Stochastic Interest Rate Model Research Articles

Backward simulation methods for pricing American options under the CIR process

In this paper, we focus on backward simulation of the CIR process. The purpose is to solve the memory requirement issue of the Least Squares Monte Carlo method when pricing American options by simulation. The concept of backward simulation is presented and it is classified into two types. Under the framework of the second type backward simulation, we seek the solutions for the existing CIR schemes. Specifically, we propose forward–backward simulation approaches for Alfonsi’s two implicit schemes, the fixed Euler schemes and the exact scheme. The proposed schemes are numerically tested and compared in pricing American options under the Heston model and the stochastic interest rate model. Some numerical properties such as the convergence order of the explicit–implicit Euler schemes, the storage requirement estimation of the forward–backward exact scheme and its computing time comparison with the squared Bessel bridge are also tested. Finally, the pros and cons of the related backward simulation schemes are summarized.

Pricing of long-dated commodity derivatives: Do stochastic interest rates matter?

Abstract Does modelling stochastic interest rates, beyond stochastic volatility, improve pricing performance on long-dated commodity derivatives? To answer this question, we consider futures price models for commodity derivatives that allow for stochastic volatility and stochastic interest rates and a correlation structure between the underlying variables. We examine the empirical pricing performance of these models on pricing long-dated crude oil derivatives. Estimating the model parameters from historical crude oil futures prices and option prices, we find that stochastic interest rate models improve pricing performance on long-dated crude oil derivatives, when the interest rate volatility is relatively high. Furthermore, increasing the model dimensionality does not tend to improve the pricing performance on long-dated crude oil option prices, but it matters for long-dated futures prices. We also find empirical evidence for a negative correlation between crude oil futures prices and interest rates that contributes to improving fit to long-dated crude oil option prices.

Valuation of correlation options under a stochastic interest rate model with regime switching

We consider the valuation of a correlation option, a two-factor analog of a European call option, under a Hull-White interest rate model with regime switching. More specifically, the model parameters are modulated by an observable, continuous-time, finite-state Markov chain. We obtain an integral pricing formula for the correlation option by adopting the techniques of measure changes and inverse Fourier transform. Numerical analysis, via the fast Fourier transform, is provided to illustrate the practical implementation of our model.

Pricing credit derivatives under fractional stochastic interest rate models with jumps

Based on the reduced-form approach, this paper investigates the pricing problems of default-risk bonds and credit default swaps (CDSs) for a fractional stochastic interest rate model with jump under the framework of primary-secondary. Using properties of the quasi-martingale with respect to the fractional Brownian motion and the jump technique in Park (2008), the authors first derive the explicit pricing formula of defaultable bonds. Then, based on the newly obtained pricing formula of defaultable bonds, the CDS is priced by the arbitrage-free principle. This paper presents an extension of the primary-secondary framework in Jarrow and Yu (2001).

Fundamental solution of bond pricing in the Ho-Lee stochastic interest rate model under the invariant criteria

Fundamental solution of bond pricing in the Ho-Lee stochastic interest rate model under the invariant criteria

PERBANDINGAN HASIL PERHITUNGAN PREMI ASURANSI JIWA ENDOWMENT SUKU BUNGA VASICEK DENGAN DAN TANPA SIMULASI MONTE CARLO

Vasicek is one of the stochastic interest rate model that can capture interest rates movement. The aim of this research was to get the comparison of the level premium for an endowment life insurance under stochastic interest rate without and by using Monte Carlo simulation. The result show that the level premium without Monte Carlo simulation is not much different from the result of the level premium by using Monte Carlo simulation. However, the premium calculation by using Monte Carlo simulation can also be searched the range of losses and gains of the insurance company at certain confidence interval. In this case using a confidence interval of 95%.

Generalized interest rate dynamics and its impacts on finance and pensions

ABSTRACTThe recent global financial crisis caused implementation of negative or close to zero interest rates. This situation implies a necessity to study a flexible and simplistic model of interest rate, which well accommodates oscillations, cycles, and negative signs. In this article, we introduce a novel nonlinear stochastic interest rate model, which, as a special case, incorporates the standard linear model of Parker. Many practical implications for finance and pensions are obtained.

Value-at-Risk estimation with stochastic interest rate models for option-bond portfolios

This article proposes a Monte Carlo simulation based approach for measuring Value-at-Risk of a portfolio consisting of options and bonds. The approach allows for jump-diffusions in underlying assets and affords to fit a variety of model layout, including both non-parametric and semi-parametric structures. Backtesting was conducted to assess the effectiveness of the method. The algorithm was tested against various trading positions, time horizons, and correlations between asset prices and market return rates. A prominent advantage of our approach is that its implementation does not require prior knowledge of the joint distribution or other statistical features of the related risk factors.

