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Journal articles on the topic 'Interest rate derivative pricing'

Author: Grafiati

Published: 20 February 2023

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1

Hosokawa, Satoshi, and Koichi Matsumoto. "Pricing interest rate derivatives with model risk." Journal of Financial Engineering 02, no. 01 (March 2015): 1550003. http://dx.doi.org/10.1142/s2345768615500038.

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This paper studies an interest rate derivative when there is the model risk in an interest rate model. We consider a mean reverting interest rate process whose volatility model is not known. Most of prices of interest rate derivatives cannot be determined uniquely, based on this interest rate model. We study the price bounds of a derivative and propose how to calculate the price bounds by a trinomial model. Further, we analyze the model risk of derivatives and their portfolios numerically.

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2

Hull, John, and Alan White. "Pricing Interest-Rate-Derivative Securities." Review of Financial Studies 3, no. 4 (October 1990): 573–92. http://dx.doi.org/10.1093/rfs/3.4.573.

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3

Ait-Sahalia, Yacine. "Nonparametric Pricing of Interest Rate Derivative Securities." Econometrica 64, no. 3 (May 1996): 527. http://dx.doi.org/10.2307/2171860.

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4

Davies, Dick, David Hillier, Andrew Marshall, and King Fui Cheah. "Pricing Interest Rate Swaps in Malaysia." Review of Pacific Basin Financial Markets and Policies 07, no. 04 (December 2004): 493–507. http://dx.doi.org/10.1142/s0219091504000251.

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This paper compares the theoretical price of interest rate swaps implied from the yield curve with the actual Kuala Lumpur Interbank Offer Rates used for swap resets in the Malaysian swap market for both semi-annual and annual interest rate swaps between 1996 and 2002. As far as we are aware no previous paper has considered pricing swaps in a less established derivative markets. Our empirical results indicate significant and persistent differences between the theoretical implied price and the actual reset price for both swaps over the sample period. This finding has implications for traders and banks in pricing swaps in Malaysia and more generally for pricing swaps in less established or illiquid markets or where capital controls have been introduced.

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5

Liu, Yuxuan. "The Pricing of New Interest Rate Derivative Futures." Science Innovation 8, no. 4 (2020): 114. http://dx.doi.org/10.11648/j.si.20200804.16.

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6

Strickland, Chris. "A comparison of models for pricing interest rate derivative securities." European Journal of Finance 2, no. 3 (September 1996): 261–87. http://dx.doi.org/10.1080/13518479600000008.

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7

Barbedo, Claudio Henrique, Octávio Bessada Lion, and Jose Valentim Machado Vicente. "Apreçamento de Opções Asiáticas de Taxa de Juros através de um Modelo HJM de Três Fatores." Brazilian Review of Finance 8, no. 1 (April 7, 2010): 9. http://dx.doi.org/10.12660/rbfin.v8n1.2010.1387.

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Pricing interest rate derivatives is a challenging task that has attracted the attention of many researchers in recent decades. Portfolio and risk managers, policymakers, traders and more generally all market participants are looking for valuable information from derivative instruments. We use a standard procedure to implement the HJM model and to price IDI options. We intend to assess the importance of the principal components of pricing and interest rate hedging derivatives in Brazil, one of the major emerging markets. Our results indicate that the HJM model consistently underprices IDI options traded in the over-the-counter market while it overprices long-term options traded in the exchange studied. We also find a direct relationship between time to maturity and pricing error and a negative relation with moneyness.

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8

Di Matteo, T., M. Airoldi, and E. Scalas. "On pricing of interest rate derivatives." Physica A: Statistical Mechanics and its Applications 339, no. 1-2 (August 2004): 189–96. http://dx.doi.org/10.1016/j.physa.2004.03.042.

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9

BAVIERA, ROBERTO. "BACK-OF-THE-ENVELOPE SWAPTIONS IN A VERY PARSIMONIOUS MULTI-CURVE INTEREST RATE MODEL." International Journal of Theoretical and Applied Finance 22, no. 05 (August 2019): 1950027. http://dx.doi.org/10.1142/s0219024919500274.

