purwanto ◽  
Abdul Kohar Irwanto
Keyword(s):  
Interest Rates ◽  
Capital Market ◽  
Stock Price ◽  
Markov Switching ◽  
Systematic Risk ◽  
Risk Identification ◽  
Pricing Model ◽  
Markov Switching Model ◽  
Switching Model ◽  
Capital Assets

<p><em>ABSTRACT</em></p><p><em>Various research including Panggabean (2010) and Usman (2016) show that the long-term trend of Indonesia's capital market is on an uptrend, marked by more bullish periods and longer duration than bearish; and the development determined by rising rates of return rather than interest rates and exchange rates (Defrizal et al, 2015). However, the research has not determined yet whether there are any difference risks in bullish and bearish conditions, especially for systematic or market risk. This study aims to 1) identify the bullish and bearish segmentation period using the Markov Switching Model, and 2) measure systematic risk using the capital assets pricing model (CAPM) with the Sharpe beta indicator. Using the composite stock price index (JCI) and trading data from TICMI (The Indonesia Capital Market Institute) period 2011-2016, consists of 560 issuers, it was found that there were 10 segments that could be identified as 5 bullish periods for 30 weeks , and 5 bearish periods for 8 weeks. Other finding indicates that the probability of switching from bullish to bearish is 3.33% and from bearish to bullish is 12.14%. That means there are positive sentiments that the market tends to be bullish rather than vice versa. The result of beta or systematic risk identification indicates that during bullish and bearish period the market proved to be different risk. Other interesting findings, in both these two different conditions there are negative betas exist that still gives a positive yield.</em></p><p><em><br /></em></p><p>ABSTRAK</p><p>Berbagai riset termasuk Panggabean (2010) dan Usman (2016) menunjukkan bahwa kecenderungan jangka panjang pasar modal Indonesia berada pada kecenderungan naik (uptrend), ditandai dengan periode bullish lebih banyak, dan durasi lebih panjang, daripada bearish.  Perkembangan perkembangan itu dipicu oleh kenaikan tingkat imbalan, alih-alih suku bunga dan nilai tukar (Defrizal et al 2015). Namun riset-riset tersebut tidak mengidentifikasi eksistensi kondisi bullish dan bearish dan berdampak perbedaan risiko, terutama risiko sistematis atau risiko pasar, kecuali mengasumsikan saja keberadaannya.  Penelitian ini bertujuan 1) mengidentifikasi segmentasi periode bullish dan bearish dengan menggunakan model perpindahan Markov (Markov Switching), dan mengukur risiko sistematis menggunakan model penilaian modal (capital assets pricing model, CAPM) dengan indikator beta Sharpe.  Menggunakan data indeks harga saham gabungan (IHSG) serta data perdagangan bersumber dari TICMI (The Indonesia Capital Market Institute) periode 2011-2016 yang mencakup 560 emiten, diperoleh hasil bahwa dalam periode tersebut terdapat 10 segmen yang dapat diidentifikasi sebagai 5 periode bullish selama 30 pekan, dan 5 periode bearish selama 8 pekan.  Temuan lain menunjukkan bahwa peluang perpindahan dari kondisi bullish ke bearish sebesar 3,33% dan dari kondisi bearish ke bullish sebesar 12,14%. Artinya terdapat sentimen positif bahwa pasar cenderung menjadi bullish daripada sebaliknya.  Hasil identifikasi risiko sistematis menunjukkan, berbeda dengan konsep dasar CAPM, bahwa beta pada periode bullish dan bearish tidak sama.  Temuan menarik lainnya, pada kedua kondisi tersebut terdapat beta negatif yang dapat memberikan tingat imbalan positif.</p>

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