Empirical Hedging Performance on Long-Dated Crude Oil Derivatives

This paper presents an empirical study on hedging long-dated crude oil futures options with forward price models incorporating stochastic interest rates and stochastic volatility. Several hedging schemes are considered including delta, gamma, vega and interest rate hedge. Factor hedging is applied to the proposed multi-dimensional models and the corresponding hedge ratios are estimated by using historical crude oil futures prices, crude oil option prices and Treasury yields. Hedge ratios from stochastic interest rate models consistently improve hedging performance over hedge ratios from deterministic interest rate models, an improvement that becomes more pronounced over periods with high interest rate volatility, such as during the GFC. An interest rate hedge consistently improves hedging beyond delta, gamma and vega hedging, especially when shorter maturity contracts are used to roll the hedge forward. Furthermore, when the market experiences high interest rate volatility and the hedge is subject to high basis risk, adding interest rate hedge to delta hedge provides an improvement, while adding gamma and/or vega to the delta hedge worsens performance.

Adaptive Interest Rate Modelling

A good description of the dynamic process of interest rates is crucial to price derivatives and to hedge corresponding risk. An unstable macroeconomic context motivates the stochastic interest rate models with time‐varying parameters. In this paper, the local parameter approach is introduced to adaptively estimate interest rate models. This method can be generally used in time‐varying coefficient parametric models. It is used not only to detect jumps and structural breaks but also to choose the largest time homogeneous interval for each time point, such that in this interval the coefficients are statistically constant. We apply this adaptive approach in both simulations and real data analysis. Using the 3‐month Treasury bill rate as a proxy of the short rate, we find that our method can detect the structural breaks as well as the stable intervals for homogeneously modelling of the interest rate process. The time homogeneous interval cannot persist in an unstable macroeconomy. Furthermore, our approach performs well in long horizon forecasting. Copyright © 2016 John Wiley & Sons, Ltd.

Long-term behavior of stochastic interest rate models with Markov switching

In this paper, we consider the long time behavior of Cox–Ingersoll–Ross (CIR) interest rate model with Markov switching. Using the ergodic theory of switching diffusions, we show that CIR model with Markov switching has a unique stationary distribution. Furthermore, we prove that the sequence X¯t:=1t∫0tXsds converges almost surely. As a by-product, we find that the marginal stationary distribution for CIR model with Markov switching can be determined uniquely by its moments.

Pricing of Guaranteed Annuity Options in a Stochastic Volatility and Interest Rate Environment

Abstract This article examines the pricing of guaranteed annuity options (GAOs) in a stochastic volatility and interest rate model. While the pricing of these options in a stochastic volatility and interest rate model has been examined in van Haastrecht, Plat, and Pelsser (2010. Insurance: Mathematics and Economics 47:266–77), the pricing is difficult under the general stochastic volatility environment. In order to overcome these difficulties, we examined the asymptotic expansion method introduced by Kim and Kunitomo (1999. Asia-Pacific Financial Markets 6:49–70) and extended by Kim (2002. Journal of the Operations Research Society of Japan 45:404–25), and Kunitomo and Kim (2007. Japanese Economic Review 58:71–106). The asymptotic expansion method obtains a closed-form approximation formula for the price of GAOs in a general stochastic volatility environment including the Schöbel–Zhu–Hull–White model and the Heston–Hull–White model, for example. We confirm the accuracy of the asymptotic expansion methods by numerical demonstrations. The sensitivity analysis of the options price to changes in the parameters for the stochastic volatility process is also analyzed.

The Optimal Strategy of Reinsurance-Investment Problem for an Insurer with Dynamic Income Under Stochastic Interest Rate

AbstractThis paper considers the reinsurance-investment problem for an insurer with dynamic income to balance the profit of insurance company and policy-holders. The insurer’s dynamic income is given by a net premium minus a dynamic reward budget item and the net premium is obtained according to the expected premium principle. Applying the stochastic control technique, a Hamilton-Jacobi-Bellman equation is established under stochastic interest rate model and the explicit solution is obtained by maximizing the insurer’s power utility of terminal wealth. In addition, the comparison with corresponding results under constant interest rate helps us to understand the role and influence of stochastic interest rates more in-depth.

LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model

In this paper, we present American option pricing under Heston---Hull---White's stochastic volatility and stochastic interest rate model. To do this, we first discretize the stochastic processes with Euler discretization scheme. Then, we price American option by using least-squares Monte Carlo algorithm. We also compare the numerical results of our model with the Heston-CIR model. Finally, numerical results show the efficiency of the proposed algorithm for pricing American option under the Heston---Hull---White model.

Pricing and hedging GLWB in the Heston and in the Black–Scholes with stochastic interest rate models

Valuing Guaranteed Lifelong Withdrawal Benefit (GLWB) has attracted significant attention from both the academic field and real world financial markets. As remarked by Forsyth and Vetzal (2014) the Black and Scholes framework seems to be inappropriate for such a long maturity products. They propose to use a regime switching model. Alternatively, we propose here to use a stochastic volatility model (Heston model) and a Black–Scholes model with stochastic interest rate (Hull–White model). For this purpose we present four numerical methods for pricing GLWB variables annuities: a hybrid tree-finite difference method and a Hybrid Monte Carlo method, an ADI finite difference scheme, and a Standard Monte Carlo method. These methods are used to determine the no-arbitrage fee for the most popular versions of the GLWB contract, and to calculate the Greeks used in hedging. Both constant withdrawal and optimal withdrawal (including lapsation) strategies are considered. Numerical results are presented which demonstrate the sensitivity of the no-arbitrage fee to economic, contractual and longevity assumptions.