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We propose an elementary model in multi-curve setting that allows to price with simple exact closed formulas European swaptions. Swaptions can be both physical delivery and cash-settled ones. The proposed model is very parsimonious: it is a three-parameter multi-curve extension of the two-parameter J. Hull & A. White (1990) [Pricing interest-rate-derivative securities. Review of Financial Studies 3(4), 573–592] model. The model allows also to obtain simple formulas for all other plain vanilla Interest Rate derivatives and convexity adjustments. Calibration issues are discussed in detail.

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10

DE GENARO, ALAN, and MARCO AVELLANEDA. "PRICING INTEREST RATE DERIVATIVES UNDER MONETARY CHANGES." International Journal of Theoretical and Applied Finance 21, no. 06 (September 2018): 1850037. http://dx.doi.org/10.1142/s0219024918500371.

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The goal of this paper is to develop a reduced-form model for pricing derivatives on the overnight rate. The model incorporates jumps around central bank (CB) meetings. More specifically, rate changes are decomposed into fluctuations between CB meetings and deterministic timed jumps following CB meetings. This approach is useful for practitioners, since it allows the extraction of expectations regarding central bank decisions embedded in liquid instruments, as well as the use of these expectations for the pricing of less liquid derivatives, such as options, in a consistent manner. We discuss applications to 30-Day Fed funds options and IDI options traded in Brazil.

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11

Tahani, Nabil, and Xiaofei Li. "Pricing interest rate derivatives under stochastic volatility." Managerial Finance 37, no. 1 (January 31, 2011): 72–91. http://dx.doi.org/10.1108/03074351111092157.

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PurposeThe purpose of this paper is to derive semi‐closed‐form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine‐term structure models.Design/methodology/approachThe paper first derives the Frobenius series solution to the cross‐moment generating function, and then inverts the related characteristic function using the Gauss‐Laguerre quadrature rule for the corresponding cumulative probabilities.FindingsThis paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.Research limitations/implicationsFuture research could extend the approach adopted in this paper to some non‐affine‐term structure models such as quadratic models.Practical implicationsThe valuation approach in this study can be used to price mortgage‐backed securities, asset‐backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed‐income portfolios.Originality/valueThis paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.

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12

Chacko, George, and Sanjiv Das. "Pricing Interest Rate Derivatives: A General Approach." Review of Financial Studies 15, no. 1 (January 2002): 195–241. http://dx.doi.org/10.1093/rfs/15.1.195.

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13

MUSLIMOV, ALEXANDER G., and NIKOLAI A. SILANT'EV. "RENORMALIZATION OF BLACK-SCHOLES EQUATION FOR STOCHASTICALLY FLUCTUATING INTEREST RATE." International Journal of Theoretical and Applied Finance 04, no. 04 (August 2001): 621–34. http://dx.doi.org/10.1142/s0219024901001164.

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We investigate the effect of stochastic fluctuations of an interest rate on the value of a derivative. We derive the modified Black-Scholes equation that describes evolution of the value of a derivative averaged over an ensemble of stochastic fluctuations of the rate of interest and depends on the "renormalized" values of volatility and rate of interest. We present the explicit expressions for the renormalized volatility and interest rate that incorporate the corrections owing to the short-term stochastic variations of the interest rate. The stochastic component of the interest rate tends to enhance the effective volatility and reduce the effective interest rate that determine an evolution of the option pricing "smoothed out" over the stochastic variations. The results of numerical solution of the modified Black-Scholes equation with the renormalized coefficients are illustrated for an American put option on non-dividend-paying stock.

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14

Rhee, Joon Hee. "Derivatives Pricing in the Positive Interest Rates." Journal of Derivatives and Quantitative Studies 12, no. 2 (November 30, 2004): 157–79. http://dx.doi.org/10.1108/jdqs-02-2004-b0007.

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This paper examines the pricing of interest rates derivatives such as caps and swaptions in the pricing kernel framework. The underlying state variable is extended to the general infinitely divisible Levy process. For computational purposes, a simple pricing kernel as in Flesaker and Hughston (1996) and Jin and Glasserman (2001) is used. The main contribution or purpose of this paper is to find several proper positive martingales, which is key role of practical applications of the pricing kernel approach with interest rates guarantee to be positive. Particularly, this paper first finds and applies a quite general type of a positive martingale process to pricing interest rate derivatives such as swaptions and range notes in the incomplete market setting. Such interest rate derivatives are hard to find analytic solutions. Consequently, this paper shows that such a choice of the positive martingale in the kernel framework is a promising approach to price interest rate derivatives

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15

Heidari, Massoud, and Liuren Wu. "A Joint Framework for Consistently Pricing Interest Rates and Interest Rate Derivatives." Journal of Financial and Quantitative Analysis 44, no. 3 (June 2009): 517–50. http://dx.doi.org/10.1017/s0022109009990093.

