Feeding back about eco-feedback: How do consumers use and respond to energy monitors?

This paper analyzes a life insurance endowment policy, paid by annual premiums, in which the benefit is annually adjusted according to the performance of a special investment portfolio and a minimum return is guaranteed to the policyholder. In particular, the author considers both the case in which the annual premium is constant and the case in which the premium also is adjusted according to the performance of the reference portfolio. Moreover, the policy under scrutiny is characterized by the presence of a surrender option, that is, of an American-style put option that enables the policyholder to give up the contract and receive the surrender value. The aim of the paper is to give sufficient conditions under which there exists a (unique) fair premium. This premium is implicitly defined by an equation (or, alternatively, can be viewed as a fixed point of a suitable function) based on a recursive binomial tree ala Cox, Ross, and Rubinstein (1979). An iterative algorithm is then implemented in orde...

http://www.ressources-actuarielles.net/EXT/ISFA/1226.nsf/9c8e3fd4d8874d60c1257052003eced6/288763214b33b405c1256d4100267a28/$FILE/Bacinello.pdf

Pricing Guaranteed Life Insurance Participating Policies with Annual Premiums and Surrender Option

We recommend the addition of a deterministic displacement to multi-factor affine models to calibrate and hedge SPX and VIX derivatives jointly. The proposed model, labeled Heston++, calibrates both markets with an average relative error (on quoted implied volatilities over two years of data) of 2%, and a maximum relative error of 4%, without additional computational costs with respect to traditional affine benchmarks. Hedging performance on both markets is also drastically improved. The displacement can be interpreted as a volatility push-up reflecting expectations about a (risk-neutral) lower bound on forward VIX dynamics. Our empirical results document substantial correlation between the dynamics of the displacement and the variance risk premium, and still provide strong support for the presence of both price/volatility negatively correlated co-jumps and idiosyncratic jumps in the volatility dynamics, even when the displacement is added.

Smiling twice: The Heston++ model

A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al [Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives, 2011, Cambridge University Press] to derive a first-order approximation of the price of options on a stock and its volatility index. This approximation is given by Heston’s quasi-closed formula and some of its Greeks. It can be efficiently calculated since it requires to compute only Fourier integrals and the solution of simple ODE systems. We exemplify the calibration of the model with S&P 500 and VIX data.

Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options

Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may not be possible to calibrate jointly these two quantities with a model with continuous sample-paths. We present the quadratic rough Heston model as a counterexample to this conjecture. The key idea is the combination of rough volatility together with a price-feedback (Zumbach) effect.

The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem

This technical report illustrates the basic principles for a fair valuation system in life insurance. The report is particularly concerned with the market consistent derivation of the Value of Business In Force (VBIF) for portfolios of profit-sharing policies, properly allowing for the cost of the embedded options and guarantees, according to the European Embedded Value Principles (EEVP) stated by the CFO Forum. Some relevant issues concerning the practical utilization of the system and the consistent interpretation of the results are illustrated by numerical examples. Particular attention has been paid to the harmonization with the results provided by more traditional valuation methods. The report is concluded by a description of some relevant details concerning the application of the valuation system to the life portfolios of the RAS Group.Results - The value of business in force (VBIF), the value of the minimum guaranteed return options (the put component of VBIF), the time value of the puts, the expected returns of the segregated funds and other quantities useful for controlling price and risk of the asset-liability portfolios are derived. Theoretical and practical issues are discussed concerning the theory of valuation, the market consistent pricing, the finance of insurance.The valuation procedure - The outstanding portfolios are analysed in the framework of the asset-liabilty valuation under uncertainty. The valuation of the financial components of future profits, as well as of the embedded options, is performed using a stochastic pricing model based on the no-arbitrage principle. The model is calibrated on market data, in order to capture the current interest rate levels, the interest rate volatilities, the stock price volatilities and correlations.In the valuation procedure closed form pricing expressions as well as Monte Carlo simulations are used. The accounting rules defining the segregated fund returns are allowed for. Financial uncertainty is analysed by modelling interest rate risk for each relevant currency, stock price risk, credit risk. Technical uncertainty is measured taking into account mortality/longevity risk, surrender risk, expenses inflation risk.Harmonization - Using the valuation system a logical connection can be created between the traditional approach - based on a single "best estimate" scenario - and the stochastic valuation model, specified under both the risk-neutral and the real world probabilities. Financial and technical risks, as well as the cost of the embedded options, are measured in terms of value (risk premiums and/or additional costs) and in terms of risk discount spread (discount rate margins).

http://mmenzietti.altervista.org/TAAV/Corso_AASNS_II.pdf

Embedded Value in Life Insurance

We recommend the addition of a deterministic displacement to multi-factor affine models to calibrate vanilla options on S&P500 and VIX derivatives jointly. The proposed model, labeled Heston , calibrates both markets with an average relative error (on quoted implied volatilities over two years of data) of 2%, and a maximum relative error of 4%, without additional computational costs with respect to traditional affine benchmarks. Our empirical results also provide strong support for the presence of both price/volatility negatively correlated co-jumps and idiosyncratic jumps in the volatility dynamics.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID2700977_code261637.pdf?abstractid=2697179&mirid=1&type=2

Smiling Twice: The Hestonpp Model

Heston model: shifting on the volatility surface

Valutazione di portafogli di polizze vita con rivalutazione agli ennesimi

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