Tenokonda Scenario Engine allows for random variables and processes modeling and simulation. Its role is fundamental in risk analysis as joint risk factors simulation allows in turn estimating tail metrics such as value at risk or expected shortfall.
Features
Time series preprocessing: aligning dates and filling gaps
Probability distributions sampling.
Stochastic processes simulation.
External random number generation.
Distribution lower and/or upper bound truncation.
Joint distribution/process sampling through variance-covariance.
Joint distribution/process sampling through copulas.
Distributions covered
Discrete, categorical, binomial, geometric, hypergeometric, logseries, multinomial, negative binomial, Poisson, zipf
Continuous beta, Cauchy, chi square, Dirichlet, exponential, f, gamma, Gumbel, Laplace, logistic, lognormal, non central chi square, non central f, normal, normal multivariate, Pareto, power, Rayleigh, t, triangular, uniform, Von Mises, Wald, Weibull
Stochastic Processes covered
Black Karazinski.
Brownian Motion.
Exponential Brownian Motion.
Geometric Brownian Motion.
Hybrid.
Normal Increments.
Ornstein Uhlenbeck.
References
- Drake, A. Fundamentals of Applied Probability Theory. New York, NY: McGraw-Hill, 1988.
- Rice, John A. Mathematical Statistics and Data Analysis. Duxbury Press, 2006.
- Karatzas, Ioannis and Steven, Shreve. Brownian Motion and Stochastic Calculus. 2nd ed. Springer-Verlag, 1991.
- Øksendal, B. Stochastic Differential Equations: An Introduction with Applications. Springer, 2010.
- Roger B. Nelsen (1999), 'An Introduction to Copulas', Springer.
- Abe Sklar (1997): 'Random variables, distribution functions, and copulas – a personal look backward and forward' in Rüschendorf, L., Schweizer, B. und Taylor, M. (eds) Distributions With Fixed Marginals & Related Topics
- Kiyosi Itô (1951). On stochastic differential equations. Memoirs, American Mathematical Society 4, 1–51.
- Black, F.; Karasinski, P. (July–August 1991). 'Bond and Option pricing when Short rates are Lognormal'. Financial Analysts Journal: 52–59.
- Uhlenbeck, G. E.; Ornstein, L. S. (1930). 'On the theory of Brownian Motion'. Phys. Rev. 36 (5): 823–841.