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AbstractDynamic term structure models explain the yield curve variation well but perform poorly in pricing and hedging interest rate options. Most existing option pricing practices take the yield curve as given, thus having little to say about the fair valuation of the underlying interest rates. This paper proposes an m + n model structure that bridges the gap in the literature by successfully pricing both interest rates and interest rate options. The first m factors capture the yield curve variation, whereas the latter n factors capture the interest rate options movements that cannot be effectively identified from the yield curve. We propose a sequential estimation procedure that identifies the m yield curve factors from the LIBOR and swap rates in the first step and the n options factors from interest rate caps in the second step. The three yield curve factors explain over 99% of the variation in the yield curve but account for less than 50% of the implied volatility variation for the caps. Incorporating three additional options factors improves the explained variation in implied volatilities to over 99%.

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16

WU, LIXIN, and DAWEI ZHANG. "xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT." International Journal of Theoretical and Applied Finance 23, no. 01 (February 2020): 2050006. http://dx.doi.org/10.1142/s0219024920500065.

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xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

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17

AKAHORI, JIRÔ, and ANDREA MACRINA. "HEAT KERNEL INTEREST RATE MODELS WITH TIME-INHOMOGENEOUS MARKOV PROCESSES." International Journal of Theoretical and Applied Finance 15, no. 01 (February 2012): 1250007. http://dx.doi.org/10.1142/s0219024911006553.

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We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over time. The result is a so-called weighted heat kernel that by construction is a supermartingale with respect to the filtration generated by the time-inhomogeneous Markov processes. As an application, we show how this framework naturally fits the information-based asset pricing framework where time-inhomogeneous Markov processes are utilized to model partial information about random economic factors. We present examples of pricing kernel models which lead to analytical formulae for bond prices along with explicit expressions for the associated interest rate and market price of risk. Furthermore, we also address the pricing of fixed-income derivatives within this framework.

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18

AVELLANEDA, MARCO, and LIXIN WU. "CREDIT CONTAGION: PRICING CROSS-COUNTRY RISK IN BRADY DEBT MARKETS." International Journal of Theoretical and Applied Finance 04, no. 06 (December 2001): 921–38. http://dx.doi.org/10.1142/s0219024901001309.

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Credit contagion means that the credit deterioration of an entity causes the credit deterioration of other entities. In this paper, we build and test a continuous-time model for defaultable securities using a diffusive process for risk-free interest rate, and a finite-state continuous-time Markov process for the correlation of credit. The credit contagion, in particular, is established by relating transition rates of various credit states. Examples of derivative pricing with calibrated credit contagion model are provided. Initial empirical results with the benchmarks of Brady bonds show that our model is a viable new technique for the pricing and risk-managing of credit derivatives.

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19

Kaibe, Bosiu C., and John G. O’Hara. "Symmetry Analysis of an Interest Rate Derivatives PDE Model in Financial Mathematics." Symmetry 11, no. 8 (August 16, 2019): 1056. http://dx.doi.org/10.3390/sym11081056.

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We perform Lie symmetry analysis to a zero-coupon bond pricing equation whose price evolution is described in terms of a partial differential equation (PDE). As a result, using the computer software package SYM, run in conjunction with Mathematica, a new family of Lie symmetry group and generators of the aforementioned pricing equation are derived. We furthermore compute the exact invariant solutions which constitute the pricing models for the bond by making use of the derived infinitesimal generators and the associated similarity reduction equations. Using known solutions, we again compute more solutions via group point transformations.

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20

Sun, Yiyao, and Shiqin Liu. "Interest-Rate Products Pricing Problems with Uncertain Jump Processes." Discrete Dynamics in Nature and Society 2021 (June 19, 2021): 1–8. http://dx.doi.org/10.1155/2021/7398770.

