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Calculating the Monthly Annuity
Calculating the Time to Maturity
Results - Monthly Annuity
Results - Time to maturity
(months)

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The share simulator creates sample paths of stochastic processes commonly used to model the share price development. The classical model was examined by Black and Scholes in order to evaluate derivatives.

There exists a diversity of tailored models of the Black Scholes model. The Heston- and the Merton Jump-Diffusion model are two of them.

Black Scholes Model Heston Model Jump-Diffusion Model

Black Scholes Model

In this model the stochastic process is a geometric Brownian motion.

Basic Share Data
Drift Volatility
Initial Value Time (years)
Indications
Show moving average Show confidence level
In days: Probability:
Show expectation Show median
Estimation using Historical data
Show drift and vol Over days:
Extended Configuration
No of realisations:
Image size x: Image size y:
Initialize random no generator with number:
Calculate
Results

Heston Model

This model is based on the Black Scholes Model but with the assumption that the square volatility is a stochastic process itself. The square of volatility is assumed to be a so called Cox-Ingersoll-Ross mean reversion process, i.e. a process which is fluctuating about a mean value.

More details about this process and ways to price derivatives with this model can be found on the homepage of Gunter Winkler and in the formula catalogue.

Jump-Diffusion Model

This model is based on the Black Scholes Model with an additional jump process. The time gap between two jumps are exponentially distributed and the hight of each jump is proportional to the current share price and to a lognormal distributed random variable.

More details about this process and a discussion of anti trend strategies in this model can be found on the homepage of Dana Uhlig-Düvelmeyer (in German only).

This calculator simulates a saving plan, where the paid capital is guaranteed at time of retirement, in the Germany market available as Riester-Rente and supported by federal bonus payments and tax benefits.

It is possible to select different capital guarantee mechanisms:

  • The return distribution of a Classical Insurance Strategy with investments in the actuarial reserve fund
  • CPPI strategy
  • Stop Loss strategy

The federal bonus payments are calculated based on your personal situation (income, children).

To model the distribution we use a jump diffusion model parameterized to resemble the MSCI World index and a Hull White generalized Vasicek Model, calibrated to the current yield curve, for the interest rate process.
It can also be analyzed how fee structures typically included in these products affect the performance of these savings plans.

See Pdf (German Version) | See Pdf (English Version)

Model Parameters If you need a more detailed analysis of a certain contract with fee structure and/or guarantee mechanism not provided here or different modeling assumptions please contact us. We can provide this as a consultancy service!

Inputs


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Federal bonus payments are dependent on the date of birth. We assume that they are paid up to the age of 23 years.
Fee Structure
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These costs are charged to pay a sales fee for the agent who closed the deal with the insured. These fees are dependent on the total cash contracted to pay into the contract until maturity. They are charged uniformly distributed over the first 5 years of the contract.
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These fees are assumed to be charged on the cash payments by the client to the contract during the entire lifetime of the contract.
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These fees are assumed to be charged on the federal bonus payments to the contract during the entire lifetime of the contract.
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Yearly fee independent on cash payments and the account value.
Strategy
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Fee equity:
Annual fee charged for the management of the equity fund, as a percentage of its value

Outperformance equity: Expected outperformance of the fund above benchmark (simulation assumption 6% annual equity return)
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Fee fixed income:
Annual fee, charged for the management of the fixed income fund, as a percentage of its value

Outperformance fixed income: Expected outperformance of the fund above benchmark (annual return implied by current zero bond curve)
Calculate

Model Parameters Model Parameters

Model Parameters:
Equity process
Total volatility 14.3%
Volatility of the diffusion part 11.69%
Jump intensity 5.209
Minimum jump size 2.31%
Expected jump size above minimum jump size 1.121%
Equity annual return 6%

Interest rate process
Mean reversion rate 0.1%
Volatility 0.01%

Additional Simulation assumptions
Guarantee rate of life insurance 2.25%
Inflation rate 2%

Results