Market Price of Longevity Risk for a Multi-Cohort Mortality Model with Application to Longevity Bond Option Pricing

2018 ◽  
Author(s):  
Michael Sherris ◽  
Yajing Xu ◽  
Jonathan Ziveyi
Keyword(s):  
Option Pricing ◽  
Market Price ◽  
Longevity Risk ◽  
Mortality Model ◽  
Bond Option

scholarly journals Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Motlatsi Molati
Keyword(s):  
Option Pricing ◽  
Three Dimensional ◽  
Mathematical Finance ◽  
Group Classification ◽  
Lie Point Symmetries ◽  
Group Invariant ◽  
Black Scholes ◽  
Group Invariant Solutions ◽  
Bond Option

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

scholarly journals Maximum Market Price of Longevity Risk Under Solvency Regimes: The Case Of Solvency II

2017 ◽  
Author(s):  
Susanna Levantesi ◽  
Massimiliano Menzietti
Keyword(s):  
Market Price ◽  
Solvency Ii ◽  
Insurance Companies ◽  
Longevity Risk ◽  
Risk Margin ◽  
Maximum Price ◽  
Upper Limits ◽  
Forward Prices ◽  
Pricing Measure ◽  
Solvency Regimes

Longevity risk constitutes an important risk factor for life insurance companies and it can be managed through longevity-linked securities. The market of longevity-linked securities is at present far from being complete and does not allow to find a unique pricing measure. We propose a method to estimate the maximum market price of longevity risk depending on the risk margin implicit within the calculation of the technical provisions as defined by Solvency II. The maximum price of longevity risk is determined for a survivor forward (S-forward), an agreement between two counterparties to exchange at maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. The maximum prices determined for the S-forwards can be used to price other longevity-linked securities, such as q-forwards. The Cairns-Blake-Dowd model is used to represent the evolution of mortality over time, that combined with the information on the risk margin, enables us to calculate upper limits for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical results can be extended for the pricing of other longevity-linked securities.

scholarly journals A Study of Black–Scholes Model’s Applicability in Indian Capital Markets

Paradigm ◽  
2020 ◽  
Vol 24 (1) ◽  
pp. 73-92
Author(s):  
Anubha Srivastava ◽  
Manjula Shastri
Keyword(s):  
Stock Market ◽  
Option Pricing ◽  
Trading Volume ◽  
Stock Exchange ◽  
Market Price ◽  
Significant Degree ◽  
Pricing Model ◽  
Fair Price ◽  
Black Scholes ◽  
Indian Stock Market

Derivative trading, started in mid-2000, has become an integral and significant part of Indian stock market. The tremendous increase in trading volume in Indian stock market has reflected into high volatility in the option prices. The pricing of options is very complex aspect of applied finance and has been subject of extensive research. Black–Scholes option model is a scientific pricing model which is applied for determining the fair price for option contracts. This article examines if Black–Scholes option pricing model (BSOPM) is a good indicator of option pricing in Indian context. The literature review highlights that various studies have been conducted on BSOPM in various stock exchange across the world with mixed outcome on its relevance and applicability. This article is an empirical study to test the relevance of BSOPM for which 10 most popular industry’s stock listed on National Stock Exchange have been taken. Then the BSOPM has been applied using volatility and risk-free rate. Furthermore, t-test has been used to test the hypothesis and determine the significant relationship between BS model values and actual model values. This study concludes that BSOPM involves significant degree of mispricing. Hence, this model alone cannot be adopted as an indicator for option pricing. The variation from market price is synchronised with respect to moneyness and time to maturity of the option.

A new method to solve fuzzy stochastic finance problem

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jayanta Kumar Dash ◽  
Sumitra Panda ◽  
Golak Bihari Panda
Keyword(s):  
Option Pricing ◽  
Market Price ◽  
Pricing Model ◽  
Strike Price ◽  
Content Type ◽  
Fuzzy Environment ◽  
Black Scholes ◽  
Option Pricing Model ◽  
A New Technique ◽  
Log Normal

PurposeThe authors discuss the value of portfolio and Black–Scholes (B–S)-option pricing model in fuzzy environment.Design/methodology/approachThe B–S option pricing model (OPM) is an important role of an OPM in finance. Here, every decision is taken under uncertainty. Due to randomness or vagueness, these uncertainties may be random or fuzzy or both. As the drift µ, the degree of volatility s, interest rate r, strike price k and other parameters of the value of the portfolio V(t), market price S_0 (t) and call option C(t) are not known exactly, so they are treated as positive fuzzy number. Partial expectation of fuzzy log normal distribution is derived. Also the value of portfolio at any time t and the B–S OPM in fuzzy environment are derived. A numerical example of B–S OPM is illustrated.FindingsFirst, the authors are studying some various paper and some stochastic books.Originality/valueThis is a new technique.

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