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Uncertain differential equations (UDEs) with jumps are an essential tool to model the dynamic uncertain systems with dramatic changes. The interest rates, impacted heavily by human uncertainty, are assumed to follow UDEs with jumps in ideal markets. Based on this assumption, two derivatives, namely, interest-rate caps (IRCs) and interest-rate floors (IRFs), are investigated. Some formulas are presented to calculate their prices, which are of too complex forms for calculation in practice. For this reason, numerical algorithms are designed by using the formulas in order to compute the prices of these structured products. Numerical experiments are performed to illustrate the effectiveness and efficiency, which also show the prices of IRCs are strictly increasing with respect to the diffusion parameter while the prices of IRFs are strictly decreasing with respect to the diffusion parameter.

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21

WU, LIXIN. "CVA AND FVA TO DERIVATIVES TRADES COLLATERALIZED BY CASH." International Journal of Theoretical and Applied Finance 18, no. 05 (July 28, 2015): 1550035. http://dx.doi.org/10.1142/s0219024915500351.

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In this paper, we consider replication pricing of derivatives that are partially collateralized by cash. We let issuer replicate the derivatives payout using shares and cash, and let buyer replicate the loss given the counterparty default using credit default swaps. The costs of funding for replication and collateral posting are taken into account in the pricing process. A partial differential equation (PDE) for the derivatives price is established, and its solution is provided in a Feynman–Kac formula, which decomposes the derivatives value into the risk-free value of the derivative plus credit valuation adjustment (CVA) and funding valuation adjustment (FVA). For most derivatives, we show that CVAs can be evaluated analytically or semi-analytically, while FVAs as well as the derivatives values can be solved recursively through numerical procedures due to their interdependence. In numerical demonstrations, continuous and discrete margin revisions are considered, respectively, for an equity call option and a vanilla interest-rate swap.

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22

Huang, Jianbo, Jian Liu, and Yulei Rao. "Binary Tree Pricing to Convertible Bonds with Credit Risk under Stochastic Interest Rates." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/270467.

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The convertible bonds usually have multiple additional provisions that make their pricing problem more difficult than straight bonds and options. This paper uses the binary tree method to model the finance market. As the underlying stock prices and the interest rates are important to the convertible bonds, we describe their dynamic processes by different binary tree. Moreover, we consider the influence of the credit risks on the convertible bonds that is described by the default rate and the recovery rate; then the two-factor binary tree model involving the credit risk is established. On the basis of the theoretical analysis, we make numerical simulation and get the pricing results when the stock prices are CRR model and the interest rates follow the constant volatility and the time-varying volatility, respectively. This model can be extended to other financial derivative instruments.

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23

Peterson, Sandra, Richard C. Stapleton, and Marti G. Subrahmanyam. "A Multifactor Spot Rate Model for the Pricing of Interest Rate Derivatives." Journal of Financial and Quantitative Analysis 38, no. 4 (December 2003): 847. http://dx.doi.org/10.2307/4126746.

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24

Dang, Duy Minh, Christina C. Christara, Kenneth R. Jackson, and Asif Lakhany. "A PDE pricing framework for cross-currency interest rate derivatives." Procedia Computer Science 1, no. 1 (May 2010): 2371–80. http://dx.doi.org/10.1016/j.procs.2010.04.267.

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25

Bernard, Carole, Olivier Le Courtois, and François Quittard-Pinon. "Pricing derivatives with barriers in a stochastic interest rate environment." Journal of Economic Dynamics and Control 32, no. 9 (September 2008): 2903–38. http://dx.doi.org/10.1016/j.jedc.2007.11.004.

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26

Lo, C. F. "Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/276238.

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The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

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27

Sisodia, Neha, and Ravi Gor. "A STUDY OF OPTION PRICING MODELS WITH DISTINCT INTEREST RATES." International Journal of Engineering Science Technologies 6, no. 2 (May 5, 2022): 90–104. http://dx.doi.org/10.29121/ijoest.v6.i2.2022.310.

