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DemoTSMC

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Returns a vector using tri-segmented Monte Carlo (TSMC) that contains three entries: Portfolio Value, Quantile and Control Variate Variance Ratio.

 

This function provides a simplified demonstration of the usefulness of tri-segmented Monte Carlo for valuing portfolios of assets and liabilities and for calculating associated risk measures of these portfolios

 

For further details of TSMC, see Efficient Monte Carlo simulation of portfolio value, value-at-risk and other portfolio metrics or speak to your contact at Nematrian. Instead of applying all simulations to a portfolio of exposures, the simulations are split into 3 subsets, (1) an “underlying”, (2) an “added” and (3) an “extended” simulation set. The extended set is usually by far the largest of these three sets. Only the underlying and added sets are actually applied to the portfolio; the extended set is instead applied to only to a fast to evaluate approximation derived principally from the underlying simulation set. The added simulation set helps to correct for inaccuracies in this approximation.

 

The demonstration of TSMC provided by MnDemoTSMC assumes a portfolio of 40 instruments which have specified strikes, , and terms,  (see MnDemoTSMCStrikes and MnDemoTSMCTerms for details) and relate to one of two specified indices,  (see MnDemoTSMCUnderlyings for details). We use  to represent the value of the ’th index at time . Each instrument is a European-style call option so has payoff equal to . Instrument terms are all 1, 2, 3, 4 or 5 years. Users can select the position sizes, i.e. PosSizes to apply to the portfolio.

 

The two indices are assumed to follow independent log-normal (Brownian) motions with (constant) annualised volatilities (cumulatively compounded) specified by the two entries of ImpliedVolatilities. It is assumed that interest rates are zero at all times, making it practical to value each instrument analytically using a Nematrian web function call along the line of:

 

PosSizes(i) * MnBSCall(K(i), 1, 0, 0, 0, T(i), ImpliedVolatilities(U(i)))

 

Please note:

 

(a)    BaseSimulationsUandA: needs to be of size (nUnderlying + nAdded) x 10 (i.e. 10 for each simulation, these corresponding to log returns in years 1-5 for first index and to log returns in years 1-5 for the second index respectively

(b)    SimulationValuesUandA: needs to be of size (nUnderlying + nAdded)

(c)     DistanceScaling: this array defines the weights to give to different dimensions in the calculation of the distance between two different points in the underlying 10-dimensional space

(d)    This function is designed to provide a simple demonstration of tri-segmented Monte Carlo. It therefore only considers “run-off” VaRs/quantiles and does not aim to demonstrate other elements of Nematrian’s full tri-segmented Monte Carlo engine such as 1-year / nested VaR calculations and use of importance sampling.

 

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-          Interactively run function

-          Interactive instructions

-          Example calculation

-          Output type / Parameter details

-          Illustrative spreadsheet

-          Other Tri-segmented Monte Carlo Demonstration functions

-          Computation units used

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