International Journal of Theoretical and Applied Finance

We consider an investment project that produces a single commodity. The project's operation yields payoff at a rate that depends on the project's installed capacity level and on an underlying economic indicator such as the output commodity's price or demand, which we model by an ergodic, one-dimensional Itô diffusion. The project's capacity level can be increased dynamically over time. The objective is to determine a capacity expansion strategy that maximizes the ergodic or long-term average payoff resulting from the project's management. We prove that it is optimal to increase the project's capacity level to a certain value and then take no further actions. The optimal capacity level depends on both the long-term average and the volatility of the underlying diffusion.

In this paper, we present a generic method for the Monte-Carlo pricing of (generalized) auto-callable products (aka. trigger products), i.e., products for which the payout function features a discontinuity with a (possibly) stochastic location (the trigger) and value (the payout).

The Monte-Carlo pricing of products with discontinuous payout is known to come with a high Monte-Carlo error. The numerical calculation of sensitivities (i.e., partial derivatives) of such prices by finite differences gives very noisy results, since the Monte-Carlo approximation (being a finite sum of discontinuous functions) is not smooth. Additionally, the Monte-Carlo error of the finite-difference approximation explodes as the shift size tends to zero.

Our method combines a product specific modification of the underlying numerical scheme, which is to some extent similar to an importance sampling and/or partial proxy simulation scheme and a reformulation of the payoff function into an equivalent smooth payout.

From the financial product we merely require that hitting of the stochastic trigger will result in an conditionally analytic value. Many complex derivatives can be written in this form. A class of products where this property is usually encountered are the so called auto-callables, where a trigger hit results in cancellation of all future payments except for one redemption payment, which can be valued analytically, conditionally on the trigger hit.

From the model we require that its numerical implementation allows for a calculation of the transition probability of survival (i.e., non-trigger hit). Many models allows this, e.g., Euler schemes of Itô processes, where the trigger is a model primitive.

The method presented is effective across a large range of cases where other methods fail, e.g. small finite difference shift sizes or short time to trigger reset (approaching maturity); this means that a practitioner can use this method and be confident that it will work consistently.

The method itself can be viewed as a generalization of the method proposed by Glasserman and Staum (2001), both with respect to the type (and shape) of the boundaries, as well as, with respect to the class of products considered. In addition we explicitly consider the calculation of sensitivities.

In this paper, we present a model to describe the evolution of the yield spread by considering the rating evaluation as the determinant of credit spreads. The underlying rating migration process is assumed to be a non-homogeneous discrete time semi-Markov process. We calculate the total sum of mean basis points paid within any given time interval. From this information we show how it is possible to extract the time evolution of expected interest rates and discount factors.

This paper proposes a simple scheme for static hedging of defaultable contingent claims. It generalizes the techniques developed by Carr and Chou (1997), Carr and Madan (1998), and Takahashi and Yamazaki (2009a) to credit-equity models. Our scheme provides a hedging strategy across credit and equity markets, where suitable defaultable contingent claims are accurately replicated by a feasible number of plain vanilla equity options. Another point is that shorter maturity options are available to hedge longer maturity defaultable contingent claims. Through numerical examples, it is shown that the scheme is applicable to both structural and intensity-based models.

In this study, we attempt to calculate the term structure of the interest rate under partial information using a model in which the mean reversion level of the short rate changes in accordance with a regime shift in the economy. Under partial information, an investor observes the history of only the short rate and not a regime shift; hence, calculating the term structure of the interest rate is reduced to the problem of filtering the current regime from observable short rates. Therefore, we calculate it using the filtering theory that estimates a stochastic process from noisy observations, and investigate the effects of the regime shift under partial information on the market price of risk and the volatility of a bond price compared with those under full information, in which the regime is assumed to be observable. We find that, under partial information, the regime-shift risk converts into the diffusion risk. As a result, we find that both the market price of diffusion risk and the volatility of a bond price under partial information become stochastic, even though these under full information are constant.

We study models for electricity pricing and derivatives in the context of a deregulated market setting. In particular we value swing options, since these are the electricity derivatives that attract the most attention from market participants. These are American style options in that they allow for multiple exercises subject to a set of constraints on the consumption process. Through the use of a penalty function, we generalize the problem by allowing for the consumption restrictions to be broken. We characterize the price function as a stochastic optimal control problem, and show that the option is exercised in a bang-bang fashion. The value of the swing option is the solution to a backward stochastic differential equation, and we show how European calls, along with forward contracts, can be used to hedge them.

We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models [Heston and Nandi (2000), Christoffersen et al. (2006), Bellini and Mercuri (2007), Mercuri (2008)] and use them for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the arithmetic average, that are used for an approximated valuation of arithmetic Asian options based on truncated Edgeworth expansions, following the approach of Turnbull and Wakeman (1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Monte Carlo prices. The results are quite good in the geometric case, while in the arithmetic case the proposed methodology seems to work well only in the Heston and Nandi case.