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This paper analyses the effect of different interest rates on Black-Scholes’ and Heston Option Pricing Model. We discuss the concept of interest rate in the two Models. We compare the two models for the parameter –‘Interest Rate’. A mathematical tool, UMBRAE (Unscaled Mean Bounded Relative Absolute Error) is used to compare the two models for pricing European call options. NSE (National Stock Exchange) is used for real market data and comparison is done through Moneyness (which is defined as the percentage difference of stock price and strike price) and Time-To-Maturity. Mathematical software – Matlab is used for all mathematical calculations. We observe that Black-Scholes’ model is preferred for lower interest rates than Heston options pricing model and vice-versa. This study is helpful in derivatives market.

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28

Brigo, Damiano, and Andrea Pallavicini. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks." Journal of Financial Engineering 01, no. 01 (March 2014): 1450001. http://dx.doi.org/10.1142/s2345768614500019.

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The introduction of Central Clearing Counterparties (CCPs) in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB Group, will lead to an overall liquidity impact of about USD 2 trillions. In this paper, we develop for the first time a comprehensive approach for pricing under CCP clearing, including variation and initial margins, gap credit risk and collateralization, showing concrete examples for interest rate swaps. This framework stems from our 2011 framework on credit, collateral and funding costs in Pallavicini et al. (Pallavicini, A., D. Perini and D. Brigo, 2011, Funding Valuation Adjustment: FVA consistent with CVA, DVA, WWR, Collateral, Netting and Re-hypothecation, arxiv.org, ssrn.com). Mathematically, the inclusion of asymmetric borrowing and lending rates in the hedge of a claim, and a replacement closeout at default, lead to nonlinearities showing up in claim dependent pricing measures, aggregation dependent prices, nonlinear Partial Differential Equations (PDEs) and Backward Stochastic Differential Equations (BSDEs). This still holds in presence of CCPs and CSA. We introduce a modeling approach that allows us to enforce rigorous separation of the interconnected nonlinear risks into different valuation adjustments where the key pricing nonlinearities are confined to a funding costs component that is analyzed through numerical schemes for BSDEs. We present a numerical case study for Interest Rate Swaps that highlights the relative size of the different valuation adjustments and the quantitative role of initial and variation margins, of liquidity bases, of credit risk, of the margin period of risk and of wrong-way risk correlations.

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29

Ben-Ameur, Hatem, Lotfi Karoui, and Walid Mnif. "Pricing Interest-Rate Derivatives with Piecewise Multilinear Interpolations and Transition Parameters." Journal of Derivatives 22, no. 2 (November 30, 2014): 82–109. http://dx.doi.org/10.3905/jod.2014.22.2.082.

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30

Zhang, Jiaojiao, Xiuchun Bi, Rong Li, and Shuguang Zhang. "Pricing credit derivatives under fractional stochastic interest rate models with jumps." Journal of Systems Science and Complexity 30, no. 3 (March 21, 2017): 645–59. http://dx.doi.org/10.1007/s11424-017-5126-8.

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31

Xu, Chenglong, Wei Guan, and Yijuan Liang. "A Comparison of Control Variate Methods for Pricing Interest Rate Derivatives in the LIBOR Market Model." Journal of Systems Science and Information 3, no. 1 (February 25, 2015): 48–58. http://dx.doi.org/10.1515/jssi-2015-0048.

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AbstractThis paper studies the control variate method for pricing interest rate derivatives driven by the LIBOR market model. Several control variates are constructed based on distinctive approximations for the LIBOR market model. Numerical results show the great efficiency of our methods. The idea in this paper can also be extended to price other interest rate derivatives under the LIBOR market model, such asSwaptions, Caps, some path dependent interest rate derivatives, and so forth.

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32

GULKO, LES. "THE ENTROPY THEORY OF STOCK OPTION PRICING." International Journal of Theoretical and Applied Finance 02, no. 03 (July 1999): 331–55. http://dx.doi.org/10.1142/s0219024999000182.

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An informationally efficient price keeps investors as a group in the state of maximum uncertainty about the next price change. The Entropy Pricing Theory (EPT) captures this intuition and suggests that, in informationally efficient markets, perfectly uncertain market beliefs must prevail. When the entropy functional is used to index the market uncertainty, then the entropy-maximizing market beliefs must prevail. The EPT resolves the ambiguity of asset valuation in incomplete markets, notably, the valuation of derivative securities. We use the EPT to derive a new stock option pricing model that is similar to Black–Scholes' with the lognormal distribution replaced by a gamma distribution. Unlike the Black–Scholes model, the gamma model does not restrict the dynamics of the stock price or the short-term interest rate. Option replication based on the gamma model accounts for random changes in the stock price, price volatility and interest rates.

