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The advent of derivatives and structured products has coincided with a proliferation of fixed income models used to analyze hedging, pricing, forecasting, and estimation for the term structure of interest rates. This article evaluates five models Ho‐Lee (HL); Black‐Derman‐Toy (BDT); Vasicek; Cox‐Ingersoll‐Ross (CIR); and Heath‐Jarrow‐Morton (HJM) (see Exhibit 1) that are currently used by structured finance practitioners. We suggest which models are most appropriate for assets with different time horizons, interest rate sensitivities and cashflow properties. The authors link model selection to structured financial instruments with the singular focus on the trade‐off between model precision/complexity and calculation costs.

Previous studies have shown the VIX futures tend to roll-down the term structure and converge towards the spot as they grow closer to maturity. The purpose of this paper is to propose an approach to improve the volatility index fear factor-level (VIX-level) prediction.

First, the authors use a forward-looking technique, the Heath–Jarrow–Morton (HJM) no-arbitrage framework to capture the convergence of the futures contract towards the spot. Second, the authors use principal component analysis (PCA) to reduce dimensionality and save substantial computational time. Third, the authors validate the model with selected VIX futures maturities and test on value-at-risk (VAR) computations.

The authors show that the use of multiple factors has a significant impact on the simulated VIX futures distribution, as well as the computations of their VAR (gain in accuracy and computing time). This impact becomes much more compelling when analysing a portfolio of VIX futures of multiple maturities.

The authors’ approach assumes the variance to be stationary and ignores the volatility smile. Nevertheless, they offer suggestions for future research.

The VIX-level prediction (the fear factor) is of paramount importance for market makers and participants, as there is no way to replicate the underlying asset of VIX futures. The authors propose a procedure that provides efficiency to both pricing and risk management.

This paper is the first to apply a forward-looking method by way of a HJM framework combined with PCA to VIX-level prediction in a portfolio context.

Outlines Heath, Jarrow and Morton’s (1992) method (MJM) for modelling interest rates and refers to other research showing that although it is generally non‐Markov, this can be modified if the volatility structure depends on relative maturity term rather than calendar maturity date. Develops a re‐indexed MJM model, applies it to 1975‐1991 data on non‐callable US treasury bills, notes and bonds; and compares its goodness of fit with Jordan (1984). Finds the forward function consistent with constant parameters, that state variables can be identified from the cross‐section estimates and that they have zero mean first differences when analysed through time series. Concludes that the forward function follows a martingale and promises further research.

The development of standardized measures of institution‐wide volatility exposures has so far lagged that for measures of asset price and interest‐rate exposure—largely because it is difficult to reconcile the various mathematical models used to value options. Recent mathematical results, however, can be used to construct standardized measures of volatility exposure. We consider here techniques for reconciling “vegas” for financial options valued using stochastic models that may be mathematically inconsistent with each other.

Using the duration measures defined by Bierwag (1996), we derive the formulae of duration far zero-coupon bonds, coupon bonds and bond portfolios under the Heath, Jarrow and Morton (1990) (HJM) term structure framework. The advantage in using Bierwag's duration measure is that it provides a one-to-one correspondence with the returns on interest rate sensitive securities. Hence, this duration measure can make the performance of risk management on interest rates better We also investigate the differences of duration for coupon bonds between our formula and the conventional Macaulay's measure. Finally, we show that the performance of dynamic immunization strategy is much better than that of static immunization strategy.

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.

We set out, in this paper, to extend the Das and Sundaram (2000) model as a means of simultaneously considering correlated default risk structure and counter-party risk. The multinomial model established by Kamrad and Ritchken (1991) is subsequently modified in order to facilitate the development of a computational algorithm for valuing two types of active credit derivatives, credit-spread options and default baskets. From our numerical examples, we find that along with the correlated default risk, the existence of counter-party risk results in a substantially lower valuation of credit derivatives. In addition, we find that different settings of the term structure of interest rate volatility also have a significant impact on the value of credit derivatives.

The authors present a model that incorporates stochastic interest rates to value equity‐linked life insurance contracts. The model generalizes some previous pricing results of Arne and Persson [1994] that are based on deterministic interest rates. The article also proposes and compares a design for a new equity‐linked product with the periodical premium contract of Brennan and Schwartz [1976]. The advantages of the proposed prod‐uct are its simplicity in pricing and its ease of hedging, by using either by long positions in the linked mutual fund or by European call options on the same fund.

Firing a worker for theft can be a tricky business—unless you catch hjm (or her) redhanded. Robert Gaitskell gives some guidance against the background of two recent tribunal cases.

We propose a new model for the dynamics of the aggregate credit portfolio loss. The model is Markovian in two dimensions with the state variables being the total accumulated loss Lt and the stochastic default intensity λt. The dynamics of the default intensity are governed by the equation dλt=κ(ρ(Lt,t)−λt)dt+σλtdWt. The function ρ depends both on time t and accumulated loss Lt, providing sufficient freedom to calibrate the model to a generic distribution of loss. We develop a computationally efficient method for model calibration to the market of synthetic single tranche collateralized debt obligations (CDOs). The method is based on the Markovian projection technique which reduces the full model to a one-step Markov chain having the same marginal distributions of loss. We show that once the intensity function of the effective Markov chain consistent with the loss distribution implied by the tranches is found, the function ρ can be recovered with a very moderate computational effort. Because our model is Markovian and has low dimensionality, it offers a convenient framework for the pricing of dynamic credit instruments, such as options on indices and tranches, by backward induction. We calibrate the model to a set of recent market quotes on CDX index tranches and apply it to the pricing of tranche options.