Between ℙ and ℚ: The ℙℚ Measure for Pricing in Asset Liability Management
Ortec Finance, 3011 XB Rotterdam, The Netherlands
DIAM—Delft Institute of Applied Mathematics, Delft University of Technology, 2628 CD Delft, The Netherlands
CWI—The Center for Mathematics and Computer Science, 1098 XG Amsterdam, The Netherlands
Author to whom correspondence should be addressed.
Received: 17 September 2018 / Revised: 18 October 2018 / Accepted: 21 October 2018 / Published: 24 October 2018
Insurance companies issue guarantees that need to be valued according to the market expectations. By calibrating option pricing models to the available implied volatility surfaces, one deals with the so-called risk-neutral measure
, which can be used to generate market consistent values for these guarantees. For asset liability management, insurers also need future values of these guarantees. Next to that, new regulations require insurance companies to value their positions on a one-year horizon. As the option prices at
are unknown, it is common practice to assume that the parameters of these option pricing models are constant, i.e., the calibrated parameters from time
are also used to value the guarantees at
. However, it is well-known that the parameters are not constant and may depend on the state of the market which evolves under the real-world measure
. In this paper, we propose improved regression models that, given a set of market variables such as the VIX index and risk-free interest rates, estimate the calibrated parameters. When the market variables are included in a real-world simulation, one is able to assess the calibrated parameters (and consequently the implied volatility surface) in line with the simulated state of the market. By performing a regression, we are able to predict
out-of-sample implied volatility surfaces accurately. Moreover, the impact on the Solvency Capital Requirement
has been evaluated for different points in time. The impact depends on the initial state of the market and may vary between −46% and +52%.
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Van Dijk, M.T.P.; De Graaf, C.S.L.; Oosterlee, C.W. Between ℙ and ℚ: The ℙℚ Measure for Pricing in Asset Liability Management. J. Risk Financial Manag. 2018, 11, 67.
Van Dijk MTP, De Graaf CSL, Oosterlee CW. Between ℙ and ℚ: The ℙℚ Measure for Pricing in Asset Liability Management. Journal of Risk and Financial Management. 2018; 11(4):67.
Van Dijk, Marcel T.P.; De Graaf, Cornelis S.L.; Oosterlee, Cornelis W. 2018. "Between ℙ and ℚ: The ℙℚ Measure for Pricing in Asset Liability Management." J. Risk Financial Manag. 11, no. 4: 67.
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