Search results

Debt-related financial derivative usage by state and local governments became a very salient topic over the last few years in light of the Great Recession and its impacts on the efficacy of these financial instruments. However, there has been a dearth of systematic research on the types and kinds of derivatives state and local governments have actually employed in recent years. While anecdotes of financial derivative usage has grabbed the headlines (such as the case of Jefferson County, Alabama), there has been little research examining the derivative portfolios among states or local governments pre- and post-Great Recession. Using descriptive research, this paper attempts to rectify this gap in the literature for state governments as a means of better understanding how the recent financial crisis has impacted the critical debt management decision to use financial derivatives.

The paper aims to propose a consistent and robust pricing/hedging methodology for callable fixed income structures with embedded caplet‐linked options.

A range of recently published (1997‐2003) works about the Libor Market Model (LMM) tackle the problems of modelling the forward curve with more than two factors and calibrating it to caps either/or to swaps. Other articles involve the pricing of Bermudan options using Monte Carlo simulation. In the form of case study, the very popular structure of multicallable range accrual bonds is used. A complete calibration methodology is described in detail, which links the structure's price to the market caps and swaptions prices as well as to the historical correlations between forward rates. We present the direct implementation of the Monte Carlo technique for this particular problem. Furthermore, we explore the application of the Longstaff–Schwartz least squares algorithm and its variations for the estimation of the expected value of continuation.

This paper suceeds in producing a consistent and robust pricing/hedging methodology for callable fixed income structures with embedded caplet‐linked options.

The increased complexity of similar fixed income structures makes traditional approaches like Black–Derman–Toy or Hull‐White trees inadequate for the task of consistent pricing and hedging. Therefore, care must be taken to ensure consisted hedging across the different volatility markets.

This article explores variations and settings of the popular LMM and the Longstaff‐Scwartz algorithm that can be relatively consistent with both the cap and swaption volatility market. The framework is built using as a benchmark the most liquid fixed income structure so that it can be tested for robustness.

In this chapter, we define the “inflation forward rates” based on arbitrage arguments and develop a dynamic model for the term structure of inflation forward rates. This new model can serve as a framework for specific no-arbitrage models, including the popular practitioners’ market model and all models based on “foreign currency analogy.” With our rebuilt market model, we can price inflation caplets, floorlets, and swaptions with the Black formula for displaced-diffusion processes, and thus can quote these derivatives using “implied Black's volatilities.” The rebuilt market model also serves as a proper platform for developing models to manage volatility smile risks.

Through this chapter, we hope to correct two major flaws in existing models or with the current practices. First, a consumer price index has no volatility, so models based on the diffusion of the index are essentially wrong. Second, the differentiation of models based on zero-coupon inflation-indexed swaps and models based on year-on-year inflation-indexed swaps is unnecessary, and the use of “convexity adjustment,” a common practice to bridge models that are based on the two kinds of swaps, is redundant.

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

Longevity risk, that is, the uncertainty of the demographic survival rate, is an important risk for insurance companies and pension funds, which have large, and long‐term, exposures to survivorship. The purpose of this paper is to propose a new model to describe this demographic survival risk.

The model proposed in this paper satisfies all the desired properties of a survival rate and has an explicit distribution for both single years and accumulative years.

The results show that it is important to consider the expected shift and risk premium of life table uncertainty and the stochastic behaviour of survival rates when pricing the survivor derivatives.

This model can be applied to the rapidly growing market for survivor derivatives.

This paper aims to describe a robust empirical approach to generating plausible historically based interest rate shocks, which can be applied to any market environment. These interest rate shocks can be readily linked to movements in other key risk factors, and used to measure market risk on institutions with large fixed-income portfolios.

Using yield curve factorization, we parameterize a time series of historical yield curves and measure interest rate shocks as the historical change in each of the model’s factors. We then demonstrate how to add these parameterized shocks to any market environment, while retaining positive rates and plausible credit spreads. Given a set of shocked interest rate curves, joint risk factor movements are calculated based upon historical, reduced form dependencies.

Our approach is based upon yield curve parameterization and requires a parsimonious yet flexible factorization model. In the process of selecting a model, we evaluate three variants of the Nelson–Siegel approach to yield curve approximation and find that, in the current low interest rate environment, a 5-factor parameterization developed by Björk and Christensen (1999) is best suited for accurately translating historical interest rate movements into plausible, current period shocks.

An accurate measure of market risk can help to inform institutions about the amount of capital needed to withstand a series of adverse market events. A plausible set of shocks is required to ensure market value, and cash flow projections are indicative of meaningful market sensitivities.

In Kampen et al.(2008), Monte Carlo estimators obtained by the WKB (Wentzel, Brillouin, Kramers) approximation had better results than Monte Carlo estimators obtained by the lognormal approximation for European swaptions and Bermudan swaptions. We compare the WKB estimators with the lognormal estimators and the pathwise derivative estimators for ratchet caplets and sticky caplets with various maturities. The results show that the WKB estimators have similar performance compared with the lognormal estimators and the pathwise derivative estimators for ratchet caplets. However, the WKB estimators show worse performance than both the lognormal estimators and the pathwise derivative estimators for sticky caplets. These results indicate that the WKB estimators would be hard to substitute for the lognormal estimators for various derivatives.

The valuation of insurance contracts using a market value (i.e., fair value) approach has recently attracted considerable interest. The authors illustrate how to determine the market value of a with‐profits insurance policy, e.g., a variable annuity or other insurance policy with a profit‐sharing provision. The method is based on finding comparables, i.e., a set of financial instruments that closely replicate the cash flows of the policy.