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33

Trolle, Anders B., and Eduardo S. Schwartz. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives." Review of Financial Studies 22, no. 5 (April 28, 2008): 2007–57. http://dx.doi.org/10.1093/rfs/hhn040.

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34

Ferreiro, Ana M., José A. García-Rodríguez, José G. López-Salas, and Carlos Vázquez. "SABR/LIBOR market models: Pricing and calibration for some interest rate derivatives." Applied Mathematics and Computation 242 (September 2014): 65–89. http://dx.doi.org/10.1016/j.amc.2014.05.017.

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35

Kramin, Marat V., Saikat Nandi, and Alexander L. Shulman. "A multi-factor Markovian HJM model for pricing American interest rate derivatives." Review of Quantitative Finance and Accounting 31, no. 4 (December 13, 2007): 359–78. http://dx.doi.org/10.1007/s11156-007-0078-z.

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36

ITKIN, A., V. SHCHERBAKOV, and A. VEYGMAN. "NEW MODEL FOR PRICING QUANTO CREDIT DEFAULT SWAPS." International Journal of Theoretical and Applied Finance 22, no. 03 (May 2019): 1950003. http://dx.doi.org/10.1142/s0219024919500031.

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We propose a new model for pricing quanto credit default swaps (CDS) and risky bonds. The model operates with four stochastic factors, namely: the hazard rate, the foreign exchange rate, the domestic interest rate, and the foreign interest rate, and allows for jumps-at-default in both the foreign exchange rate and the foreign interest rate. Corresponding systems of partial differential equations are derived similar to how this is done by Bielecki et al. [PDE approach to valuation and hedging of credit derivatives, Quantitative Finance 5 (3), 257–270]. A localized version of the Radial Basis Function partition of unity method is used to solve these four-dimensional equations. The results of our numerical experiments qualitatively explain the discrepancies observed in the marked values of CDS spreads traded in domestic and foreign economies.

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37

Yoon, Ji-Hun, Jeong-Hoon Kim, Sun-Yong Choi, and Youngchul Han. "Stochastic volatility asymptotics of defaultable interest rate derivatives under a quadratic Gaussian model." Stochastics and Dynamics 17, no. 01 (December 15, 2016): 1750003. http://dx.doi.org/10.1142/s0219493717500034.

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Stochastic volatility of underlying assets has been shown to affect significantly the price of many financial derivatives. In particular, a fast mean-reverting factor of the stochastic volatility plays a major role in the pricing of options. This paper deals with the interest rate model dependence of the stochastic volatility impact on defaultable interest rate derivatives. We obtain an asymptotic formula of the price of defaultable bonds and bond options based on a quadratic term structure model and investigate the stochastic volatility and default risk effects and compare the results with those of the Vasicek model.

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38

BANERJEE, TAMAL, MRINAL K. GHOSH, and SRIKANTH K. IYER. "PRICING CREDIT DERIVATIVES IN A MARKOV-MODULATED REDUCED-FORM MODEL." International Journal of Theoretical and Applied Finance 16, no. 04 (June 2013): 1350018. http://dx.doi.org/10.1142/s0219024913500180.

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Numerous incidents in the financial world have exposed the need for the design and analysis of models for correlated default timings. Some models have been studied in this regard which can capture the feedback in case of a major credit event. We extend the research in the same direction by proposing a new family of models having the feedback phenomena and capturing the effects of regime switching economy on the market. The regime switching economy is modeled by a continuous time Markov chain. The Markov chain may also be interpreted to represent the credit rating of the firm whose bond we seek to price. We model the default intensity in a pool of firms using the Markov chain and a risk factor process. We price some single-name and multi-name credit derivatives in terms of certain transforms of the default and loss processes. These transforms can be calculated explicitly in case the default intensity is modeled as a linear function of a conditionally affine jump diffusion process. In such a case, under suitable technical conditions, the price of credit derivatives are obtained as solutions to a system of ODEs with weak coupling, subject to appropriate terminal conditions. Solving the system of ODEs numerically, we analyze the credit derivative spreads and compare their behavior with the nonswitching counterparts. We show that our model can easily incorporate the effects of business cycle. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low floating interest rate, high default intensity rate, and high volatility. We also model the effects of firm restructuring on the credit spread, in case of a default.

