PRICING OPTIONS UNDER STOCHASTIC INTEREST RATE AND THE FRASCA–FARINA PROCESS: A SIMPLE, EXPLICIT FORMULA

2021 ◽  
pp. 2150003
Author(s):  
MOAWIA ALGHALITH
Keyword(s):  
Interest Rate ◽  
Simple Formula ◽  
Stochastic Interest Rate ◽  
European Options ◽  
Pricing Options ◽  
Black Scholes Model ◽  
Stochastic Interest ◽  
Black Scholes ◽  
Practical Complexity ◽  
Theoretical Limitation

Assuming a stochastic interest rate, we introduce a simple formula for pricing European options. In doing so, we provide a complete closed-form formula that does not require any numerical/computational methods. Furthermore, the model and formula are far simpler than the previous models/formulas. Our formula is as simple as the classical Black–Scholes pricing formula. Moreover, it removes the theoretical limitation of the original Black–Scholes model without any added practical complexity.

scholarly journals TAXATION OF A GMWB VARIABLE ANNUITY IN A STOCHASTIC INTEREST RATE MODEL

2020 ◽  
Vol 50 (3) ◽  
pp. 1001-1035
Author(s):  
Andrea Molent
Keyword(s):  
Interest Rate ◽  
Fair Value ◽  
Stochastic Interest Rate ◽  
Financial Evaluation ◽  
Financial Cost ◽  
Stochastic Interest ◽  
Black Scholes ◽  
Interest Rate Model ◽  
The Cost

AbstractModeling taxation of Variable Annuities has been frequently neglected, but accounting for it can significantly improve the explanation of the withdrawal dynamics and lead to a better modeling of the financial cost of these insurance products. The importance of including a model for taxation has first been observed by Moenig and Bauer (2016) while considering a Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity. In particular, they consider the simple Black–Scholes dynamics to describe the underlying security. Nevertheless, GMWB are long-term products, and thus accounting for stochastic interest rate has relevant effects on both the financial evaluation and the policyholder behavior, as observed by Goudenège et al. (2018). In this paper, we investigate the outcomes of these two elements together on GMWB evaluation. To this aim, we develop a numerical framework which allows one to efficiently compute the fair value of a policy. Numerical results show that accounting for both taxation and stochastic interest rate has a determinant impact on the withdrawal strategy and on the cost of GMWB contracts. In addition, it can explain why these products are so popular with people looking for a protected form of investment for retirement.

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