An FFT approach for option pricing under a regime-switching stochastic interest rate model

ABSTRACTIn this article, we investigate the pricing of European-style options under a Markovian regime-switching Hull–White interest rate model. The parameters of this model, including the mean-reversion level, the volatility of the stochastic interest rate, and the volatility of an asset’s value, are modulated by an observable, continuous-time, finite-state Markov chain. A closed-form expression for the characteristic function of the logarithmic terminal asset price is derived. Then, using the fast Fourier transform, a price of a European-style option is computed. In a two-state Markov chain case, numerical examples and empirical studies are presented to illustrate the practical implementation of the model.

THE PRICING OF QUANTO OPTIONS UNDER THE VASICEK'S SHORT RATE MODEL

We derive a closed-form expression for the price of a Euro- pean quanto call option when both foreign and domestic interest rates follow the Vasicek's short rate model. A quanto is a type of financial derivative whose pay-out currency differs from the natural denomination of its underlying financial variable. A quanto option is a cash-settled, cross-currency derivative whose underlying asset has a payoff in one currency, but the payoff is converted to another currency when the option is settled. For that reason, the correlation between underlying asset and currency exchange rate plays an important role in pricing quanto option. Quanto options in this paper have both the strike price and the underlying asset price denominated in foreign currency. At exercise, the value of the option is calculated as the options intrinsic value in foreign currency, which is then converted to the domestic currency at the fixed exchange rate. This allows investors to obtain exposure to foreign assets without the corresponding foreign exchange risk. Pricing quanto options based on the classical Black-Scholes (1) model, on which most of the research on quanto options has focused, has a weakness of assuming a constant volatility and constant interest rates. To overcome such weakness, in valuing quanto option, it is natural to consider a stochastic volatility or stochastic interest rate models. Despite its importance, very few researches have been done on finding analytic solutions of quanto option prices under a stochastic volatility model primarily due to the sophisticated stochastic processes and inability to obtain the general closed form. However, by assuming constant interest rates, Giese (4) provided a closed-form expression for the price of a quanto option in the Stein-Stein stochastic volatility model, and then Y. Lee et al. (5) got a closed-form expression for the price of a European quanto

Valuation of American Options: Monte-Carlo Simulation and Mathematical Approximation Methods

The use of American style equity options as hedging instrument has gained currency in recent times. This phenomenon devolves from the ever-expanding need by individuals, corporations and governments to hedge away their financial risks and the clarion call for derivative securities that give the holder increased flexibility in exercise. Nevertheless, pricing American options is complex and there exists no analytic solution to the problem except a profusion of approximation and finite difference techniques. Indeed, many researchers have shown that these methods cannot handle multifactor situations where the underlying asset follows a jump-diffusion process and where the derivative security depends on multiple sources of uncertainty such as stochastic volatility, stochastic interest rate among others. Monte-Carlo simulation techniques therefore developed out of the search for a pricing formula that has the capacity to accommodate all forms of uncertainty and at the same time able to produce speedy and accurate results. Some scholars at first rejected these techniques as yielding inaccurate results but in recent times, many researchers have demonstrated the efficacy of Monte-Carlo simulation in option pricing. The aim of this study is to assess the effectiveness of Monte-Carlo simulation methods in comparison with other option pricing techniques. To achieve this objective, the research builds an algorithm to compute Call and Put prices based on a wide range of input parameters. It also develops a model where volatility or interest rate is stochastic and a deterministic function of time. The results indicate that Monte-Carlo simulation techniques produce option values and exercise boundaries that are very similar to the Binomial, Barone-Adesi and Whaley as well as the Explicit Finite Difference methods. The results also show that the stochastic volatility and stochastic interest rate models yield slightly different but more accurate results. Consequently, the study recommends simulation techniques that incorporate multiple sources of uncertainty simultaneously for fast, efficient and more accurate option pricing.

Pricing regime-switching risk in an HJM interest rate environment

Modelling the term structure of interest rates is a long-standing topic in financial economics. In the past several decades or so, many stochastic interest rate models have been proposed with a vie...

Interest rates risk-premium and shape of the yield curve

We apply the general theory of pricing in incomplete markets, due to the author, on the problem of pricing bonds for theHull-White stochastic interest rate model. As pricing in incomplete markets involves more market parameters than the classical theory, and as thederived risk premium is time-dependent, the proposed methodology might offer a better way for replicating different shapes of the empirically observedyield curves. For example, the so-called humped yield curve can be obtained from a normal yield curve by only increasing the investors risk aversion.