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Cairns, Andrew J. G., David Blake, and Kevin Dowd. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk." ASTIN Bulletin 36, no. 01 (May 2006): 79–120. http://dx.doi.org/10.2143/ast.36.1.2014145.

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It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

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40

Cairns, Andrew J. G., David Blake, and Kevin Dowd. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk." ASTIN Bulletin 36, no. 1 (May 2006): 79–120. http://dx.doi.org/10.1017/s0515036100014410.

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It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

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41

Samuelides, Y., and E. Nahum. "A tractable market model with jumps for pricing short-term interest rate derivatives." Quantitative Finance 1, no. 2 (February 2001): 270–83. http://dx.doi.org/10.1088/1469-7688/1/2/309.

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42

Goldys, Beniamin. "A note on pricing interest rate derivatives when forward LIBOR rates are lognormal." Finance and Stochastics 1, no. 4 (September 1, 1997): 345–52. http://dx.doi.org/10.1007/s007800050028.

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43

Akhigbe, Aigbe, Stephen Makar, Li Wang, and Ann Marie Whyte. "Interest rate derivatives use in banking: Market pricing implications of cash flow hedges." Journal of Banking & Finance 86 (January 2018): 113–26. http://dx.doi.org/10.1016/j.jbankfin.2017.09.009.

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PIRJOL, DAN. "EXPLOSIVE BEHAVIOR IN A LOG-NORMAL INTEREST RATE MODEL." International Journal of Theoretical and Applied Finance 16, no. 04 (June 2013): 1350023. http://dx.doi.org/10.1142/s0219024913500234.

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We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, at low and high volatilities, with different qualitative behavior. The two regimes are separated by a sharp transition, which is similar to a phase transition in condensed matter physics. We study the behavior of the model in the large volatility phase, and discuss the implications of the phase transition for the pricing of interest rates derivatives. In the large volatility phase, certain expectation values and convexity adjustments have an explosive behavior. For sufficiently low volatilities the caplet smile is log-normal to a very good approximation, while in the large volatility phase the model develops a non-trivial caplet skew. The phenomenon discussed here imposes thus an upper limit on the volatilities for which the model behaves as intended.

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JORDAN, RICHARD, and CHARLES TIER. "ASYMPTOTIC APPROXIMATIONS FOR PRICING DERIVATIVES UNDER MEAN-REVERTING PROCESSES." International Journal of Theoretical and Applied Finance 19, no. 05 (July 29, 2016): 1650030. http://dx.doi.org/10.1142/s0219024916500308.

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The problem of fast pricing, hedging, and calibrating of derivatives is considered when the underlying does not follow the standard Black–Scholes–Merton model but rather a mean-reverting and deterministic volatility model. Mean-reverting models are often used for volatility, commodities, and interest-rate derivatives, while the deterministic volatility accounts for the nonconstant implied volatility. Trading desks often use numerical methods for real-time pricing, hedging, and calibration when implementing such models. A more efficient alternative is to use an analytic formula, even if only approximate. A systematic approach is presented, based on the WKB or ray method, to derive asymptotic approximations to the density function that can be used to derive simple formulas for pricing derivatives. Such approximations are usually only valid away from any boundaries, yet for some derivatives the values of the underlying near the boundaries are needed such as when interest rates are very low or for pricing put options. Hence, the ray approximation may not yield acceptable results. A new asymptotic approximation near boundaries is derived, which is shown to be of value for pricing certain derivatives. The results are illustrated by deriving new analytic approximations for European derivatives and their high accuracy is demonstrated numerically.

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Benth, Fred Espen, Asma Khedher, and Michèle Vanmaele. "Pricing of Commodity Derivatives on Processes with Memory." Risks 8, no. 1 (January 21, 2020): 8. http://dx.doi.org/10.3390/risks8010008.

