Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

Haastrecht, A. van; Lord, Roger; Pelsser, Antoon; Schrager, David

doi:10.1016/j.insmatheco.2009.09.003

Cited by 71 publications

(56 citation statements)

References 33 publications

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“…The functions α andᾱ are then determined by a straightforward integration. We do not report the results here because they are a particular case of those obtained in van Haastrecht et al [9]. For simplicity, in our numerical analysis we suppose that the objective measure and the risk-neutral measure coincide.…”

Section: Options On Equitiesmentioning

confidence: 95%

“…If the Cox, Ingersoll and Ross model ( [3]) is used for the interest rate, the resulting two-dimensional model would be affine if and only if the correlation is zero. A model that includes stochastic volatility as well as stochastic interest rate is studied in van Haastrecht et al [9]. Pan [8] studied a four-dimensional affine model combining stochastic volatility, interest rates and dividend yield.…”

Section: The Computational Algorithmmentioning

confidence: 99%

“…As an example, we consider a simple two-dimensional affine model, where the underlying evolves according to the Black-Scholes dynamics, while the short-term interest rate follows the process of the Vasicek model, and the stock and the interest rate may be correlated. This is a particular case of a model considered in van Haastrecht et al [9] to price long-term derivatives. Within this model, we implement two types of Delta strategies: the correct strategy that takes into account the randomness of the interest rate, which may be called the model Delta, and the plain Black-Scholes Delta with deterministic rate.…”

Section: Introductionmentioning

confidence: 99%

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Delta hedging in discrete time under stochastic interest rate

Angelini

Herzel

2014

Journal of Computational and Applied Mathematics

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We propose a methodology based on the Laplace transform to compute the variance of the hedging error due to time discretization for financial derivatives when the interest rate is stochastic. Our approach can be applied to any affine model for asset prices and to a very general class of hedging strategies, including Delta hedging. We apply it in a two-dimensional market model, obtained by combining the models of Black-Scholes and Vasicek, where we compare a strategy that correctly takes into account the variability of interest rates to one that erroneously assumes that they are deterministic. We show that the differences between the two strategies can be very significant. The factors with stronger influence are the ratio between the standard deviations of the equity and that of the interest rate, and their correlation. The methodology is also applied to study the Delta hedging strategy for an interest rate option in the Cox-Ingersoll and Ross model, measuring the variance of the hedging error as a function of the frequency of the rebalancing dates. We compare the results obtained to those coming from a classical Monte Carlo simulation.

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Section: Options On Equitiesmentioning

confidence: 95%

Section: The Computational Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Delta hedging in discrete time under stochastic interest rate

Angelini

Herzel

2014

Journal of Computational and Applied Mathematics

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“…The essentiality of this property was later illustrated for the Heston-Vasicek and Heston-CIR++ model by imposing indirect correlations through approximations. A detailed description regarding correlation effects among interest rate, volatility and the equity respectively can be found in [61] which provided comparisons in terms of graph shapes and maturity time. According to these authors, the correlation effects between equity and interest rates were more distinct compared with the correlation effects between interest rates and volatility.…”

Section: Literature Reviewmentioning

confidence: 99%

Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate

2014

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“…The exact pricing of FX options under Schöbel and Zhu (1999) stochastic volatility, single-factor Gaussian rates and a full correlation structure was only recently considered in van Haastrecht et al (2008). In this paper, building forth on the results of van Haastrecht et al (2008), Antonov et al (2008), Andreasen (2006) and Piterbarg (2005), we consider the pricing of foreign exchange, inflation and stock options under Schöbel and Zhu (1999) and Heston (1993) stochastic volatility and under multi-factor Gaussian interest rates with a full correlation structure. Since stock and FX options are a special (nested) cases of inflation-indexed caps/floors 4 we will mainly focus on the pricing of inflation index derivatives.…”

Section: Introductionmentioning

confidence: 99%

Generic Pricing of FX, Inflation and Stock Options Under Stochastic Interest Rates and Stochastic Volatility

Haastrecht

Pelsser

2009

SSRN Journal

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In this paper we deal with the pricing of stock, foreign exchange and inflation options under stochastic interest rates and stochastic volatility. We consider a foreign exchange framework for the pricing inflation-indexed options in which the valuation of stock and foreign exchange options can be treated as a nested case. We assume multi-factor Gaussian rates for both the nominal (domestic) as the real (foreign) economy, which economies (currencies) can be exchanged against each other by means of the inflation index (exchange rate) which is driven by log-normal dynamics with a stochastic volatility component. Furthermore we allow for a general correlation structure between the drivers of the volatility, the inflation index, the nominal and the real rates. We derive explicit option pricing formulas for various securities, like vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. All these options can be valued in closed-form under Schöbel-Zhu (1999) stochastic volatility, whereas we device an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston (1993) model.

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Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

Cited by 71 publications

References 33 publications

Delta hedging in discrete time under stochastic interest rate

Delta hedging in discrete time under stochastic interest rate

Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate

Generic Pricing of FX, Inflation and Stock Options Under Stochastic Interest Rates and Stochastic Volatility

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