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Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process ξ with memory as, e.g., a Volterra equation driven by a Lévy process. Moreover, the interest rate and a risk premium ρ representing storage costs, illiquidity, convenience yield or insurance costs, are assumed to be stochastic. When the interest rate is deterministic and the risk premium is explicitly modelled as an Ornstein-Uhlenbeck type of dynamics with a mean level that depends on the same memory term as the commodity, the process ( ξ ; ρ ) has an affine structure under the pricing measure Q and an explicit expression for the option price is derived in terms of the Fourier transform of the payoff function.

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BRODY, DORJE C., LANE P. HUGHSTON, and DAVID M. MEIER. "LÉVY–VASICEK MODELS AND THE LONG-BOND RETURN PROCESS." International Journal of Theoretical and Applied Finance 21, no. 03 (May 2018): 1850026. http://dx.doi.org/10.1142/s0219024918500267.

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The classical derivation of the well-known Vasicek model for interest rates is reformulated in terms of the associated pricing kernel. An advantage of the pricing kernel method is that it allows one to generalize the construction to the Lévy–Vasicek case, avoiding issues of market incompleteness. In the Lévy–Vasicek model the short rate is taken in the real-world measure to be a mean-reverting process with a general one-dimensional Lévy driver admitting exponential moments. Expressions are obtained for the Lévy–Vasicek bond prices and interest rates, along with a formula for the return on a unit investment in the long bond, defined by [Formula: see text], where [Formula: see text] is the price at time [Formula: see text] of a [Formula: see text]-maturity discount bond. We show that the pricing kernel of a Lévy–Vasicek model is uniformly integrable if and only if the long rate of interest is strictly positive.

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BRIGO, DAMIANO, AGOSTINO CAPPONI, ANDREA PALLAVICINI, and VASILEIOS PAPATHEODOROU. "PRICING COUNTERPARTY RISK INCLUDING COLLATERALIZATION, NETTING RULES, RE-HYPOTHECATION AND WRONG-WAY RISK." International Journal of Theoretical and Applied Finance 16, no. 02 (March 2013): 1350007. http://dx.doi.org/10.1142/s0219024913500076.

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This article is concerned with the arbitrage-free valuation of bilateral counterparty risk through stochastic dynamical models when collateral is included, with possible rehypothecation. The payout of claims is modified to account for collateral margining in agreement with International Swap and Derivatives Association (ISDA) documentation. The analysis is specialized to interest-rate and credit derivatives. In particular, credit default swaps are considered to show that a perfect collateralization cannot be achieved under default correlation. Interest rate and credit spread volatilities are fully accounted for, as is the impact of re-hypothecation, collateral margining frequency, and dependencies.

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NGUYEN, THE ANH, and FRANK THOMAS SEIFRIED. "THE MULTI-CURVE POTENTIAL MODEL." International Journal of Theoretical and Applied Finance 18, no. 07 (November 2015): 1550049. http://dx.doi.org/10.1142/s0219024915500491.

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We develop a general class of multi-curve potential models for post-crisis interest rates. Our model features positive stochastic basis spreads, positive term structures, and analytic pricing formulae for interest rate derivatives. Making a quanto interpretation of LIBOR lending transactions, we use a multi-currency analogy to model multiple term structures and formulate a general, tractable model of multiple term structures. As a special case of our approach, we obtain a rational lognormal model that extends the original Flesaker–Hughston (1996) rational lognormal model to a multi-curve setting. In this setting we obtain analytic pricing formulae for caps and swaptions.

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HELL, PHILIPP, THILO MEYER-BRANDIS, and THORSTEN RHEINLÄNDER. "CONSISTENT FACTOR MODELS FOR TEMPERATURE MARKETS." International Journal of Theoretical and Applied Finance 15, no. 04 (June 2012): 1250027. http://dx.doi.org/10.1142/s0219024912500276.

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We propose an approach for pricing and hedging weather derivatives based on including forward looking information about the temperature available to the market. This is achieved by modeling temperature forecasts by a finite dimensional factor model. Temperature dynamics are then inferred in the short end. In analogy to interest rate theory, we establish conditions which guarantee consistency of a factor model with the martingale dynamics of temperature forecasts. Finally, we consider a specific two-factor model and examine in more detail pricing and hedging of weather derivatives in this context.

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